Actual source code: rk.c

  1: /*
  2:   Code for time stepping with the Runge-Kutta method

  4:   Notes:
  5:   The general system is written as

  7:   Udot = F(t,U)

  9: */

 11: #include <petsc/private/tsimpl.h>
 12: #include <petscdm.h>
 13: #include <../src/ts/impls/explicit/rk/rk.h>
 14: #include <../src/ts/impls/explicit/rk/mrk.h>

 16: static TSRKType  TSRKDefault = TSRK3BS;
 17: static PetscBool TSRKRegisterAllCalled;
 18: static PetscBool TSRKPackageInitialized;

 20: static RKTableauLink RKTableauList;

 22: /*MC
 23:      TSRK1FE - First order forward Euler scheme.

 25:      This method has one stage.

 27:      Options Database Key:
 28: .     -ts_rk_type 1fe - use type 1fe

 30:      Level: advanced

 32: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 33: M*/
 34: /*MC
 35:      TSRK2A - Second order RK scheme (Heun's method).

 37:      This method has two stages.

 39:      Options Database Key:
 40: .     -ts_rk_type 2a - use type 2a

 42:      Level: advanced

 44: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 45: M*/
 46: /*MC
 47:      TSRK2B - Second order RK scheme (the midpoint method).

 49:      This method has two stages.

 51:      Options Database Key:
 52: .     -ts_rk_type 2b - use type 2b

 54:      Level: advanced

 56: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 57: M*/
 58: /*MC
 59:      TSRK3 - Third order RK scheme.

 61:      This method has three stages.

 63:      Options Database Key:
 64: .     -ts_rk_type 3 - use type 3

 66:      Level: advanced

 68: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 69: M*/
 70: /*MC
 71:      TSRK3BS - Third order RK scheme of Bogacki-Shampine with 2nd order embedded method.

 73:      This method has four stages with the First Same As Last (FSAL) property.

 75:      Options Database Key:
 76: .     -ts_rk_type 3bs - use type 3bs

 78:      Level: advanced

 80:      References:
 81: . * - https://doi.org/10.1016/0893-9659(89)90079-7

 83: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 84: M*/
 85: /*MC
 86:      TSRK4 - Fourth order RK scheme.

 88:      This is the classical Runge-Kutta method with four stages.

 90:      Options Database Key:
 91: .     -ts_rk_type 4 - use type 4

 93:      Level: advanced

 95: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
 96: M*/
 97: /*MC
 98:      TSRK5F - Fifth order Fehlberg RK scheme with a 4th order embedded method.

100:      This method has six stages.

102:      Options Database Key:
103: .     -ts_rk_type 5f - use type 5f

105:      Level: advanced

107: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
108: M*/
109: /*MC
110:      TSRK5DP - Fifth order Dormand-Prince RK scheme with the 4th order embedded method.

112:      This method has seven stages with the First Same As Last (FSAL) property.

114:      Options Database Key:
115: .     -ts_rk_type 5dp - use type 5dp

117:      Level: advanced

119:      References:
120: . * - https://doi.org/10.1016/0771-050X(80)90013-3

122: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
123: M*/
124: /*MC
125:      TSRK5BS - Fifth order Bogacki-Shampine RK scheme with 4th order embedded method.

127:      This method has eight stages with the First Same As Last (FSAL) property.

129:      Options Database Key:
130: .     -ts_rk_type 5bs - use type 5bs

132:      Level: advanced

134:      References:
135: . * - https://doi.org/10.1016/0898-1221(96)00141-1

137: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
138: M*/
139: /*MC
140:      TSRK6VR - Sixth order robust Verner RK scheme with fifth order embedded method.

142:      This method has nine stages with the First Same As Last (FSAL) property.

144:      Options Database Key:
145: .     -ts_rk_type 6vr - use type 6vr

147:      Level: advanced

149:      References:
150: . * - http://people.math.sfu.ca/~jverner/RKV65.IIIXb.Robust.00010102836.081204.CoeffsOnlyRAT

152: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
153: M*/
154: /*MC
155:      TSRK7VR - Seventh order robust Verner RK scheme with sixth order embedded method.

157:      This method has ten stages.

159:      Options Database Key:
160: .     -ts_rk_type 7vr - use type 7vr

162:      Level: advanced

164:      References:
165: . * - http://people.math.sfu.ca/~jverner/RKV76.IIa.Robust.000027015646.081206.CoeffsOnlyRAT

167: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
168: M*/
169: /*MC
170:      TSRK8VR - Eighth order robust Verner RK scheme with seventh order embedded method.

172:      This method has thirteen stages.

174:      Options Database Key:
175: .     -ts_rk_type 8vr - use type 8vr

177:      Level: advanced

179:      References:
180: . * - http://people.math.sfu.ca/~jverner/RKV87.IIa.Robust.00000754677.081208.CoeffsOnlyRATandFLOAT

182: .seealso: [](ch_ts), `TSRK`, `TSRKType`, `TSRKSetType()`
183: M*/

185: /*@C
186:   TSRKRegisterAll - Registers all of the Runge-Kutta explicit methods in `TSRK`

188:   Not Collective, but should be called by all processes which will need the schemes to be registered

190:   Level: advanced

192: .seealso: [](ch_ts), `TSRKRegisterDestroy()`, `TSRKRegister()`
193: @*/
194: PetscErrorCode TSRKRegisterAll(void)
195: {
196:   PetscFunctionBegin;
197:   if (TSRKRegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
198:   TSRKRegisterAllCalled = PETSC_TRUE;

200: #define RC PetscRealConstant
201:   {
202:     const PetscReal A[1][1] = {{0}};
203:     const PetscReal b[1]    = {RC(1.0)};
204:     PetscCall(TSRKRegister(TSRK1FE, 1, 1, &A[0][0], b, NULL, NULL, 0, NULL));
205:   }
206:   {
207:     const PetscReal A[2][2] = {
208:       {0,       0},
209:       {RC(1.0), 0}
210:     };
211:     const PetscReal b[2]      = {RC(0.5), RC(0.5)};
212:     const PetscReal bembed[2] = {RC(1.0), 0};
213:     PetscCall(TSRKRegister(TSRK2A, 2, 2, &A[0][0], b, NULL, bembed, 0, NULL));
214:   }
215:   {
216:     const PetscReal A[2][2] = {
217:       {0,       0},
218:       {RC(0.5), 0}
219:     };
220:     const PetscReal b[2] = {0, RC(1.0)};
221:     PetscCall(TSRKRegister(TSRK2B, 2, 2, &A[0][0], b, NULL, NULL, 0, NULL));
222:   }
223:   {
224:     const PetscReal A[3][3] = {
225:       {0,                  0,       0},
226:       {RC(2.0) / RC(3.0),  0,       0},
227:       {RC(-1.0) / RC(3.0), RC(1.0), 0}
228:     };
229:     const PetscReal b[3] = {RC(0.25), RC(0.5), RC(0.25)};
230:     PetscCall(TSRKRegister(TSRK3, 3, 3, &A[0][0], b, NULL, NULL, 0, NULL));
231:   }
232:   {
233:     const PetscReal A[4][4] = {
234:       {0,                 0,                 0,                 0},
235:       {RC(1.0) / RC(2.0), 0,                 0,                 0},
236:       {0,                 RC(3.0) / RC(4.0), 0,                 0},
237:       {RC(2.0) / RC(9.0), RC(1.0) / RC(3.0), RC(4.0) / RC(9.0), 0}
238:     };
239:     const PetscReal b[4]      = {RC(2.0) / RC(9.0), RC(1.0) / RC(3.0), RC(4.0) / RC(9.0), 0};
240:     const PetscReal bembed[4] = {RC(7.0) / RC(24.0), RC(1.0) / RC(4.0), RC(1.0) / RC(3.0), RC(1.0) / RC(8.0)};
241:     PetscCall(TSRKRegister(TSRK3BS, 3, 4, &A[0][0], b, NULL, bembed, 0, NULL));
242:   }
243:   {
244:     const PetscReal A[4][4] = {
245:       {0,       0,       0,       0},
246:       {RC(0.5), 0,       0,       0},
247:       {0,       RC(0.5), 0,       0},
248:       {0,       0,       RC(1.0), 0}
249:     };
250:     const PetscReal b[4] = {RC(1.0) / RC(6.0), RC(1.0) / RC(3.0), RC(1.0) / RC(3.0), RC(1.0) / RC(6.0)};
251:     PetscCall(TSRKRegister(TSRK4, 4, 4, &A[0][0], b, NULL, NULL, 0, NULL));
252:   }
253:   {
254:     const PetscReal A[6][6] = {
255:       {0,                       0,                        0,                        0,                       0,                    0},
256:       {RC(0.25),                0,                        0,                        0,                       0,                    0},
257:       {RC(3.0) / RC(32.0),      RC(9.0) / RC(32.0),       0,                        0,                       0,                    0},
258:       {RC(1932.0) / RC(2197.0), RC(-7200.0) / RC(2197.0), RC(7296.0) / RC(2197.0),  0,                       0,                    0},
259:       {RC(439.0) / RC(216.0),   RC(-8.0),                 RC(3680.0) / RC(513.0),   RC(-845.0) / RC(4104.0), 0,                    0},
260:       {RC(-8.0) / RC(27.0),     RC(2.0),                  RC(-3544.0) / RC(2565.0), RC(1859.0) / RC(4104.0), RC(-11.0) / RC(40.0), 0}
261:     };
262:     const PetscReal b[6]      = {RC(16.0) / RC(135.0), 0, RC(6656.0) / RC(12825.0), RC(28561.0) / RC(56430.0), RC(-9.0) / RC(50.0), RC(2.0) / RC(55.0)};
263:     const PetscReal bembed[6] = {RC(25.0) / RC(216.0), 0, RC(1408.0) / RC(2565.0), RC(2197.0) / RC(4104.0), RC(-1.0) / RC(5.0), 0};
264:     PetscCall(TSRKRegister(TSRK5F, 5, 6, &A[0][0], b, NULL, bembed, 0, NULL));
265:   }
266:   {
267:     const PetscReal A[7][7] = {
268:       {0,                        0,                         0,                        0,                      0,                         0,                   0},
269:       {RC(1.0) / RC(5.0),        0,                         0,                        0,                      0,                         0,                   0},
270:       {RC(3.0) / RC(40.0),       RC(9.0) / RC(40.0),        0,                        0,                      0,                         0,                   0},
271:       {RC(44.0) / RC(45.0),      RC(-56.0) / RC(15.0),      RC(32.0) / RC(9.0),       0,                      0,                         0,                   0},
272:       {RC(19372.0) / RC(6561.0), RC(-25360.0) / RC(2187.0), RC(64448.0) / RC(6561.0), RC(-212.0) / RC(729.0), 0,                         0,                   0},
273:       {RC(9017.0) / RC(3168.0),  RC(-355.0) / RC(33.0),     RC(46732.0) / RC(5247.0), RC(49.0) / RC(176.0),   RC(-5103.0) / RC(18656.0), 0,                   0},
274:       {RC(35.0) / RC(384.0),     0,                         RC(500.0) / RC(1113.0),   RC(125.0) / RC(192.0),  RC(-2187.0) / RC(6784.0),  RC(11.0) / RC(84.0), 0}
275:     };
276:     const PetscReal b[7]          = {RC(35.0) / RC(384.0), 0, RC(500.0) / RC(1113.0), RC(125.0) / RC(192.0), RC(-2187.0) / RC(6784.0), RC(11.0) / RC(84.0), 0};
277:     const PetscReal bembed[7]     = {RC(5179.0) / RC(57600.0), 0, RC(7571.0) / RC(16695.0), RC(393.0) / RC(640.0), RC(-92097.0) / RC(339200.0), RC(187.0) / RC(2100.0), RC(1.0) / RC(40.0)};
278:     const PetscReal binterp[7][5] = {
279:       {RC(1.0), RC(-4034104133.0) / RC(1410260304.0),   RC(105330401.0) / RC(33982176.0),    RC(-13107642775.0) / RC(11282082432.0),  RC(6542295.0) / RC(470086768.0)       },
280:       {0,       0,                                      0,                                   0,                                       0                                     },
281:       {0,       RC(132343189600.0) / RC(32700410799.0), RC(-833316000.0) / RC(131326951.0),  RC(91412856700.0) / RC(32700410799.0),   RC(-523383600.0) / RC(10900136933.0)  },
282:       {0,       RC(-115792950.0) / RC(29380423.0),      RC(185270875.0) / RC(16991088.0),    RC(-12653452475.0) / RC(1880347072.0),   RC(98134425.0) / RC(235043384.0)      },
283:       {0,       RC(70805911779.0) / RC(24914598704.0),  RC(-4531260609.0) / RC(600351776.0), RC(988140236175.0) / RC(199316789632.0), RC(-14307999165.0) / RC(24914598704.0)},
284:       {0,       RC(-331320693.0) / RC(205662961.0),     RC(31361737.0) / RC(7433601.0),      RC(-2426908385.0) / RC(822651844.0),     RC(97305120.0) / RC(205662961.0)      },
285:       {0,       RC(44764047.0) / RC(29380423.0),        RC(-1532549.0) / RC(353981.0),       RC(90730570.0) / RC(29380423.0),         RC(-8293050.0) / RC(29380423.0)       }
286:     };
287:     PetscCall(TSRKRegister(TSRK5DP, 5, 7, &A[0][0], b, NULL, bembed, 5, binterp[0]));
288:   }
289:   {
290:     const PetscReal A[8][8] = {
291:       {0,                           0,                          0,                              0,                            0,                          0,                           0,                        0},
292:       {RC(1.0) / RC(6.0),           0,                          0,                              0,                            0,                          0,                           0,                        0},
293:       {RC(2.0) / RC(27.0),          RC(4.0) / RC(27.0),         0,                              0,                            0,                          0,                           0,                        0},
294:       {RC(183.0) / RC(1372.0),      RC(-162.0) / RC(343.0),     RC(1053.0) / RC(1372.0),        0,                            0,                          0,                           0,                        0},
295:       {RC(68.0) / RC(297.0),        RC(-4.0) / RC(11.0),        RC(42.0) / RC(143.0),           RC(1960.0) / RC(3861.0),      0,                          0,                           0,                        0},
296:       {RC(597.0) / RC(22528.0),     RC(81.0) / RC(352.0),       RC(63099.0) / RC(585728.0),     RC(58653.0) / RC(366080.0),   RC(4617.0) / RC(20480.0),   0,                           0,                        0},
297:       {RC(174197.0) / RC(959244.0), RC(-30942.0) / RC(79937.0), RC(8152137.0) / RC(19744439.0), RC(666106.0) / RC(1039181.0), RC(-29421.0) / RC(29068.0), RC(482048.0) / RC(414219.0), 0,                        0},
298:       {RC(587.0) / RC(8064.0),      0,                          RC(4440339.0) / RC(15491840.0), RC(24353.0) / RC(124800.0),   RC(387.0) / RC(44800.0),    RC(2152.0) / RC(5985.0),     RC(7267.0) / RC(94080.0), 0}
299:     };
300:     const PetscReal b[8]      = {RC(587.0) / RC(8064.0), 0, RC(4440339.0) / RC(15491840.0), RC(24353.0) / RC(124800.0), RC(387.0) / RC(44800.0), RC(2152.0) / RC(5985.0), RC(7267.0) / RC(94080.0), 0};
301:     const PetscReal bembed[8] = {RC(2479.0) / RC(34992.0), 0, RC(123.0) / RC(416.0), RC(612941.0) / RC(3411720.0), RC(43.0) / RC(1440.0), RC(2272.0) / RC(6561.0), RC(79937.0) / RC(1113912.0), RC(3293.0) / RC(556956.0)};
302:     PetscCall(TSRKRegister(TSRK5BS, 5, 8, &A[0][0], b, NULL, bembed, 0, NULL));
303:   }
304:   {
305:     const PetscReal A[9][9] = {
306:       {0,                                                   0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0},
307:       {RC(1.8000000000000000000000000000000000000000e-01),  0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0},
308:       {RC(8.9506172839506172839506172839506172839506e-02),  RC(7.7160493827160493827160493827160493827160e-02), 0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0},
309:       {RC(6.2500000000000000000000000000000000000000e-02),  0,                                                  RC(1.8750000000000000000000000000000000000000e-01),  0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0},
310:       {RC(3.1651600000000000000000000000000000000000e-01),  0,                                                  RC(-1.0449480000000000000000000000000000000000e+00), RC(1.2584320000000000000000000000000000000000e+00),  0,                                                   0,                                                   0,                                                  0,                                                  0},
311:       {RC(2.7232612736485626257225065566674305502508e-01),  0,                                                  RC(-8.2513360323886639676113360323886639676113e-01), RC(1.0480917678812415654520917678812415654521e+00),  RC(1.0471570799276856873679117969088177628396e-01),  0,                                                   0,                                                  0,                                                  0},
312:       {RC(-1.6699418599716514314329607278961797333198e-01), 0,                                                  RC(6.3170850202429149797570850202429149797571e-01),  RC(1.7461044552773876082146758838488161796432e-01),  RC(-1.0665356459086066122525194734018680677781e+00), RC(1.2272108843537414965986394557823129251701e+00),  0,                                                  0,                                                  0},
313:       {RC(3.6423751686909581646423751686909581646424e-01),  0,                                                  RC(-2.0404858299595141700404858299595141700405e-01), RC(-3.4883737816068643136312309244640071707741e-01), RC(3.2619323032856867443333608747142581729048e+00),  RC(-2.7551020408163265306122448979591836734694e+00), RC(6.8181818181818181818181818181818181818182e-01), 0,                                                  0},
314:       {RC(7.6388888888888888888888888888888888888889e-02),  0,                                                  0,                                                   RC(3.6940836940836940836940836940836940836941e-01),  0,                                                   RC(2.4801587301587301587301587301587301587302e-01),  RC(2.3674242424242424242424242424242424242424e-01), RC(6.9444444444444444444444444444444444444444e-02), 0}
315:     };
316:     const PetscReal b[9] = {RC(7.6388888888888888888888888888888888888889e-02), 0, 0, RC(3.6940836940836940836940836940836940836941e-01), 0, RC(2.4801587301587301587301587301587301587302e-01), RC(2.3674242424242424242424242424242424242424e-01),
317:                             RC(6.9444444444444444444444444444444444444444e-02), 0};
318:     const PetscReal bembed[9] = {RC(5.8700209643605870020964360587002096436059e-02), 0, 0, RC(4.8072562358276643990929705215419501133787e-01), RC(-8.5341242076919085578832094861228313083563e-01), RC(1.2046485260770975056689342403628117913832e+00), 0, RC(-5.9242373072160306202859394348756050883710e-02), RC(1.6858043453788134639198468985703028256220e-01)};
319:     PetscCall(TSRKRegister(TSRK6VR, 6, 9, &A[0][0], b, NULL, bembed, 0, NULL));
320:   }
321:   {
322:     const PetscReal A[10][10] = {
323:       {0,                                                   0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
324:       {RC(5.0000000000000000000000000000000000000000e-03),  0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
325:       {RC(-1.0767901234567901234567901234567901234568e+00), RC(1.1856790123456790123456790123456790123457e+00), 0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
326:       {RC(4.0833333333333333333333333333333333333333e-02),  0,                                                  RC(1.2250000000000000000000000000000000000000e-01),  0,                                                   0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
327:       {RC(6.3607142857142857142857142857142857142857e-01),  0,                                                  RC(-2.4444642857142857142857142857142857142857e+00), RC(2.2633928571428571428571428571428571428571e+00),  0,                                                   0,                                                   0,                                                  0,                                                  0, 0},
328:       {RC(-2.5351211079349245229256383554660215487207e+00), 0,                                                  RC(1.0299374654449267920438514460756024913612e+01),  RC(-7.9513032885990579949493217458266876536482e+00), RC(7.9301148923100592201226014271115261823800e-01),  0,                                                   0,                                                  0,                                                  0, 0},
329:       {RC(1.0018765812524632961969196583094999808207e+00),  0,                                                  RC(-4.1665712824423798331313938005470971453189e+00), RC(3.8343432929128642412552665218251378665197e+00),  RC(-5.0233333560710847547464330228611765612403e-01), RC(6.6768474388416077115385092269857695410259e-01),  0,                                                  0,                                                  0, 0},
330:       {RC(2.7255018354630767130333963819175005717348e+01),  0,                                                  RC(-4.2004617278410638355318645443909295369611e+01), RC(-1.0535713126619489917921081600546526103722e+01), RC(8.0495536711411937147983652158926826634202e+01),  RC(-6.7343882271790513468549075963212975640927e+01), RC(1.3048657610777937463471187029566964762710e+01), 0,                                                  0, 0},
331:       {RC(-3.0397378057114965146943658658755763226883e+00), 0,                                                  RC(1.0138161410329801111857946190709700150441e+01),  RC(-6.4293056748647215721462825629555298064437e+00), RC(-1.5864371483408276587115312853798610579467e+00), RC(1.8921781841968424410864308909131353365021e+00),  RC(1.9699335407608869061292360163336442838006e-02), RC(5.4416989827933235465102724247952572977903e-03), 0, 0},
332:       {RC(-1.4449518916777735137351003179355712360517e+00), 0,                                                  RC(8.0318913859955919224117033223019560435041e+00),  RC(-7.5831741663401346820798883023671588604984e+00), RC(3.5816169353190074211247685442452878696855e+00),  RC(-2.4369722632199529411183809065693752383733e+00), RC(8.5158999992326179339689766032486142173390e-01), 0,                                                  0, 0}
333:     };
334:     const PetscReal b[10] = {RC(4.7425837833706756083569172717574534698932e-02), 0, 0, RC(2.5622361659370562659961727458274623448160e-01), RC(2.6951376833074206619473817258075952886764e-01), RC(1.2686622409092782845989138364739173247882e-01), RC(2.4887225942060071622046449427647492767292e-01), RC(3.0744837408200631335304388479099184768645e-03), RC(4.8023809989496943308189063347143123323209e-02), 0};
335:     const PetscReal bembed[10] = {RC(4.7485247699299631037531273805727961552268e-02), 0, 0, RC(2.5599412588690633297154918245905393870497e-01), RC(2.7058478081067688722530891099268135732387e-01), RC(1.2505618684425992913638822323746917920448e-01),
336:                                   RC(2.5204468723743860507184043820197442562182e-01), 0, 0, RC(4.8834971521418614557381971303093137592592e-02)};
337:     PetscCall(TSRKRegister(TSRK7VR, 7, 10, &A[0][0], b, NULL, bembed, 0, NULL));
338:   }
339:   {
340:     const PetscReal A[13][13] = {
341:       {0,                                                   0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
342:       {RC(2.5000000000000000000000000000000000000000e-01),  0,                                                  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
343:       {RC(8.7400846504915232052686327594877411977046e-02),  RC(2.5487604938654321753087950620345685135815e-02), 0,                                                   0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
344:       {RC(4.2333169291338582677165354330708661417323e-02),  0,                                                  RC(1.2699950787401574803149606299212598425197e-01),  0,                                                   0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
345:       {RC(4.2609505888742261494881445237572274090942e-01),  0,                                                  RC(-1.5987952846591523265427733230657181117089e+00), RC(1.5967002257717297115939588706899953707994e+00),  0,                                                   0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
346:       {RC(5.0719337296713929515090618138513639239329e-02),  0,                                                  0,                                                   RC(2.5433377264600407582754714408877778031369e-01),  RC(2.0394689005728199465736223777270858044698e-01),  0,                                                   0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
347:       {RC(-2.9000374717523110970388379285425896124091e-01), 0,                                                  0,                                                   RC(1.3441873910260789889438681109414337003184e+00),  RC(-2.8647779433614427309611103827036562829470e+00), RC(2.6775942995105948517211260646164815438695e+00),  0,                                                   0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
348:       {RC(9.8535011337993546469740402980727014284756e-02),  0,                                                  0,                                                   0,                                                   RC(2.2192680630751384842024036498197387903583e-01),  RC(-1.8140622911806994312690338288073952457474e-01), RC(1.0944411472562548236922614918038631254153e-02),  0,                                                  0,                                                   0,                                                  0,                                                  0, 0},
349:       {RC(3.8711052545731144679444618165166373405645e-01),  0,                                                  0,                                                   RC(-1.4424454974855277571256745553077927767173e+00), RC(2.9053981890699509317691346449233848441744e+00),  RC(-1.8537710696301059290843332675811978025183e+00), RC(1.4003648098728154269497325109771241479223e-01),  RC(5.7273940811495816575746774624447706488753e-01), 0,                                                   0,                                                  0,                                                  0, 0},
350:       {RC(-1.6124403444439308100630016197913480595436e-01), 0,                                                  0,                                                   RC(-1.7339602957358984083578404473962567894901e-01), RC(-1.3012892814065147406016812745172492529744e+00), RC(1.1379503751738617308558792131431003472124e+00),  RC(-3.1747649663966880106923521138043024698980e-02), RC(9.3351293824933666439811064486056884856590e-01), RC(-8.3786318334733852703300855629616433201504e-02), 0,                                                  0,                                                  0, 0},
351:       {RC(-1.9199444881589533281510804651483576073142e-02), 0,                                                  0,                                                   RC(2.7330857265264284907942326254016124275617e-01),  RC(-6.7534973206944372919691611210942380856240e-01), RC(3.4151849813846016071738489974728382711981e-01),  RC(-6.7950064803375772478920516198524629391910e-02), RC(9.6591752247623878884265586491216376509746e-02), RC(1.3253082511182101180721038466545389951226e-01),  RC(3.6854959360386113446906329951531666812946e-01), 0,                                                  0, 0},
352:       {RC(6.0918774036452898676888412111588817784584e-01),  0,                                                  0,                                                   RC(-2.2725690858980016768999800931413088399719e+00), RC(4.7578983426940290068155255881914785497547e+00),  RC(-5.5161067066927584824294689667844248244842e+00), RC(2.9005963696801192709095818565946174378180e-01),  RC(5.6914239633590368229109858454801849145630e-01), RC(7.9267957603321670271339916205893327579951e-01),  RC(1.5473720453288822894126190771849898232047e-01), RC(1.6149708956621816247083215106334544434974e+00), 0, 0},
353:       {RC(8.8735762208534719663211694051981022704884e-01),  0,                                                  0,                                                   RC(-2.9754597821085367558513632804709301581977e+00), RC(5.6007170094881630597990392548350098923829e+00),  RC(-5.9156074505366744680014930189941657351840e+00), RC(2.2029689156134927016879142540807638331238e-01),  RC(1.0155097824462216666143271340902996997549e-01), RC(1.1514345647386055909780397752125850553556e+00),  RC(1.9297101665271239396134361900805843653065e+00), 0,                                                  0, 0}
354:     };
355:     const PetscReal b[13] = {RC(4.4729564666695714203015840429049382466467e-02), 0, 0, 0, 0, RC(1.5691033527708199813368698010726645409175e-01), RC(1.8460973408151637740702451873526277892035e-01), RC(2.2516380602086991042479419400350721970920e-01), RC(1.4794615651970234687005179885449141753736e-01), RC(7.6055542444955825269798361910336491012732e-02), RC(1.2277290235018619610824346315921437388535e-01), RC(4.1811958638991631583384842800871882376786e-02), 0};
356:     const PetscReal bembed[13] = {RC(4.5847111400495925878664730122010282095875e-02), 0, 0, 0, 0, RC(2.6231891404152387437443356584845803392392e-01), RC(1.9169372337852611904485738635688429008025e-01), RC(2.1709172327902618330978407422906448568196e-01), RC(1.2738189624833706796803169450656737867900e-01), RC(1.1510530385365326258240515750043192148894e-01), 0, 0, RC(4.0561327798437566841823391436583608050053e-02)};
357:     PetscCall(TSRKRegister(TSRK8VR, 8, 13, &A[0][0], b, NULL, bembed, 0, NULL));
358:   }
359: #undef RC
360:   PetscFunctionReturn(PETSC_SUCCESS);
361: }

363: /*@C
364:   TSRKRegisterDestroy - Frees the list of schemes that were registered by `TSRKRegister()`.

366:   Not Collective

368:   Level: advanced

370: .seealso: [](ch_ts), `TSRK`, `TSRKRegister()`, `TSRKRegisterAll()`
371: @*/
372: PetscErrorCode TSRKRegisterDestroy(void)
373: {
374:   RKTableauLink link;

376:   PetscFunctionBegin;
377:   while ((link = RKTableauList)) {
378:     RKTableau t   = &link->tab;
379:     RKTableauList = link->next;
380:     PetscCall(PetscFree3(t->A, t->b, t->c));
381:     PetscCall(PetscFree(t->bembed));
382:     PetscCall(PetscFree(t->binterp));
383:     PetscCall(PetscFree(t->name));
384:     PetscCall(PetscFree(link));
385:   }
386:   TSRKRegisterAllCalled = PETSC_FALSE;
387:   PetscFunctionReturn(PETSC_SUCCESS);
388: }

390: /*@C
391:   TSRKInitializePackage - This function initializes everything in the `TSRK` package. It is called
392:   from `TSInitializePackage()`.

394:   Level: developer

396: .seealso: [](ch_ts), `TSInitializePackage()`, `PetscInitialize()`, `TSRKFinalizePackage()`
397: @*/
398: PetscErrorCode TSRKInitializePackage(void)
399: {
400:   PetscFunctionBegin;
401:   if (TSRKPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
402:   TSRKPackageInitialized = PETSC_TRUE;
403:   PetscCall(TSRKRegisterAll());
404:   PetscCall(PetscRegisterFinalize(TSRKFinalizePackage));
405:   PetscFunctionReturn(PETSC_SUCCESS);
406: }

408: /*@C
409:   TSRKFinalizePackage - This function destroys everything in the `TSRK` package. It is
410:   called from `PetscFinalize()`.

412:   Level: developer

414: .seealso: [](ch_ts), `PetscFinalize()`, `TSRKInitializePackage()`
415: @*/
416: PetscErrorCode TSRKFinalizePackage(void)
417: {
418:   PetscFunctionBegin;
419:   TSRKPackageInitialized = PETSC_FALSE;
420:   PetscCall(TSRKRegisterDestroy());
421:   PetscFunctionReturn(PETSC_SUCCESS);
422: }

424: /*@C
425:   TSRKRegister - register an `TSRK` scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation

427:   Not Collective, but the same schemes should be registered on all processes on which they will be used

429:   Input Parameters:
430: + name    - identifier for method
431: . order   - approximation order of method
432: . s       - number of stages, this is the dimension of the matrices below
433: . A       - stage coefficients (dimension s*s, row-major)
434: . b       - step completion table (dimension s; NULL to use last row of A)
435: . c       - abscissa (dimension s; NULL to use row sums of A)
436: . bembed  - completion table for embedded method (dimension s; NULL if not available)
437: . p       - Order of the interpolation scheme, equal to the number of columns of binterp
438: - binterp - Coefficients of the interpolation formula (dimension s*p; NULL to reuse b with p=1)

440:   Level: advanced

442:   Note:
443:   Several `TSRK` methods are provided, this function is only needed to create new methods.

445: .seealso: [](ch_ts), `TSRK`
446: @*/
447: PetscErrorCode TSRKRegister(TSRKType name, PetscInt order, PetscInt s, const PetscReal A[], const PetscReal b[], const PetscReal c[], const PetscReal bembed[], PetscInt p, const PetscReal binterp[])
448: {
449:   RKTableauLink link;
450:   RKTableau     t;
451:   PetscInt      i, j;

453:   PetscFunctionBegin;
454:   PetscAssertPointer(name, 1);
455:   PetscAssertPointer(A, 4);
456:   if (b) PetscAssertPointer(b, 5);
457:   if (c) PetscAssertPointer(c, 6);
458:   if (bembed) PetscAssertPointer(bembed, 7);
459:   if (binterp || p > 1) PetscAssertPointer(binterp, 9);
460:   PetscCheck(s >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expected number of stages s %" PetscInt_FMT " >= 0", s);

462:   PetscCall(TSRKInitializePackage());
463:   PetscCall(PetscNew(&link));
464:   t = &link->tab;

466:   PetscCall(PetscStrallocpy(name, &t->name));
467:   t->order = order;
468:   t->s     = s;
469:   PetscCall(PetscMalloc3(s * s, &t->A, s, &t->b, s, &t->c));
470:   PetscCall(PetscArraycpy(t->A, A, s * s));
471:   if (b) PetscCall(PetscArraycpy(t->b, b, s));
472:   else
473:     for (i = 0; i < s; i++) t->b[i] = A[(s - 1) * s + i];
474:   if (c) PetscCall(PetscArraycpy(t->c, c, s));
475:   else
476:     for (i = 0; i < s; i++)
477:       for (j = 0, t->c[i] = 0; j < s; j++) t->c[i] += A[i * s + j];
478:   t->FSAL = PETSC_TRUE;
479:   for (i = 0; i < s; i++)
480:     if (t->A[(s - 1) * s + i] != t->b[i]) t->FSAL = PETSC_FALSE;

482:   if (bembed) {
483:     PetscCall(PetscMalloc1(s, &t->bembed));
484:     PetscCall(PetscArraycpy(t->bembed, bembed, s));
485:   }

487:   if (!binterp) {
488:     p       = 1;
489:     binterp = t->b;
490:   }
491:   t->p = p;
492:   PetscCall(PetscMalloc1(s * p, &t->binterp));
493:   PetscCall(PetscArraycpy(t->binterp, binterp, s * p));

495:   link->next    = RKTableauList;
496:   RKTableauList = link;
497:   PetscFunctionReturn(PETSC_SUCCESS);
498: }

500: static PetscErrorCode TSRKGetTableau_RK(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed, PetscInt *p, const PetscReal **binterp, PetscBool *FSAL)
501: {
502:   TS_RK    *rk  = (TS_RK *)ts->data;
503:   RKTableau tab = rk->tableau;

505:   PetscFunctionBegin;
506:   if (s) *s = tab->s;
507:   if (A) *A = tab->A;
508:   if (b) *b = tab->b;
509:   if (c) *c = tab->c;
510:   if (bembed) *bembed = tab->bembed;
511:   if (p) *p = tab->p;
512:   if (binterp) *binterp = tab->binterp;
513:   if (FSAL) *FSAL = tab->FSAL;
514:   PetscFunctionReturn(PETSC_SUCCESS);
515: }

517: /*@C
518:   TSRKGetTableau - Get info on the `TSRK` tableau

520:   Not Collective

522:   Input Parameter:
523: . ts - timestepping context

525:   Output Parameters:
526: + s       - number of stages, this is the dimension of the matrices below
527: . A       - stage coefficients (dimension s*s, row-major)
528: . b       - step completion table (dimension s)
529: . c       - abscissa (dimension s)
530: . bembed  - completion table for embedded method (dimension s; NULL if not available)
531: . p       - Order of the interpolation scheme, equal to the number of columns of binterp
532: . binterp - Coefficients of the interpolation formula (dimension s*p)
533: - FSAL    - whether or not the scheme has the First Same As Last property

535:   Level: developer

537: .seealso: [](ch_ts), `TSRK`, `TSRKRegister()`, `TSRKSetType()`
538: @*/
539: PetscErrorCode TSRKGetTableau(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed, PetscInt *p, const PetscReal **binterp, PetscBool *FSAL)
540: {
541:   PetscFunctionBegin;
543:   PetscUseMethod(ts, "TSRKGetTableau_C", (TS, PetscInt *, const PetscReal **, const PetscReal **, const PetscReal **, const PetscReal **, PetscInt *, const PetscReal **, PetscBool *), (ts, s, A, b, c, bembed, p, binterp, FSAL));
544:   PetscFunctionReturn(PETSC_SUCCESS);
545: }

547: /*
548:  This is for single-step RK method
549:  The step completion formula is

551:  x1 = x0 + h b^T YdotRHS

553:  This function can be called before or after ts->vec_sol has been updated.
554:  Suppose we have a completion formula (b) and an embedded formula (be) of different order.
555:  We can write

557:  x1e = x0 + h be^T YdotRHS
558:      = x1 - h b^T YdotRHS + h be^T YdotRHS
559:      = x1 + h (be - b)^T YdotRHS

561:  so we can evaluate the method with different order even after the step has been optimistically completed.
562: */
563: static PetscErrorCode TSEvaluateStep_RK(TS ts, PetscInt order, Vec X, PetscBool *done)
564: {
565:   TS_RK       *rk  = (TS_RK *)ts->data;
566:   RKTableau    tab = rk->tableau;
567:   PetscScalar *w   = rk->work;
568:   PetscReal    h;
569:   PetscInt     s = tab->s, j;

571:   PetscFunctionBegin;
572:   switch (rk->status) {
573:   case TS_STEP_INCOMPLETE:
574:   case TS_STEP_PENDING:
575:     h = ts->time_step;
576:     break;
577:   case TS_STEP_COMPLETE:
578:     h = ts->ptime - ts->ptime_prev;
579:     break;
580:   default:
581:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
582:   }
583:   if (order == tab->order) {
584:     if (rk->status == TS_STEP_INCOMPLETE) {
585:       PetscCall(VecCopy(ts->vec_sol, X));
586:       for (j = 0; j < s; j++) w[j] = h * tab->b[j] / rk->dtratio;
587:       PetscCall(VecMAXPY(X, s, w, rk->YdotRHS));
588:     } else PetscCall(VecCopy(ts->vec_sol, X));
589:     PetscFunctionReturn(PETSC_SUCCESS);
590:   } else if (order == tab->order - 1) {
591:     if (!tab->bembed) goto unavailable;
592:     if (rk->status == TS_STEP_INCOMPLETE) { /*Complete with the embedded method (be)*/
593:       PetscCall(VecCopy(ts->vec_sol, X));
594:       for (j = 0; j < s; j++) w[j] = h * tab->bembed[j];
595:       PetscCall(VecMAXPY(X, s, w, rk->YdotRHS));
596:     } else { /*Rollback and re-complete using (be-b) */
597:       PetscCall(VecCopy(ts->vec_sol, X));
598:       for (j = 0; j < s; j++) w[j] = h * (tab->bembed[j] - tab->b[j]);
599:       PetscCall(VecMAXPY(X, s, w, rk->YdotRHS));
600:     }
601:     if (done) *done = PETSC_TRUE;
602:     PetscFunctionReturn(PETSC_SUCCESS);
603:   }
604: unavailable:
605:   if (done) *done = PETSC_FALSE;
606:   else
607:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "RK '%s' of order %" PetscInt_FMT " cannot evaluate step at order %" PetscInt_FMT ". Consider using -ts_adapt_type none or a different method that has an embedded estimate.", tab->name, tab->order, order);
608:   PetscFunctionReturn(PETSC_SUCCESS);
609: }

611: static PetscErrorCode TSForwardCostIntegral_RK(TS ts)
612: {
613:   TS_RK           *rk     = (TS_RK *)ts->data;
614:   TS               quadts = ts->quadraturets;
615:   RKTableau        tab    = rk->tableau;
616:   const PetscInt   s      = tab->s;
617:   const PetscReal *b = tab->b, *c = tab->c;
618:   Vec             *Y = rk->Y;
619:   PetscInt         i;

621:   PetscFunctionBegin;
622:   /* No need to backup quadts->vec_sol since it can be reverted in TSRollBack_RK */
623:   for (i = s - 1; i >= 0; i--) {
624:     /* Evolve quadrature TS solution to compute integrals */
625:     PetscCall(TSComputeRHSFunction(quadts, rk->ptime + rk->time_step * c[i], Y[i], ts->vec_costintegrand));
626:     PetscCall(VecAXPY(quadts->vec_sol, rk->time_step * b[i], ts->vec_costintegrand));
627:   }
628:   PetscFunctionReturn(PETSC_SUCCESS);
629: }

631: static PetscErrorCode TSAdjointCostIntegral_RK(TS ts)
632: {
633:   TS_RK           *rk     = (TS_RK *)ts->data;
634:   RKTableau        tab    = rk->tableau;
635:   TS               quadts = ts->quadraturets;
636:   const PetscInt   s      = tab->s;
637:   const PetscReal *b = tab->b, *c = tab->c;
638:   Vec             *Y = rk->Y;
639:   PetscInt         i;

641:   PetscFunctionBegin;
642:   for (i = s - 1; i >= 0; i--) {
643:     /* Evolve quadrature TS solution to compute integrals */
644:     PetscCall(TSComputeRHSFunction(quadts, ts->ptime + ts->time_step * (1.0 - c[i]), Y[i], ts->vec_costintegrand));
645:     PetscCall(VecAXPY(quadts->vec_sol, -ts->time_step * b[i], ts->vec_costintegrand));
646:   }
647:   PetscFunctionReturn(PETSC_SUCCESS);
648: }

650: static PetscErrorCode TSRollBack_RK(TS ts)
651: {
652:   TS_RK           *rk     = (TS_RK *)ts->data;
653:   TS               quadts = ts->quadraturets;
654:   RKTableau        tab    = rk->tableau;
655:   const PetscInt   s      = tab->s;
656:   const PetscReal *b = tab->b, *c = tab->c;
657:   PetscScalar     *w = rk->work;
658:   Vec             *Y = rk->Y, *YdotRHS = rk->YdotRHS;
659:   PetscInt         j;
660:   PetscReal        h;

662:   PetscFunctionBegin;
663:   switch (rk->status) {
664:   case TS_STEP_INCOMPLETE:
665:   case TS_STEP_PENDING:
666:     h = ts->time_step;
667:     break;
668:   case TS_STEP_COMPLETE:
669:     h = ts->ptime - ts->ptime_prev;
670:     break;
671:   default:
672:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
673:   }
674:   for (j = 0; j < s; j++) w[j] = -h * b[j];
675:   PetscCall(VecMAXPY(ts->vec_sol, s, w, YdotRHS));
676:   if (quadts && ts->costintegralfwd) {
677:     for (j = 0; j < s; j++) {
678:       /* Revert the quadrature TS solution */
679:       PetscCall(TSComputeRHSFunction(quadts, rk->ptime + h * c[j], Y[j], ts->vec_costintegrand));
680:       PetscCall(VecAXPY(quadts->vec_sol, -h * b[j], ts->vec_costintegrand));
681:     }
682:   }
683:   PetscFunctionReturn(PETSC_SUCCESS);
684: }

686: static PetscErrorCode TSForwardStep_RK(TS ts)
687: {
688:   TS_RK           *rk  = (TS_RK *)ts->data;
689:   RKTableau        tab = rk->tableau;
690:   Mat              J, *MatsFwdSensipTemp = rk->MatsFwdSensipTemp;
691:   const PetscInt   s = tab->s;
692:   const PetscReal *A = tab->A, *c = tab->c, *b = tab->b;
693:   Vec             *Y = rk->Y;
694:   PetscInt         i, j;
695:   PetscReal        stage_time, h = ts->time_step;
696:   PetscBool        zero;

698:   PetscFunctionBegin;
699:   PetscCall(MatCopy(ts->mat_sensip, rk->MatFwdSensip0, SAME_NONZERO_PATTERN));
700:   PetscCall(TSGetRHSJacobian(ts, &J, NULL, NULL, NULL));

702:   for (i = 0; i < s; i++) {
703:     stage_time = ts->ptime + h * c[i];
704:     zero       = PETSC_FALSE;
705:     if (b[i] == 0 && i == s - 1) zero = PETSC_TRUE;
706:     /* TLM Stage values */
707:     if (!i) {
708:       PetscCall(MatCopy(ts->mat_sensip, rk->MatsFwdStageSensip[i], SAME_NONZERO_PATTERN));
709:     } else if (!zero) {
710:       PetscCall(MatZeroEntries(rk->MatsFwdStageSensip[i]));
711:       for (j = 0; j < i; j++) PetscCall(MatAXPY(rk->MatsFwdStageSensip[i], h * A[i * s + j], MatsFwdSensipTemp[j], SAME_NONZERO_PATTERN));
712:       PetscCall(MatAXPY(rk->MatsFwdStageSensip[i], 1., ts->mat_sensip, SAME_NONZERO_PATTERN));
713:     } else {
714:       PetscCall(MatZeroEntries(rk->MatsFwdStageSensip[i]));
715:     }

717:     PetscCall(TSComputeRHSJacobian(ts, stage_time, Y[i], J, J));
718:     PetscCall(MatMatMult(J, rk->MatsFwdStageSensip[i], MAT_REUSE_MATRIX, PETSC_DEFAULT, &MatsFwdSensipTemp[i]));
719:     if (ts->Jacprhs) {
720:       PetscCall(TSComputeRHSJacobianP(ts, stage_time, Y[i], ts->Jacprhs)); /* get f_p */
721:       if (ts->vecs_sensi2p) {                                              /* TLM used for 2nd-order adjoint */
722:         PetscScalar *xarr;
723:         PetscCall(MatDenseGetColumn(MatsFwdSensipTemp[i], 0, &xarr));
724:         PetscCall(VecPlaceArray(rk->VecDeltaFwdSensipCol, xarr));
725:         PetscCall(MatMultAdd(ts->Jacprhs, ts->vec_dir, rk->VecDeltaFwdSensipCol, rk->VecDeltaFwdSensipCol));
726:         PetscCall(VecResetArray(rk->VecDeltaFwdSensipCol));
727:         PetscCall(MatDenseRestoreColumn(MatsFwdSensipTemp[i], &xarr));
728:       } else {
729:         PetscCall(MatAXPY(MatsFwdSensipTemp[i], 1., ts->Jacprhs, SUBSET_NONZERO_PATTERN));
730:       }
731:     }
732:   }

734:   for (i = 0; i < s; i++) PetscCall(MatAXPY(ts->mat_sensip, h * b[i], rk->MatsFwdSensipTemp[i], SAME_NONZERO_PATTERN));
735:   rk->status = TS_STEP_COMPLETE;
736:   PetscFunctionReturn(PETSC_SUCCESS);
737: }

739: static PetscErrorCode TSForwardGetStages_RK(TS ts, PetscInt *ns, Mat **stagesensip)
740: {
741:   TS_RK    *rk  = (TS_RK *)ts->data;
742:   RKTableau tab = rk->tableau;

744:   PetscFunctionBegin;
745:   if (ns) *ns = tab->s;
746:   if (stagesensip) *stagesensip = rk->MatsFwdStageSensip;
747:   PetscFunctionReturn(PETSC_SUCCESS);
748: }

750: static PetscErrorCode TSForwardSetUp_RK(TS ts)
751: {
752:   TS_RK    *rk  = (TS_RK *)ts->data;
753:   RKTableau tab = rk->tableau;
754:   PetscInt  i;

756:   PetscFunctionBegin;
757:   /* backup sensitivity results for roll-backs */
758:   PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &rk->MatFwdSensip0));

760:   PetscCall(PetscMalloc1(tab->s, &rk->MatsFwdStageSensip));
761:   PetscCall(PetscMalloc1(tab->s, &rk->MatsFwdSensipTemp));
762:   for (i = 0; i < tab->s; i++) {
763:     PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &rk->MatsFwdStageSensip[i]));
764:     PetscCall(MatDuplicate(ts->mat_sensip, MAT_DO_NOT_COPY_VALUES, &rk->MatsFwdSensipTemp[i]));
765:   }
766:   PetscCall(VecDuplicate(ts->vec_sol, &rk->VecDeltaFwdSensipCol));
767:   PetscFunctionReturn(PETSC_SUCCESS);
768: }

770: static PetscErrorCode TSForwardReset_RK(TS ts)
771: {
772:   TS_RK    *rk  = (TS_RK *)ts->data;
773:   RKTableau tab = rk->tableau;
774:   PetscInt  i;

776:   PetscFunctionBegin;
777:   PetscCall(MatDestroy(&rk->MatFwdSensip0));
778:   if (rk->MatsFwdStageSensip) {
779:     for (i = 0; i < tab->s; i++) PetscCall(MatDestroy(&rk->MatsFwdStageSensip[i]));
780:     PetscCall(PetscFree(rk->MatsFwdStageSensip));
781:   }
782:   if (rk->MatsFwdSensipTemp) {
783:     for (i = 0; i < tab->s; i++) PetscCall(MatDestroy(&rk->MatsFwdSensipTemp[i]));
784:     PetscCall(PetscFree(rk->MatsFwdSensipTemp));
785:   }
786:   PetscCall(VecDestroy(&rk->VecDeltaFwdSensipCol));
787:   PetscFunctionReturn(PETSC_SUCCESS);
788: }

790: static PetscErrorCode TSStep_RK(TS ts)
791: {
792:   TS_RK           *rk  = (TS_RK *)ts->data;
793:   RKTableau        tab = rk->tableau;
794:   const PetscInt   s   = tab->s;
795:   const PetscReal *A = tab->A, *c = tab->c;
796:   PetscScalar     *w = rk->work;
797:   Vec             *Y = rk->Y, *YdotRHS = rk->YdotRHS;
798:   PetscBool        FSAL = (PetscBool)(tab->FSAL && !rk->newtableau);
799:   TSAdapt          adapt;
800:   PetscInt         i, j;
801:   PetscInt         rejections = 0;
802:   PetscBool        stageok, accept = PETSC_TRUE;
803:   PetscReal        next_time_step = ts->time_step;

805:   PetscFunctionBegin;
806:   if (ts->steprollback || ts->steprestart) FSAL = PETSC_FALSE;
807:   if (FSAL) PetscCall(VecCopy(YdotRHS[s - 1], YdotRHS[0]));
808:   rk->newtableau = PETSC_FALSE;

810:   rk->status = TS_STEP_INCOMPLETE;
811:   while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
812:     PetscReal t = ts->ptime;
813:     PetscReal h = ts->time_step;
814:     for (i = 0; i < s; i++) {
815:       rk->stage_time = t + h * c[i];
816:       PetscCall(TSPreStage(ts, rk->stage_time));
817:       PetscCall(VecCopy(ts->vec_sol, Y[i]));
818:       for (j = 0; j < i; j++) w[j] = h * A[i * s + j];
819:       PetscCall(VecMAXPY(Y[i], i, w, YdotRHS));
820:       PetscCall(TSPostStage(ts, rk->stage_time, i, Y));
821:       PetscCall(TSGetAdapt(ts, &adapt));
822:       PetscCall(TSAdaptCheckStage(adapt, ts, rk->stage_time, Y[i], &stageok));
823:       if (!stageok) goto reject_step;
824:       if (FSAL && !i) continue;
825:       PetscCall(TSComputeRHSFunction(ts, t + h * c[i], Y[i], YdotRHS[i]));
826:     }

828:     rk->status = TS_STEP_INCOMPLETE;
829:     PetscCall(TSEvaluateStep(ts, tab->order, ts->vec_sol, NULL));
830:     rk->status = TS_STEP_PENDING;
831:     PetscCall(TSGetAdapt(ts, &adapt));
832:     PetscCall(TSAdaptCandidatesClear(adapt));
833:     PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
834:     PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, NULL, &next_time_step, &accept));
835:     rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
836:     if (!accept) { /* Roll back the current step */
837:       PetscCall(TSRollBack_RK(ts));
838:       ts->time_step = next_time_step;
839:       goto reject_step;
840:     }

842:     if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */
843:       rk->ptime     = ts->ptime;
844:       rk->time_step = ts->time_step;
845:     }

847:     ts->ptime += ts->time_step;
848:     ts->time_step = next_time_step;
849:     break;

851:   reject_step:
852:     ts->reject++;
853:     accept = PETSC_FALSE;
854:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
855:       ts->reason = TS_DIVERGED_STEP_REJECTED;
856:       PetscCall(PetscInfo(ts, "Step=%" PetscInt_FMT ", step rejections %" PetscInt_FMT " greater than current TS allowed, stopping solve\n", ts->steps, rejections));
857:     }
858:   }
859:   PetscFunctionReturn(PETSC_SUCCESS);
860: }

862: static PetscErrorCode TSAdjointSetUp_RK(TS ts)
863: {
864:   TS_RK    *rk  = (TS_RK *)ts->data;
865:   RKTableau tab = rk->tableau;
866:   PetscInt  s   = tab->s;

868:   PetscFunctionBegin;
869:   if (ts->adjointsetupcalled++) PetscFunctionReturn(PETSC_SUCCESS);
870:   PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], s * ts->numcost, &rk->VecsDeltaLam));
871:   PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], ts->numcost, &rk->VecsSensiTemp));
872:   if (ts->vecs_sensip) PetscCall(VecDuplicate(ts->vecs_sensip[0], &rk->VecDeltaMu));
873:   if (ts->vecs_sensi2) {
874:     PetscCall(VecDuplicateVecs(ts->vecs_sensi[0], s * ts->numcost, &rk->VecsDeltaLam2));
875:     PetscCall(VecDuplicateVecs(ts->vecs_sensi2[0], ts->numcost, &rk->VecsSensi2Temp));
876:   }
877:   if (ts->vecs_sensi2p) PetscCall(VecDuplicate(ts->vecs_sensi2p[0], &rk->VecDeltaMu2));
878:   PetscFunctionReturn(PETSC_SUCCESS);
879: }

881: /*
882:   Assumptions:
883:     - TSStep_RK() always evaluates the step with b, not bembed.
884: */
885: static PetscErrorCode TSAdjointStep_RK(TS ts)
886: {
887:   TS_RK           *rk     = (TS_RK *)ts->data;
888:   TS               quadts = ts->quadraturets;
889:   RKTableau        tab    = rk->tableau;
890:   Mat              J, Jpre, Jquad;
891:   const PetscInt   s = tab->s;
892:   const PetscReal *A = tab->A, *b = tab->b, *c = tab->c;
893:   PetscScalar     *w = rk->work, *xarr;
894:   Vec             *Y = rk->Y, *VecsDeltaLam = rk->VecsDeltaLam, VecDeltaMu = rk->VecDeltaMu, *VecsSensiTemp = rk->VecsSensiTemp;
895:   Vec             *VecsDeltaLam2 = rk->VecsDeltaLam2, VecDeltaMu2 = rk->VecDeltaMu2, *VecsSensi2Temp = rk->VecsSensi2Temp;
896:   Vec              VecDRDUTransCol = ts->vec_drdu_col, VecDRDPTransCol = ts->vec_drdp_col;
897:   PetscInt         i, j, nadj;
898:   PetscReal        t = ts->ptime;
899:   PetscReal        h = ts->time_step;

901:   PetscFunctionBegin;
902:   rk->status = TS_STEP_INCOMPLETE;

904:   PetscCall(TSGetRHSJacobian(ts, &J, &Jpre, NULL, NULL));
905:   if (quadts) PetscCall(TSGetRHSJacobian(quadts, &Jquad, NULL, NULL, NULL));
906:   for (i = s - 1; i >= 0; i--) {
907:     if (tab->FSAL && i == s - 1) {
908:       /* VecsDeltaLam[nadj*s+s-1] are initialized with zeros and the values never change.*/
909:       continue;
910:     }
911:     rk->stage_time = t + h * (1.0 - c[i]);
912:     PetscCall(TSComputeSNESJacobian(ts, Y[i], J, Jpre));
913:     if (quadts) { PetscCall(TSComputeRHSJacobian(quadts, rk->stage_time, Y[i], Jquad, Jquad)); /* get r_u^T */ }
914:     if (ts->vecs_sensip) {
915:       PetscCall(TSComputeRHSJacobianP(ts, rk->stage_time, Y[i], ts->Jacprhs)); /* get f_p */
916:       if (quadts) { PetscCall(TSComputeRHSJacobianP(quadts, rk->stage_time, Y[i], quadts->Jacprhs)); /* get f_p for the quadrature */ }
917:     }

919:     if (b[i]) {
920:       for (j = i + 1; j < s; j++) w[j - i - 1] = A[j * s + i] / b[i]; /* coefficients for computing VecsSensiTemp */
921:     } else {
922:       for (j = i + 1; j < s; j++) w[j - i - 1] = A[j * s + i]; /* coefficients for computing VecsSensiTemp */
923:     }

925:     for (nadj = 0; nadj < ts->numcost; nadj++) {
926:       /* Stage values of lambda */
927:       if (b[i]) {
928:         /* lambda_{n+1} + \sum_{j=i+1}^s a_{ji}/b[i]*lambda_{s,j} */
929:         PetscCall(VecCopy(ts->vecs_sensi[nadj], VecsSensiTemp[nadj])); /* VecDeltaLam is an vec array of size s by numcost */
930:         PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
931:         PetscCall(MatMultTranspose(J, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i])); /* VecsSensiTemp will be reused by 2nd-order adjoint */
932:         PetscCall(VecScale(VecsDeltaLam[nadj * s + i], -h * b[i]));
933:         if (quadts) {
934:           PetscCall(MatDenseGetColumn(Jquad, nadj, &xarr));
935:           PetscCall(VecPlaceArray(VecDRDUTransCol, xarr));
936:           PetscCall(VecAXPY(VecsDeltaLam[nadj * s + i], -h * b[i], VecDRDUTransCol));
937:           PetscCall(VecResetArray(VecDRDUTransCol));
938:           PetscCall(MatDenseRestoreColumn(Jquad, &xarr));
939:         }
940:       } else {
941:         /* \sum_{j=i+1}^s a_{ji}*lambda_{s,j} */
942:         PetscCall(VecSet(VecsSensiTemp[nadj], 0));
943:         PetscCall(VecMAXPY(VecsSensiTemp[nadj], s - i - 1, w, &VecsDeltaLam[nadj * s + i + 1]));
944:         PetscCall(MatMultTranspose(J, VecsSensiTemp[nadj], VecsDeltaLam[nadj * s + i]));
945:         PetscCall(VecScale(VecsDeltaLam[nadj * s + i], -h));
946:       }

948:       /* Stage values of mu */
949:       if (ts->vecs_sensip) {
950:         if (b[i]) {
951:           PetscCall(MatMultTranspose(ts->Jacprhs, VecsSensiTemp[nadj], VecDeltaMu));
952:           PetscCall(VecScale(VecDeltaMu, -h * b[i]));
953:           if (quadts) {
954:             PetscCall(MatDenseGetColumn(quadts->Jacprhs, nadj, &xarr));
955:             PetscCall(VecPlaceArray(VecDRDPTransCol, xarr));
956:             PetscCall(VecAXPY(VecDeltaMu, -h * b[i], VecDRDPTransCol));
957:             PetscCall(VecResetArray(VecDRDPTransCol));
958:             PetscCall(MatDenseRestoreColumn(quadts->Jacprhs, &xarr));
959:           }
960:         } else {
961:           PetscCall(VecScale(VecDeltaMu, -h));
962:         }
963:         PetscCall(VecAXPY(ts->vecs_sensip[nadj], 1., VecDeltaMu)); /* update sensip for each stage */
964:       }
965:     }

967:     if (ts->vecs_sensi2 && ts->forward_solve) { /* 2nd-order adjoint, TLM mode has to be turned on */
968:       /* Get w1 at t_{n+1} from TLM matrix */
969:       PetscCall(MatDenseGetColumn(rk->MatsFwdStageSensip[i], 0, &xarr));
970:       PetscCall(VecPlaceArray(ts->vec_sensip_col, xarr));
971:       /* lambda_s^T F_UU w_1 */
972:       PetscCall(TSComputeRHSHessianProductFunctionUU(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_sensip_col, ts->vecs_guu));
973:       if (quadts) {
974:         /* R_UU w_1 */
975:         PetscCall(TSComputeRHSHessianProductFunctionUU(quadts, rk->stage_time, Y[i], NULL, ts->vec_sensip_col, ts->vecs_guu));
976:       }
977:       if (ts->vecs_sensip) {
978:         /* lambda_s^T F_UP w_2 */
979:         PetscCall(TSComputeRHSHessianProductFunctionUP(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_dir, ts->vecs_gup));
980:         if (quadts) {
981:           /* R_UP w_2 */
982:           PetscCall(TSComputeRHSHessianProductFunctionUP(quadts, rk->stage_time, Y[i], NULL, ts->vec_sensip_col, ts->vecs_gup));
983:         }
984:       }
985:       if (ts->vecs_sensi2p) {
986:         /* lambda_s^T F_PU w_1 */
987:         PetscCall(TSComputeRHSHessianProductFunctionPU(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_sensip_col, ts->vecs_gpu));
988:         /* lambda_s^T F_PP w_2 */
989:         PetscCall(TSComputeRHSHessianProductFunctionPP(ts, rk->stage_time, Y[i], VecsSensiTemp, ts->vec_dir, ts->vecs_gpp));
990:         if (b[i] && quadts) {
991:           /* R_PU w_1 */
992:           PetscCall(TSComputeRHSHessianProductFunctionPU(quadts, rk->stage_time, Y[i], NULL, ts->vec_sensip_col, ts->vecs_gpu));
993:           /* R_PP w_2 */
994:           PetscCall(TSComputeRHSHessianProductFunctionPP(quadts, rk->stage_time, Y[i], NULL, ts->vec_dir, ts->vecs_gpp));
995:         }
996:       }
997:       PetscCall(VecResetArray(ts->vec_sensip_col));
998:       PetscCall(MatDenseRestoreColumn(rk->MatsFwdStageSensip[i], &xarr));

1000:       for (nadj = 0; nadj < ts->numcost; nadj++) {
1001:         /* Stage values of lambda */
1002:         if (b[i]) {
1003:           /* J_i^T*(Lambda_{n+1}+\sum_{j=i+1}^s a_{ji}/b_i*Lambda_{s,j} */
1004:           PetscCall(VecCopy(ts->vecs_sensi2[nadj], VecsSensi2Temp[nadj]));
1005:           PetscCall(VecMAXPY(VecsSensi2Temp[nadj], s - i - 1, w, &VecsDeltaLam2[nadj * s + i + 1]));
1006:           PetscCall(MatMultTranspose(J, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj * s + i]));
1007:           PetscCall(VecScale(VecsDeltaLam2[nadj * s + i], -h * b[i]));
1008:           PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h * b[i], ts->vecs_guu[nadj]));
1009:           if (ts->vecs_sensip) PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h * b[i], ts->vecs_gup[nadj]));
1010:         } else {
1011:           /* \sum_{j=i+1}^s a_{ji}*Lambda_{s,j} */
1012:           PetscCall(VecSet(VecsDeltaLam2[nadj * s + i], 0));
1013:           PetscCall(VecMAXPY(VecsSensi2Temp[nadj], s - i - 1, w, &VecsDeltaLam2[nadj * s + i + 1]));
1014:           PetscCall(MatMultTranspose(J, VecsSensi2Temp[nadj], VecsDeltaLam2[nadj * s + i]));
1015:           PetscCall(VecScale(VecsDeltaLam2[nadj * s + i], -h));
1016:           PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h, ts->vecs_guu[nadj]));
1017:           if (ts->vecs_sensip) PetscCall(VecAXPY(VecsDeltaLam2[nadj * s + i], -h, ts->vecs_gup[nadj]));
1018:         }
1019:         if (ts->vecs_sensi2p) { /* 2nd-order adjoint for parameters */
1020:           PetscCall(MatMultTranspose(ts->Jacprhs, VecsSensi2Temp[nadj], VecDeltaMu2));
1021:           if (b[i]) {
1022:             PetscCall(VecScale(VecDeltaMu2, -h * b[i]));
1023:             PetscCall(VecAXPY(VecDeltaMu2, -h * b[i], ts->vecs_gpu[nadj]));
1024:             PetscCall(VecAXPY(VecDeltaMu2, -h * b[i], ts->vecs_gpp[nadj]));
1025:           } else {
1026:             PetscCall(VecScale(VecDeltaMu2, -h));
1027:             PetscCall(VecAXPY(VecDeltaMu2, -h, ts->vecs_gpu[nadj]));
1028:             PetscCall(VecAXPY(VecDeltaMu2, -h, ts->vecs_gpp[nadj]));
1029:           }
1030:           PetscCall(VecAXPY(ts->vecs_sensi2p[nadj], 1, VecDeltaMu2)); /* update sensi2p for each stage */
1031:         }
1032:       }
1033:     }
1034:   }

1036:   for (j = 0; j < s; j++) w[j] = 1.0;
1037:   for (nadj = 0; nadj < ts->numcost; nadj++) { /* no need to do this for mu's */
1038:     PetscCall(VecMAXPY(ts->vecs_sensi[nadj], s, w, &VecsDeltaLam[nadj * s]));
1039:     if (ts->vecs_sensi2) PetscCall(VecMAXPY(ts->vecs_sensi2[nadj], s, w, &VecsDeltaLam2[nadj * s]));
1040:   }
1041:   rk->status = TS_STEP_COMPLETE;
1042:   PetscFunctionReturn(PETSC_SUCCESS);
1043: }

1045: static PetscErrorCode TSAdjointReset_RK(TS ts)
1046: {
1047:   TS_RK    *rk  = (TS_RK *)ts->data;
1048:   RKTableau tab = rk->tableau;

1050:   PetscFunctionBegin;
1051:   PetscCall(VecDestroyVecs(tab->s * ts->numcost, &rk->VecsDeltaLam));
1052:   PetscCall(VecDestroyVecs(ts->numcost, &rk->VecsSensiTemp));
1053:   PetscCall(VecDestroy(&rk->VecDeltaMu));
1054:   PetscCall(VecDestroyVecs(tab->s * ts->numcost, &rk->VecsDeltaLam2));
1055:   PetscCall(VecDestroy(&rk->VecDeltaMu2));
1056:   PetscCall(VecDestroyVecs(ts->numcost, &rk->VecsSensi2Temp));
1057:   PetscFunctionReturn(PETSC_SUCCESS);
1058: }

1060: static PetscErrorCode TSInterpolate_RK(TS ts, PetscReal itime, Vec X)
1061: {
1062:   TS_RK           *rk = (TS_RK *)ts->data;
1063:   PetscInt         s = rk->tableau->s, p = rk->tableau->p, i, j;
1064:   PetscReal        h;
1065:   PetscReal        tt, t;
1066:   PetscScalar     *b;
1067:   const PetscReal *B = rk->tableau->binterp;

1069:   PetscFunctionBegin;
1070:   PetscCheck(B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSRK %s does not have an interpolation formula", rk->tableau->name);

1072:   switch (rk->status) {
1073:   case TS_STEP_INCOMPLETE:
1074:   case TS_STEP_PENDING:
1075:     h = ts->time_step;
1076:     t = (itime - ts->ptime) / h;
1077:     break;
1078:   case TS_STEP_COMPLETE:
1079:     h = ts->ptime - ts->ptime_prev;
1080:     t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
1081:     break;
1082:   default:
1083:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
1084:   }
1085:   PetscCall(PetscMalloc1(s, &b));
1086:   for (i = 0; i < s; i++) b[i] = 0;
1087:   for (j = 0, tt = t; j < p; j++, tt *= t) {
1088:     for (i = 0; i < s; i++) b[i] += h * B[i * p + j] * tt;
1089:   }
1090:   PetscCall(VecCopy(rk->Y[0], X));
1091:   PetscCall(VecMAXPY(X, s, b, rk->YdotRHS));
1092:   PetscCall(PetscFree(b));
1093:   PetscFunctionReturn(PETSC_SUCCESS);
1094: }

1096: /*------------------------------------------------------------*/

1098: static PetscErrorCode TSRKTableauReset(TS ts)
1099: {
1100:   TS_RK    *rk  = (TS_RK *)ts->data;
1101:   RKTableau tab = rk->tableau;

1103:   PetscFunctionBegin;
1104:   if (!tab) PetscFunctionReturn(PETSC_SUCCESS);
1105:   PetscCall(PetscFree(rk->work));
1106:   PetscCall(VecDestroyVecs(tab->s, &rk->Y));
1107:   PetscCall(VecDestroyVecs(tab->s, &rk->YdotRHS));
1108:   PetscFunctionReturn(PETSC_SUCCESS);
1109: }

1111: static PetscErrorCode TSReset_RK(TS ts)
1112: {
1113:   PetscFunctionBegin;
1114:   PetscCall(TSRKTableauReset(ts));
1115:   if (ts->use_splitrhsfunction) {
1116:     PetscTryMethod(ts, "TSReset_RK_MultirateSplit_C", (TS), (ts));
1117:   } else {
1118:     PetscTryMethod(ts, "TSReset_RK_MultirateNonsplit_C", (TS), (ts));
1119:   }
1120:   PetscFunctionReturn(PETSC_SUCCESS);
1121: }

1123: static PetscErrorCode DMCoarsenHook_TSRK(DM fine, DM coarse, void *ctx)
1124: {
1125:   PetscFunctionBegin;
1126:   PetscFunctionReturn(PETSC_SUCCESS);
1127: }

1129: static PetscErrorCode DMRestrictHook_TSRK(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
1130: {
1131:   PetscFunctionBegin;
1132:   PetscFunctionReturn(PETSC_SUCCESS);
1133: }

1135: static PetscErrorCode DMSubDomainHook_TSRK(DM dm, DM subdm, void *ctx)
1136: {
1137:   PetscFunctionBegin;
1138:   PetscFunctionReturn(PETSC_SUCCESS);
1139: }

1141: static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
1142: {
1143:   PetscFunctionBegin;
1144:   PetscFunctionReturn(PETSC_SUCCESS);
1145: }

1147: static PetscErrorCode TSRKTableauSetUp(TS ts)
1148: {
1149:   TS_RK    *rk  = (TS_RK *)ts->data;
1150:   RKTableau tab = rk->tableau;

1152:   PetscFunctionBegin;
1153:   PetscCall(PetscMalloc1(tab->s, &rk->work));
1154:   PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &rk->Y));
1155:   PetscCall(VecDuplicateVecs(ts->vec_sol, tab->s, &rk->YdotRHS));
1156:   rk->newtableau = PETSC_TRUE;
1157:   PetscFunctionReturn(PETSC_SUCCESS);
1158: }

1160: static PetscErrorCode TSSetUp_RK(TS ts)
1161: {
1162:   TS quadts = ts->quadraturets;
1163:   DM dm;

1165:   PetscFunctionBegin;
1166:   PetscCall(TSCheckImplicitTerm(ts));
1167:   PetscCall(TSRKTableauSetUp(ts));
1168:   if (quadts && ts->costintegralfwd) {
1169:     Mat Jquad;
1170:     PetscCall(TSGetRHSJacobian(quadts, &Jquad, NULL, NULL, NULL));
1171:   }
1172:   PetscCall(TSGetDM(ts, &dm));
1173:   PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSRK, DMRestrictHook_TSRK, ts));
1174:   PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSRK, DMSubDomainRestrictHook_TSRK, ts));
1175:   if (ts->use_splitrhsfunction) {
1176:     PetscTryMethod(ts, "TSSetUp_RK_MultirateSplit_C", (TS), (ts));
1177:   } else {
1178:     PetscTryMethod(ts, "TSSetUp_RK_MultirateNonsplit_C", (TS), (ts));
1179:   }
1180:   PetscFunctionReturn(PETSC_SUCCESS);
1181: }

1183: static PetscErrorCode TSSetFromOptions_RK(TS ts, PetscOptionItems *PetscOptionsObject)
1184: {
1185:   TS_RK *rk = (TS_RK *)ts->data;

1187:   PetscFunctionBegin;
1188:   PetscOptionsHeadBegin(PetscOptionsObject, "RK ODE solver options");
1189:   {
1190:     RKTableauLink link;
1191:     PetscInt      count, choice;
1192:     PetscBool     flg, use_multirate = PETSC_FALSE;
1193:     const char  **namelist;

1195:     for (link = RKTableauList, count = 0; link; link = link->next, count++)
1196:       ;
1197:     PetscCall(PetscMalloc1(count, (char ***)&namelist));
1198:     for (link = RKTableauList, count = 0; link; link = link->next, count++) namelist[count] = link->tab.name;
1199:     PetscCall(PetscOptionsBool("-ts_rk_multirate", "Use interpolation-based multirate RK method", "TSRKSetMultirate", rk->use_multirate, &use_multirate, &flg));
1200:     if (flg) PetscCall(TSRKSetMultirate(ts, use_multirate));
1201:     PetscCall(PetscOptionsEList("-ts_rk_type", "Family of RK method", "TSRKSetType", (const char *const *)namelist, count, rk->tableau->name, &choice, &flg));
1202:     if (flg) PetscCall(TSRKSetType(ts, namelist[choice]));
1203:     PetscCall(PetscFree(namelist));
1204:   }
1205:   PetscOptionsHeadEnd();
1206:   PetscOptionsBegin(PetscObjectComm((PetscObject)ts), NULL, "Multirate methods options", "");
1207:   PetscCall(PetscOptionsInt("-ts_rk_dtratio", "time step ratio between slow and fast", "", rk->dtratio, &rk->dtratio, NULL));
1208:   PetscOptionsEnd();
1209:   PetscFunctionReturn(PETSC_SUCCESS);
1210: }

1212: static PetscErrorCode TSView_RK(TS ts, PetscViewer viewer)
1213: {
1214:   TS_RK    *rk = (TS_RK *)ts->data;
1215:   PetscBool iascii;

1217:   PetscFunctionBegin;
1218:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1219:   if (iascii) {
1220:     RKTableau        tab = rk->tableau;
1221:     TSRKType         rktype;
1222:     const PetscReal *c;
1223:     PetscInt         s;
1224:     char             buf[512];
1225:     PetscBool        FSAL;

1227:     PetscCall(TSRKGetType(ts, &rktype));
1228:     PetscCall(TSRKGetTableau(ts, &s, NULL, NULL, &c, NULL, NULL, NULL, &FSAL));
1229:     PetscCall(PetscViewerASCIIPrintf(viewer, "  RK type %s\n", rktype));
1230:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Order: %" PetscInt_FMT "\n", tab->order));
1231:     PetscCall(PetscViewerASCIIPrintf(viewer, "  FSAL property: %s\n", FSAL ? "yes" : "no"));
1232:     PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", s, c));
1233:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Abscissa c = %s\n", buf));
1234:   }
1235:   PetscFunctionReturn(PETSC_SUCCESS);
1236: }

1238: static PetscErrorCode TSLoad_RK(TS ts, PetscViewer viewer)
1239: {
1240:   TSAdapt adapt;

1242:   PetscFunctionBegin;
1243:   PetscCall(TSGetAdapt(ts, &adapt));
1244:   PetscCall(TSAdaptLoad(adapt, viewer));
1245:   PetscFunctionReturn(PETSC_SUCCESS);
1246: }

1248: /*@
1249:   TSRKGetOrder - Get the order of the `TSRK` scheme

1251:   Not Collective

1253:   Input Parameter:
1254: . ts - timestepping context

1256:   Output Parameter:
1257: . order - order of `TSRK` scheme

1259:   Level: intermediate

1261: .seealso: [](ch_ts), `TSRK`, `TSRKGetType()`
1262: @*/
1263: PetscErrorCode TSRKGetOrder(TS ts, PetscInt *order)
1264: {
1265:   PetscFunctionBegin;
1267:   PetscAssertPointer(order, 2);
1268:   PetscUseMethod(ts, "TSRKGetOrder_C", (TS, PetscInt *), (ts, order));
1269:   PetscFunctionReturn(PETSC_SUCCESS);
1270: }

1272: /*@C
1273:   TSRKSetType - Set the type of the `TSRK` scheme

1275:   Logically Collective

1277:   Input Parameters:
1278: + ts     - timestepping context
1279: - rktype - type of `TSRK` scheme

1281:   Options Database Key:
1282: . -ts_rk_type - <1fe,2a,3,3bs,4,5f,5dp,5bs>

1284:   Level: intermediate

1286: .seealso: [](ch_ts), `TSRKGetType()`, `TSRK`, `TSRKType`, `TSRK1FE`, `TSRK2A`, `TSRK2B`, `TSRK3`, `TSRK3BS`, `TSRK4`, `TSRK5F`, `TSRK5DP`, `TSRK5BS`, `TSRK6VR`, `TSRK7VR`, `TSRK8VR`
1287: @*/
1288: PetscErrorCode TSRKSetType(TS ts, TSRKType rktype)
1289: {
1290:   PetscFunctionBegin;
1292:   PetscAssertPointer(rktype, 2);
1293:   PetscTryMethod(ts, "TSRKSetType_C", (TS, TSRKType), (ts, rktype));
1294:   PetscFunctionReturn(PETSC_SUCCESS);
1295: }

1297: /*@C
1298:   TSRKGetType - Get the type of `TSRK` scheme

1300:   Not Collective

1302:   Input Parameter:
1303: . ts - timestepping context

1305:   Output Parameter:
1306: . rktype - type of `TSRK`-scheme

1308:   Level: intermediate

1310: .seealso: [](ch_ts), `TSRKSetType()`
1311: @*/
1312: PetscErrorCode TSRKGetType(TS ts, TSRKType *rktype)
1313: {
1314:   PetscFunctionBegin;
1316:   PetscUseMethod(ts, "TSRKGetType_C", (TS, TSRKType *), (ts, rktype));
1317:   PetscFunctionReturn(PETSC_SUCCESS);
1318: }

1320: static PetscErrorCode TSRKGetOrder_RK(TS ts, PetscInt *order)
1321: {
1322:   TS_RK *rk = (TS_RK *)ts->data;

1324:   PetscFunctionBegin;
1325:   *order = rk->tableau->order;
1326:   PetscFunctionReturn(PETSC_SUCCESS);
1327: }

1329: static PetscErrorCode TSRKGetType_RK(TS ts, TSRKType *rktype)
1330: {
1331:   TS_RK *rk = (TS_RK *)ts->data;

1333:   PetscFunctionBegin;
1334:   *rktype = rk->tableau->name;
1335:   PetscFunctionReturn(PETSC_SUCCESS);
1336: }

1338: static PetscErrorCode TSRKSetType_RK(TS ts, TSRKType rktype)
1339: {
1340:   TS_RK        *rk = (TS_RK *)ts->data;
1341:   PetscBool     match;
1342:   RKTableauLink link;

1344:   PetscFunctionBegin;
1345:   if (rk->tableau) {
1346:     PetscCall(PetscStrcmp(rk->tableau->name, rktype, &match));
1347:     if (match) PetscFunctionReturn(PETSC_SUCCESS);
1348:   }
1349:   for (link = RKTableauList; link; link = link->next) {
1350:     PetscCall(PetscStrcmp(link->tab.name, rktype, &match));
1351:     if (match) {
1352:       if (ts->setupcalled) PetscCall(TSRKTableauReset(ts));
1353:       rk->tableau = &link->tab;
1354:       if (ts->setupcalled) PetscCall(TSRKTableauSetUp(ts));
1355:       ts->default_adapt_type = rk->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1356:       PetscFunctionReturn(PETSC_SUCCESS);
1357:     }
1358:   }
1359:   SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", rktype);
1360: }

1362: static PetscErrorCode TSGetStages_RK(TS ts, PetscInt *ns, Vec **Y)
1363: {
1364:   TS_RK *rk = (TS_RK *)ts->data;

1366:   PetscFunctionBegin;
1367:   if (ns) *ns = rk->tableau->s;
1368:   if (Y) *Y = rk->Y;
1369:   PetscFunctionReturn(PETSC_SUCCESS);
1370: }

1372: static PetscErrorCode TSDestroy_RK(TS ts)
1373: {
1374:   PetscFunctionBegin;
1375:   PetscCall(TSReset_RK(ts));
1376:   if (ts->dm) {
1377:     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSRK, DMRestrictHook_TSRK, ts));
1378:     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSRK, DMSubDomainRestrictHook_TSRK, ts));
1379:   }
1380:   PetscCall(PetscFree(ts->data));
1381:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetOrder_C", NULL));
1382:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetType_C", NULL));
1383:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetType_C", NULL));
1384:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetTableau_C", NULL));
1385:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetMultirate_C", NULL));
1386:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetMultirate_C", NULL));
1387:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateSplit_C", NULL));
1388:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateSplit_C", NULL));
1389:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSSetUp_RK_MultirateNonsplit_C", NULL));
1390:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSReset_RK_MultirateNonsplit_C", NULL));
1391:   PetscFunctionReturn(PETSC_SUCCESS);
1392: }

1394: /*
1395:   This defines the nonlinear equation that is to be solved with SNES
1396:   We do not need to solve the equation; we just use SNES to approximate the Jacobian
1397: */
1398: static PetscErrorCode SNESTSFormFunction_RK(SNES snes, Vec x, Vec y, TS ts)
1399: {
1400:   TS_RK *rk = (TS_RK *)ts->data;
1401:   DM     dm, dmsave;

1403:   PetscFunctionBegin;
1404:   PetscCall(SNESGetDM(snes, &dm));
1405:   /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
1406:   dmsave = ts->dm;
1407:   ts->dm = dm;
1408:   PetscCall(TSComputeRHSFunction(ts, rk->stage_time, x, y));
1409:   ts->dm = dmsave;
1410:   PetscFunctionReturn(PETSC_SUCCESS);
1411: }

1413: static PetscErrorCode SNESTSFormJacobian_RK(SNES snes, Vec x, Mat A, Mat B, TS ts)
1414: {
1415:   TS_RK *rk = (TS_RK *)ts->data;
1416:   DM     dm, dmsave;

1418:   PetscFunctionBegin;
1419:   PetscCall(SNESGetDM(snes, &dm));
1420:   dmsave = ts->dm;
1421:   ts->dm = dm;
1422:   PetscCall(TSComputeRHSJacobian(ts, rk->stage_time, x, A, B));
1423:   ts->dm = dmsave;
1424:   PetscFunctionReturn(PETSC_SUCCESS);
1425: }

1427: /*@C
1428:   TSRKSetMultirate - Use the interpolation-based multirate `TSRK` method

1430:   Logically Collective

1432:   Input Parameters:
1433: + ts            - timestepping context
1434: - use_multirate - `PETSC_TRUE` enables the multirate `TSRK` method, sets the basic method to be RK2A and sets the ratio between slow stepsize and fast stepsize to be 2

1436:   Options Database Key:
1437: . -ts_rk_multirate - <true,false>

1439:   Level: intermediate

1441:   Note:
1442:   The multirate method requires interpolation. The default interpolation works for 1st- and 2nd- order RK, but not for high-order RKs except `TSRK5DP` which comes with the interpolation coefficients (binterp).

1444: .seealso: [](ch_ts), `TSRK`, `TSRKGetMultirate()`
1445: @*/
1446: PetscErrorCode TSRKSetMultirate(TS ts, PetscBool use_multirate)
1447: {
1448:   PetscFunctionBegin;
1449:   PetscTryMethod(ts, "TSRKSetMultirate_C", (TS, PetscBool), (ts, use_multirate));
1450:   PetscFunctionReturn(PETSC_SUCCESS);
1451: }

1453: /*@C
1454:   TSRKGetMultirate - Gets whether to use the interpolation-based multirate `TSRK` method

1456:   Not Collective

1458:   Input Parameter:
1459: . ts - timestepping context

1461:   Output Parameter:
1462: . use_multirate - `PETSC_TRUE` if the multirate RK method is enabled, `PETSC_FALSE` otherwise

1464:   Level: intermediate

1466: .seealso: [](ch_ts), `TSRK`, `TSRKSetMultirate()`
1467: @*/
1468: PetscErrorCode TSRKGetMultirate(TS ts, PetscBool *use_multirate)
1469: {
1470:   PetscFunctionBegin;
1471:   PetscUseMethod(ts, "TSRKGetMultirate_C", (TS, PetscBool *), (ts, use_multirate));
1472:   PetscFunctionReturn(PETSC_SUCCESS);
1473: }

1475: /*MC
1476:       TSRK - ODE and DAE solver using Runge-Kutta schemes

1478:   The user should provide the right hand side of the equation
1479:   using `TSSetRHSFunction()`.

1481:   Level: beginner

1483:   Notes:
1484:   The default is `TSRK3BS`, it can be changed with `TSRKSetType()` or -ts_rk_type

1486: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSRK`, `TSSetType()`, `TSRKSetType()`, `TSRKGetType()`, `TSRK2D`, `TSRK2E`, `TSRK3`,
1487:           `TSRK4`, `TSRK5`, `TSRKPRSSP2`, `TSRKBPR3`, `TSRKType`, `TSRKRegister()`, `TSRKSetMultirate()`, `TSRKGetMultirate()`, `TSType`
1488: M*/
1489: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
1490: {
1491:   TS_RK *rk;

1493:   PetscFunctionBegin;
1494:   PetscCall(TSRKInitializePackage());

1496:   ts->ops->reset          = TSReset_RK;
1497:   ts->ops->destroy        = TSDestroy_RK;
1498:   ts->ops->view           = TSView_RK;
1499:   ts->ops->load           = TSLoad_RK;
1500:   ts->ops->setup          = TSSetUp_RK;
1501:   ts->ops->interpolate    = TSInterpolate_RK;
1502:   ts->ops->step           = TSStep_RK;
1503:   ts->ops->evaluatestep   = TSEvaluateStep_RK;
1504:   ts->ops->rollback       = TSRollBack_RK;
1505:   ts->ops->setfromoptions = TSSetFromOptions_RK;
1506:   ts->ops->getstages      = TSGetStages_RK;

1508:   ts->ops->snesfunction    = SNESTSFormFunction_RK;
1509:   ts->ops->snesjacobian    = SNESTSFormJacobian_RK;
1510:   ts->ops->adjointintegral = TSAdjointCostIntegral_RK;
1511:   ts->ops->adjointsetup    = TSAdjointSetUp_RK;
1512:   ts->ops->adjointstep     = TSAdjointStep_RK;
1513:   ts->ops->adjointreset    = TSAdjointReset_RK;

1515:   ts->ops->forwardintegral  = TSForwardCostIntegral_RK;
1516:   ts->ops->forwardsetup     = TSForwardSetUp_RK;
1517:   ts->ops->forwardreset     = TSForwardReset_RK;
1518:   ts->ops->forwardstep      = TSForwardStep_RK;
1519:   ts->ops->forwardgetstages = TSForwardGetStages_RK;

1521:   PetscCall(PetscNew(&rk));
1522:   ts->data = (void *)rk;

1524:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetOrder_C", TSRKGetOrder_RK));
1525:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetType_C", TSRKGetType_RK));
1526:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetType_C", TSRKSetType_RK));
1527:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetTableau_C", TSRKGetTableau_RK));
1528:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKSetMultirate_C", TSRKSetMultirate_RK));
1529:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSRKGetMultirate_C", TSRKGetMultirate_RK));

1531:   PetscCall(TSRKSetType(ts, TSRKDefault));
1532:   rk->dtratio = 1;
1533:   PetscFunctionReturn(PETSC_SUCCESS);
1534: }