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:
 28: .     -ts_rk_type 1fe - use type 1fe

 30:      Level: advanced

 32: .seealso: 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:
 40: .     -ts_rk_type 2a - use type 2a

 42:      Level: advanced

 44: .seealso: 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:
 52: .     -ts_rk_type 2b - use type 2b

 54:      Level: advanced

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

 61:      This method has three stages.

 63:      Options database:
 64: .     -ts_rk_type 3 - use type 3

 66:      Level: advanced

 68: .seealso: 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:
 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: 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:
 91: .     -ts_rk_type 4 - use type 4

 93:      Level: advanced

 95: .seealso: 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:
103: .     -ts_rk_type 5f - use type 5f

105:      Level: advanced

107: .seealso: 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:
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: 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:
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: 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:
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: 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:
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: TSRK, TSRKType, TSRKSetType()
168: M*/
169: /*MC
170:      TSRK8VR - Eigth order robust Verner RK scheme with seventh order embedded method.

172:      This method has thirteen stages.

174:      Options database:
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: 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:  TSRKRegisterDestroy()
193: @*/
194: PetscErrorCode TSRKRegisterAll(void)
195: {
196:   if (TSRKRegisterAllCalled) return 0;
197:   TSRKRegisterAllCalled = PETSC_TRUE;

199: #define RC PetscRealConstant
200:   {
201:     const PetscReal
202:       A[1][1] = {{0}},
203:       b[1]    = {RC(1.0)};
204:     TSRKRegister(TSRK1FE,1,1,&A[0][0],b,NULL,NULL,0,NULL);
205:   }
206:   {
207:     const PetscReal
208:       A[2][2]   = {{0,0},
209:                    {RC(1.0),0}},
210:       b[2]      =  {RC(0.5),RC(0.5)},
211:       bembed[2] =  {RC(1.0),0};
212:     TSRKRegister(TSRK2A,2,2,&A[0][0],b,NULL,bembed,0,NULL);
213:   }
214:   {
215:     const PetscReal
216:       A[2][2]   = {{0,0},
217:                    {RC(0.5),0}},
218:       b[2]      =  {0,RC(1.0)};
219:     TSRKRegister(TSRK2B,2,2,&A[0][0],b,NULL,NULL,0,NULL);
220:   }
221:   {
222:     const PetscReal
223:       A[3][3] = {{0,0,0},
224:                  {RC(2.0)/RC(3.0),0,0},
225:                  {RC(-1.0)/RC(3.0),RC(1.0),0}},
226:       b[3]    =  {RC(0.25),RC(0.5),RC(0.25)};
227:     TSRKRegister(TSRK3,3,3,&A[0][0],b,NULL,NULL,0,NULL);
228:   }
229:   {
230:     const PetscReal
231:       A[4][4]   = {{0,0,0,0},
232:                    {RC(1.0)/RC(2.0),0,0,0},
233:                    {0,RC(3.0)/RC(4.0),0,0},
234:                    {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0}},
235:       b[4]      =  {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0},
236:       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)};
237:     TSRKRegister(TSRK3BS,3,4,&A[0][0],b,NULL,bembed,0,NULL);
238:   }
239:   {
240:     const PetscReal
241:       A[4][4] = {{0,0,0,0},
242:                  {RC(0.5),0,0,0},
243:                  {0,RC(0.5),0,0},
244:                  {0,0,RC(1.0),0}},
245:       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)};
246:     TSRKRegister(TSRK4,4,4,&A[0][0],b,NULL,NULL,0,NULL);
247:   }
248:   {
249:     const PetscReal
250:       A[6][6]   = {{0,0,0,0,0,0},
251:                    {RC(0.25),0,0,0,0,0},
252:                    {RC(3.0)/RC(32.0),RC(9.0)/RC(32.0),0,0,0,0},
253:                    {RC(1932.0)/RC(2197.0),RC(-7200.0)/RC(2197.0),RC(7296.0)/RC(2197.0),0,0,0},
254:                    {RC(439.0)/RC(216.0),RC(-8.0),RC(3680.0)/RC(513.0),RC(-845.0)/RC(4104.0),0,0},
255:                    {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}},
256:       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)},
257:       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};
258:     TSRKRegister(TSRK5F,5,6,&A[0][0],b,NULL,bembed,0,NULL);
259:   }
260:   {
261:     const PetscReal
262:       A[7][7]       = {{0,0,0,0,0,0,0},
263:                        {RC(1.0)/RC(5.0),0,0,0,0,0,0},
264:                        {RC(3.0)/RC(40.0),RC(9.0)/RC(40.0),0,0,0,0,0},
265:                        {RC(44.0)/RC(45.0),RC(-56.0)/RC(15.0),RC(32.0)/RC(9.0),0,0,0,0},
266:                        {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},
267:                        {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},
268:                        {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}},
269:       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},
270:       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)},
271:       binterp[7][5] = {{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)},
272:                        {0,0,0,0,0},
273:                        {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)},
274:                        {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)},
275:                        {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)},
276:                        {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)},
277:                        {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)}};
278:       TSRKRegister(TSRK5DP,5,7,&A[0][0],b,NULL,bembed,5,binterp[0]);
279:   }
280:   {
281:     const PetscReal
282:       A[8][8]   = {{0,0,0,0,0,0,0,0},
283:                    {RC(1.0)/RC(6.0),0,0,0,0,0,0,0},
284:                    {RC(2.0)/RC(27.0),RC(4.0)/RC(27.0),0,0,0,0,0,0},
285:                    {RC(183.0)/RC(1372.0),RC(-162.0)/RC(343.0),RC(1053.0)/RC(1372.0),0,0,0,0,0},
286:                    {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},
287:                    {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},
288:                    {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},
289:                    {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}},
290:       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},
291:       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)};
292:     TSRKRegister(TSRK5BS,5,8,&A[0][0],b,NULL,bembed,0,NULL);
293:   }
294:   {
295:     const PetscReal
296:       A[9][9]   = {{0,0,0,0,0,0,0,0,0},
297:                    {RC(1.8000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0},
298:                    {RC(8.9506172839506172839506172839506172839506e-02),RC(7.7160493827160493827160493827160493827160e-02),0,0,0,0,0,0,0},
299:                    {RC(6.2500000000000000000000000000000000000000e-02),0,RC(1.8750000000000000000000000000000000000000e-01),0,0,0,0,0,0},
300:                    {RC(3.1651600000000000000000000000000000000000e-01),0,RC(-1.0449480000000000000000000000000000000000e+00),RC(1.2584320000000000000000000000000000000000e+00),0,0,0,0,0},
301:                    {RC(2.7232612736485626257225065566674305502508e-01),0,RC(-8.2513360323886639676113360323886639676113e-01),RC(1.0480917678812415654520917678812415654521e+00),RC(1.0471570799276856873679117969088177628396e-01),0,0,0,0},
302:                    {RC(-1.6699418599716514314329607278961797333198e-01),0,RC(6.3170850202429149797570850202429149797571e-01),RC(1.7461044552773876082146758838488161796432e-01),RC(-1.0665356459086066122525194734018680677781e+00),RC(1.2272108843537414965986394557823129251701e+00),0,0,0},
303:                    {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},
304:                    {RC(7.6388888888888888888888888888888888888889e-02),0,0,RC(3.6940836940836940836940836940836940836941e-01),0,RC(2.4801587301587301587301587301587301587302e-01),RC(2.3674242424242424242424242424242424242424e-01),RC(6.9444444444444444444444444444444444444444e-02),0}},
305:       b[9]      =  {RC(7.6388888888888888888888888888888888888889e-02),0,0,RC(3.6940836940836940836940836940836940836941e-01),0,RC(2.4801587301587301587301587301587301587302e-01),RC(2.3674242424242424242424242424242424242424e-01),RC(6.9444444444444444444444444444444444444444e-02),0},
306:       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)};
307:     TSRKRegister(TSRK6VR,6,9,&A[0][0],b,NULL,bembed,0,NULL);
308:   }
309:   {
310:     const PetscReal
311:       A[10][10]  = {{0,0,0,0,0,0,0,0,0,0},
312:                     {RC(5.0000000000000000000000000000000000000000e-03),0,0,0,0,0,0,0,0,0},
313:                     {RC(-1.0767901234567901234567901234567901234568e+00),RC(1.1856790123456790123456790123456790123457e+00),0,0,0,0,0,0,0,0},
314:                     {RC(4.0833333333333333333333333333333333333333e-02),0,RC(1.2250000000000000000000000000000000000000e-01),0,0,0,0,0,0,0},
315:                     {RC(6.3607142857142857142857142857142857142857e-01),0,RC(-2.4444642857142857142857142857142857142857e+00),RC(2.2633928571428571428571428571428571428571e+00),0,0,0,0,0,0},
316:                     {RC(-2.5351211079349245229256383554660215487207e+00),0,RC(1.0299374654449267920438514460756024913612e+01),RC(-7.9513032885990579949493217458266876536482e+00),RC(7.9301148923100592201226014271115261823800e-01),0,0,0,0,0},
317:                     {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},
318:                     {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},
319:                     {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},
320:                     {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}},
321:       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},
322:       bembed[10] =  {RC(4.7485247699299631037531273805727961552268e-02),0,0,RC(2.5599412588690633297154918245905393870497e-01),RC(2.7058478081067688722530891099268135732387e-01),RC(1.2505618684425992913638822323746917920448e-01),RC(2.5204468723743860507184043820197442562182e-01),0,0,RC(4.8834971521418614557381971303093137592592e-02)};
323:     TSRKRegister(TSRK7VR,7,10,&A[0][0],b,NULL,bembed,0,NULL);
324:   }
325:   {
326:     const PetscReal
327:       A[13][13]  = {{0,0,0,0,0,0,0,0,0,0,0,0,0},
328:                     {RC(2.5000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0,0,0,0,0},
329:                     {RC(8.7400846504915232052686327594877411977046e-02),RC(2.5487604938654321753087950620345685135815e-02),0,0,0,0,0,0,0,0,0,0,0},
330:                     {RC(4.2333169291338582677165354330708661417323e-02),0,RC(1.2699950787401574803149606299212598425197e-01),0,0,0,0,0,0,0,0,0,0},
331:                     {RC(4.2609505888742261494881445237572274090942e-01),0,RC(-1.5987952846591523265427733230657181117089e+00),RC(1.5967002257717297115939588706899953707994e+00),0,0,0,0,0,0,0,0,0},
332:                     {RC(5.0719337296713929515090618138513639239329e-02),0,0,RC(2.5433377264600407582754714408877778031369e-01),RC(2.0394689005728199465736223777270858044698e-01),0,0,0,0,0,0,0,0},
333:                     {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},
334:                     {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},
335:                     {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},
336:                     {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},
337:                     {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},
338:                     {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},
339:                     {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}},
340:       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},
341:       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)};
342:     TSRKRegister(TSRK8VR,8,13,&A[0][0],b,NULL,bembed,0,NULL);
343:   }
344: #undef RC
345:   return 0;
346: }

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

351:    Not Collective

353:    Level: advanced

355: .seealso: TSRKRegister(), TSRKRegisterAll()
356: @*/
357: PetscErrorCode TSRKRegisterDestroy(void)
358: {
359:   RKTableauLink  link;

361:   while ((link = RKTableauList)) {
362:     RKTableau t = &link->tab;
363:     RKTableauList = link->next;
364:     PetscFree3(t->A,t->b,t->c);
365:     PetscFree(t->bembed);
366:     PetscFree(t->binterp);
367:     PetscFree(t->name);
368:     PetscFree(link);
369:   }
370:   TSRKRegisterAllCalled = PETSC_FALSE;
371:   return 0;
372: }

374: /*@C
375:   TSRKInitializePackage - This function initializes everything in the TSRK package. It is called
376:   from TSInitializePackage().

378:   Level: developer

380: .seealso: PetscInitialize()
381: @*/
382: PetscErrorCode TSRKInitializePackage(void)
383: {
384:   if (TSRKPackageInitialized) return 0;
385:   TSRKPackageInitialized = PETSC_TRUE;
386:   TSRKRegisterAll();
387:   PetscRegisterFinalize(TSRKFinalizePackage);
388:   return 0;
389: }

391: /*@C
392:   TSRKFinalizePackage - This function destroys everything in the TSRK package. It is
393:   called from PetscFinalize().

395:   Level: developer

397: .seealso: PetscFinalize()
398: @*/
399: PetscErrorCode TSRKFinalizePackage(void)
400: {
401:   TSRKPackageInitialized = PETSC_FALSE;
402:   TSRKRegisterDestroy();
403:   return 0;
404: }

406: /*@C
407:    TSRKRegister - register an RK scheme by providing the entries in the Butcher tableau and optionally embedded approximations and interpolation

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

411:    Input Parameters:
412: +  name - identifier for method
413: .  order - approximation order of method
414: .  s - number of stages, this is the dimension of the matrices below
415: .  A - stage coefficients (dimension s*s, row-major)
416: .  b - step completion table (dimension s; NULL to use last row of A)
417: .  c - abscissa (dimension s; NULL to use row sums of A)
418: .  bembed - completion table for embedded method (dimension s; NULL if not available)
419: .  p - Order of the interpolation scheme, equal to the number of columns of binterp
420: -  binterp - Coefficients of the interpolation formula (dimension s*p; NULL to reuse b with p=1)

422:    Notes:
423:    Several RK methods are provided, this function is only needed to create new methods.

425:    Level: advanced

427: .seealso: TSRK
428: @*/
429: PetscErrorCode TSRKRegister(TSRKType name,PetscInt order,PetscInt s,
430:                             const PetscReal A[],const PetscReal b[],const PetscReal c[],
431:                             const PetscReal bembed[],PetscInt p,const PetscReal binterp[])
432: {
433:   RKTableauLink   link;
434:   RKTableau       t;
435:   PetscInt        i,j;


444:   TSRKInitializePackage();
445:   PetscNew(&link);
446:   t = &link->tab;

448:   PetscStrallocpy(name,&t->name);
449:   t->order = order;
450:   t->s = s;
451:   PetscMalloc3(s*s,&t->A,s,&t->b,s,&t->c);
452:   PetscArraycpy(t->A,A,s*s);
453:   if (b)  PetscArraycpy(t->b,b,s);
454:   else for (i=0; i<s; i++) t->b[i] = A[(s-1)*s+i];
455:   if (c)  PetscArraycpy(t->c,c,s);
456:   else for (i=0; i<s; i++) for (j=0,t->c[i]=0; j<s; j++) t->c[i] += A[i*s+j];
457:   t->FSAL = PETSC_TRUE;
458:   for (i=0; i<s; i++) if (t->A[(s-1)*s+i] != t->b[i]) t->FSAL = PETSC_FALSE;

460:   if (bembed) {
461:     PetscMalloc1(s,&t->bembed);
462:     PetscArraycpy(t->bembed,bembed,s);
463:   }

465:   if (!binterp) { p = 1; binterp = t->b; }
466:   t->p = p;
467:   PetscMalloc1(s*p,&t->binterp);
468:   PetscArraycpy(t->binterp,binterp,s*p);

470:   link->next = RKTableauList;
471:   RKTableauList = link;
472:   return 0;
473: }

475: PetscErrorCode TSRKGetTableau_RK(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed,
476:                                         PetscInt *p, const PetscReal **binterp, PetscBool *FSAL)
477: {
478:   TS_RK     *rk   = (TS_RK*)ts->data;
479:   RKTableau tab  = rk->tableau;

481:   if (s) *s = tab->s;
482:   if (A) *A = tab->A;
483:   if (b) *b = tab->b;
484:   if (c) *c = tab->c;
485:   if (bembed) *bembed = tab->bembed;
486:   if (p) *p = tab->p;
487:   if (binterp) *binterp = tab->binterp;
488:   if (FSAL) *FSAL = tab->FSAL;
489:   return 0;
490: }

492: /*@C
493:    TSRKGetTableau - Get info on the RK tableau

495:    Not Collective

497:    Input Parameter:
498: .  ts - timestepping context

500:    Output Parameters:
501: +  s - number of stages, this is the dimension of the matrices below
502: .  A - stage coefficients (dimension s*s, row-major)
503: .  b - step completion table (dimension s)
504: .  c - abscissa (dimension s)
505: .  bembed - completion table for embedded method (dimension s; NULL if not available)
506: .  p - Order of the interpolation scheme, equal to the number of columns of binterp
507: .  binterp - Coefficients of the interpolation formula (dimension s*p)
508: -  FSAL - wheather or not the scheme has the First Same As Last property

510:    Level: developer

512: .seealso: TSRK
513: @*/
514: PetscErrorCode TSRKGetTableau(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed,
515:                                      PetscInt *p, const PetscReal **binterp, PetscBool *FSAL)
516: {

520:   PetscUseMethod(ts,"TSRKGetTableau_C",(TS,PetscInt*,const PetscReal**,const PetscReal**,const PetscReal**,const PetscReal**,
521:                                                   PetscInt*,const PetscReal**,PetscBool*),(ts,s,A,b,c,bembed,p,binterp,FSAL));
522:   return 0;
523: }

525: /*
526:  This is for single-step RK method
527:  The step completion formula is

529:  x1 = x0 + h b^T YdotRHS

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

535:  x1e = x0 + h be^T YdotRHS
536:      = x1 - h b^T YdotRHS + h be^T YdotRHS
537:      = x1 + h (be - b)^T YdotRHS

539:  so we can evaluate the method with different order even after the step has been optimistically completed.
540: */
541: static PetscErrorCode TSEvaluateStep_RK(TS ts,PetscInt order,Vec X,PetscBool *done)
542: {
543:   TS_RK          *rk   = (TS_RK*)ts->data;
544:   RKTableau      tab  = rk->tableau;
545:   PetscScalar    *w    = rk->work;
546:   PetscReal      h;
547:   PetscInt       s    = tab->s,j;

549:   switch (rk->status) {
550:   case TS_STEP_INCOMPLETE:
551:   case TS_STEP_PENDING:
552:     h = ts->time_step; break;
553:   case TS_STEP_COMPLETE:
554:     h = ts->ptime - ts->ptime_prev; break;
555:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
556:   }
557:   if (order == tab->order) {
558:     if (rk->status == TS_STEP_INCOMPLETE) {
559:       VecCopy(ts->vec_sol,X);
560:       for (j=0; j<s; j++) w[j] = h*tab->b[j]/rk->dtratio;
561:       VecMAXPY(X,s,w,rk->YdotRHS);
562:     } else VecCopy(ts->vec_sol,X);
563:     return 0;
564:   } else if (order == tab->order-1) {
565:     if (!tab->bembed) goto unavailable;
566:     if (rk->status == TS_STEP_INCOMPLETE) { /*Complete with the embedded method (be)*/
567:       VecCopy(ts->vec_sol,X);
568:       for (j=0; j<s; j++) w[j] = h*tab->bembed[j];
569:       VecMAXPY(X,s,w,rk->YdotRHS);
570:     } else {  /*Rollback and re-complete using (be-b) */
571:       VecCopy(ts->vec_sol,X);
572:       for (j=0; j<s; j++) w[j] = h*(tab->bembed[j] - tab->b[j]);
573:       VecMAXPY(X,s,w,rk->YdotRHS);
574:     }
575:     if (done) *done = PETSC_TRUE;
576:     return 0;
577:   }
578: unavailable:
579:   if (done) *done = PETSC_FALSE;
580:   else SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"RK '%s' of order %D cannot evaluate step at order %D. Consider using -ts_adapt_type none or a different method that has an embedded estimate.",tab->name,tab->order,order);
581:   return 0;
582: }

584: static PetscErrorCode TSForwardCostIntegral_RK(TS ts)
585: {
586:   TS_RK           *rk = (TS_RK*)ts->data;
587:   TS              quadts = ts->quadraturets;
588:   RKTableau       tab = rk->tableau;
589:   const PetscInt  s = tab->s;
590:   const PetscReal *b = tab->b,*c = tab->c;
591:   Vec             *Y = rk->Y;
592:   PetscInt        i;

594:   /* No need to backup quadts->vec_sol since it can be reverted in TSRollBack_RK */
595:   for (i=s-1; i>=0; i--) {
596:     /* Evolve quadrature TS solution to compute integrals */
597:     TSComputeRHSFunction(quadts,rk->ptime+rk->time_step*c[i],Y[i],ts->vec_costintegrand);
598:     VecAXPY(quadts->vec_sol,rk->time_step*b[i],ts->vec_costintegrand);
599:   }
600:   return 0;
601: }

603: static PetscErrorCode TSAdjointCostIntegral_RK(TS ts)
604: {
605:   TS_RK           *rk = (TS_RK*)ts->data;
606:   RKTableau       tab = rk->tableau;
607:   TS              quadts = ts->quadraturets;
608:   const PetscInt  s = tab->s;
609:   const PetscReal *b = tab->b,*c = tab->c;
610:   Vec             *Y = rk->Y;
611:   PetscInt        i;

613:   for (i=s-1; i>=0; i--) {
614:     /* Evolve quadrature TS solution to compute integrals */
615:     TSComputeRHSFunction(quadts,ts->ptime+ts->time_step*(1.0-c[i]),Y[i],ts->vec_costintegrand);
616:     VecAXPY(quadts->vec_sol,-ts->time_step*b[i],ts->vec_costintegrand);
617:   }
618:   return 0;
619: }

621: static PetscErrorCode TSRollBack_RK(TS ts)
622: {
623:   TS_RK           *rk = (TS_RK*)ts->data;
624:   TS              quadts = ts->quadraturets;
625:   RKTableau       tab = rk->tableau;
626:   const PetscInt  s  = tab->s;
627:   const PetscReal *b = tab->b,*c = tab->c;
628:   PetscScalar     *w = rk->work;
629:   Vec             *Y = rk->Y,*YdotRHS = rk->YdotRHS;
630:   PetscInt        j;
631:   PetscReal       h;

633:   switch (rk->status) {
634:   case TS_STEP_INCOMPLETE:
635:   case TS_STEP_PENDING:
636:     h = ts->time_step; break;
637:   case TS_STEP_COMPLETE:
638:     h = ts->ptime - ts->ptime_prev; break;
639:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
640:   }
641:   for (j=0; j<s; j++) w[j] = -h*b[j];
642:   VecMAXPY(ts->vec_sol,s,w,YdotRHS);
643:   if (quadts && ts->costintegralfwd) {
644:     for (j=0; j<s; j++) {
645:       /* Revert the quadrature TS solution */
646:       TSComputeRHSFunction(quadts,rk->ptime+h*c[j],Y[j],ts->vec_costintegrand);
647:       VecAXPY(quadts->vec_sol,-h*b[j],ts->vec_costintegrand);
648:     }
649:   }
650:   return 0;
651: }

653: static PetscErrorCode TSForwardStep_RK(TS ts)
654: {
655:   TS_RK           *rk = (TS_RK*)ts->data;
656:   RKTableau       tab = rk->tableau;
657:   Mat             J,*MatsFwdSensipTemp = rk->MatsFwdSensipTemp;
658:   const PetscInt  s = tab->s;
659:   const PetscReal *A = tab->A,*c = tab->c,*b = tab->b;
660:   Vec             *Y = rk->Y;
661:   PetscInt        i,j;
662:   PetscReal       stage_time,h = ts->time_step;
663:   PetscBool       zero;

665:   MatCopy(ts->mat_sensip,rk->MatFwdSensip0,SAME_NONZERO_PATTERN);
666:   TSGetRHSJacobian(ts,&J,NULL,NULL,NULL);

668:   for (i=0; i<s; i++) {
669:     stage_time = ts->ptime + h*c[i];
670:     zero = PETSC_FALSE;
671:     if (b[i] == 0 && i == s-1) zero = PETSC_TRUE;
672:     /* TLM Stage values */
673:     if (!i) {
674:       MatCopy(ts->mat_sensip,rk->MatsFwdStageSensip[i],SAME_NONZERO_PATTERN);
675:     } else if (!zero) {
676:       MatZeroEntries(rk->MatsFwdStageSensip[i]);
677:       for (j=0; j<i; j++) {
678:         MatAXPY(rk->MatsFwdStageSensip[i],h*A[i*s+j],MatsFwdSensipTemp[j],SAME_NONZERO_PATTERN);
679:       }
680:       MatAXPY(rk->MatsFwdStageSensip[i],1.,ts->mat_sensip,SAME_NONZERO_PATTERN);
681:     } else {
682:       MatZeroEntries(rk->MatsFwdStageSensip[i]);
683:     }

685:     TSComputeRHSJacobian(ts,stage_time,Y[i],J,J);
686:     MatMatMult(J,rk->MatsFwdStageSensip[i],MAT_REUSE_MATRIX,PETSC_DEFAULT,&MatsFwdSensipTemp[i]);
687:     if (ts->Jacprhs) {
688:       TSComputeRHSJacobianP(ts,stage_time,Y[i],ts->Jacprhs); /* get f_p */
689:       if (ts->vecs_sensi2p) { /* TLM used for 2nd-order adjoint */
690:         PetscScalar *xarr;
691:         MatDenseGetColumn(MatsFwdSensipTemp[i],0,&xarr);
692:         VecPlaceArray(rk->VecDeltaFwdSensipCol,xarr);
693:         MatMultAdd(ts->Jacprhs,ts->vec_dir,rk->VecDeltaFwdSensipCol,rk->VecDeltaFwdSensipCol);
694:         VecResetArray(rk->VecDeltaFwdSensipCol);
695:         MatDenseRestoreColumn(MatsFwdSensipTemp[i],&xarr);
696:       } else {
697:         MatAXPY(MatsFwdSensipTemp[i],1.,ts->Jacprhs,SUBSET_NONZERO_PATTERN);
698:       }
699:     }
700:   }

702:   for (i=0; i<s; i++) {
703:     MatAXPY(ts->mat_sensip,h*b[i],rk->MatsFwdSensipTemp[i],SAME_NONZERO_PATTERN);
704:   }
705:   rk->status = TS_STEP_COMPLETE;
706:   return 0;
707: }

709: static PetscErrorCode TSForwardGetStages_RK(TS ts,PetscInt *ns,Mat **stagesensip)
710: {
711:   TS_RK     *rk = (TS_RK*)ts->data;
712:   RKTableau tab  = rk->tableau;

714:   if (ns) *ns = tab->s;
715:   if (stagesensip) *stagesensip = rk->MatsFwdStageSensip;
716:   return 0;
717: }

719: static PetscErrorCode TSForwardSetUp_RK(TS ts)
720: {
721:   TS_RK          *rk = (TS_RK*)ts->data;
722:   RKTableau      tab  = rk->tableau;
723:   PetscInt       i;

725:   /* backup sensitivity results for roll-backs */
726:   MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatFwdSensip0);

728:   PetscMalloc1(tab->s,&rk->MatsFwdStageSensip);
729:   PetscMalloc1(tab->s,&rk->MatsFwdSensipTemp);
730:   for (i=0; i<tab->s; i++) {
731:     MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdStageSensip[i]);
732:     MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdSensipTemp[i]);
733:   }
734:   VecDuplicate(ts->vec_sol,&rk->VecDeltaFwdSensipCol);
735:   return 0;
736: }

738: static PetscErrorCode TSForwardReset_RK(TS ts)
739: {
740:   TS_RK          *rk = (TS_RK*)ts->data;
741:   RKTableau      tab  = rk->tableau;
742:   PetscInt       i;

744:   MatDestroy(&rk->MatFwdSensip0);
745:   if (rk->MatsFwdStageSensip) {
746:     for (i=0; i<tab->s; i++) {
747:       MatDestroy(&rk->MatsFwdStageSensip[i]);
748:     }
749:     PetscFree(rk->MatsFwdStageSensip);
750:   }
751:   if (rk->MatsFwdSensipTemp) {
752:     for (i=0; i<tab->s; i++) {
753:       MatDestroy(&rk->MatsFwdSensipTemp[i]);
754:     }
755:     PetscFree(rk->MatsFwdSensipTemp);
756:   }
757:   VecDestroy(&rk->VecDeltaFwdSensipCol);
758:   return 0;
759: }

761: static PetscErrorCode TSStep_RK(TS ts)
762: {
763:   TS_RK           *rk  = (TS_RK*)ts->data;
764:   RKTableau       tab  = rk->tableau;
765:   const PetscInt  s = tab->s;
766:   const PetscReal *A = tab->A,*c = tab->c;
767:   PetscScalar     *w = rk->work;
768:   Vec             *Y = rk->Y,*YdotRHS = rk->YdotRHS;
769:   PetscBool       FSAL = tab->FSAL;
770:   TSAdapt         adapt;
771:   PetscInt        i,j;
772:   PetscInt        rejections = 0;
773:   PetscBool       stageok,accept = PETSC_TRUE;
774:   PetscReal       next_time_step = ts->time_step;

776:   if (ts->steprollback || ts->steprestart) FSAL = PETSC_FALSE;
777:   if (FSAL) VecCopy(YdotRHS[s-1],YdotRHS[0]);

779:   rk->status = TS_STEP_INCOMPLETE;
780:   while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
781:     PetscReal t = ts->ptime;
782:     PetscReal h = ts->time_step;
783:     for (i=0; i<s; i++) {
784:       rk->stage_time = t + h*c[i];
785:       TSPreStage(ts,rk->stage_time);
786:       VecCopy(ts->vec_sol,Y[i]);
787:       for (j=0; j<i; j++) w[j] = h*A[i*s+j];
788:       VecMAXPY(Y[i],i,w,YdotRHS);
789:       TSPostStage(ts,rk->stage_time,i,Y);
790:       TSGetAdapt(ts,&adapt);
791:       TSAdaptCheckStage(adapt,ts,rk->stage_time,Y[i],&stageok);
792:       if (!stageok) goto reject_step;
793:       if (FSAL && !i) continue;
794:       TSComputeRHSFunction(ts,t+h*c[i],Y[i],YdotRHS[i]);
795:     }

797:     rk->status = TS_STEP_INCOMPLETE;
798:     TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);
799:     rk->status = TS_STEP_PENDING;
800:     TSGetAdapt(ts,&adapt);
801:     TSAdaptCandidatesClear(adapt);
802:     TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,(PetscReal)tab->s,PETSC_TRUE);
803:     TSAdaptChoose(adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
804:     rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
805:     if (!accept) { /* Roll back the current step */
806:       TSRollBack_RK(ts);
807:       ts->time_step = next_time_step;
808:       goto reject_step;
809:     }

811:     if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */
812:       rk->ptime     = ts->ptime;
813:       rk->time_step = ts->time_step;
814:     }

816:     ts->ptime += ts->time_step;
817:     ts->time_step = next_time_step;
818:     break;

820:     reject_step:
821:     ts->reject++; accept = PETSC_FALSE;
822:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
823:       ts->reason = TS_DIVERGED_STEP_REJECTED;
824:       PetscInfo(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
825:     }
826:   }
827:   return 0;
828: }

830: static PetscErrorCode TSAdjointSetUp_RK(TS ts)
831: {
832:   TS_RK          *rk  = (TS_RK*)ts->data;
833:   RKTableau      tab = rk->tableau;
834:   PetscInt       s   = tab->s;

836:   if (ts->adjointsetupcalled++) return 0;
837:   VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam);
838:   VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&rk->VecsSensiTemp);
839:   if (ts->vecs_sensip) {
840:     VecDuplicate(ts->vecs_sensip[0],&rk->VecDeltaMu);
841:   }
842:   if (ts->vecs_sensi2) {
843:     VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam2);
844:     VecDuplicateVecs(ts->vecs_sensi2[0],ts->numcost,&rk->VecsSensi2Temp);
845:   }
846:   if (ts->vecs_sensi2p) {
847:     VecDuplicate(ts->vecs_sensi2p[0],&rk->VecDeltaMu2);
848:   }
849:   return 0;
850: }

852: /*
853:   Assumptions:
854:     - TSStep_RK() always evaluates the step with b, not bembed.
855: */
856: static PetscErrorCode TSAdjointStep_RK(TS ts)
857: {
858:   TS_RK            *rk = (TS_RK*)ts->data;
859:   TS               quadts = ts->quadraturets;
860:   RKTableau        tab = rk->tableau;
861:   Mat              J,Jpre,Jquad;
862:   const PetscInt   s = tab->s;
863:   const PetscReal  *A = tab->A,*b = tab->b,*c = tab->c;
864:   PetscScalar      *w = rk->work,*xarr;
865:   Vec              *Y = rk->Y,*VecsDeltaLam = rk->VecsDeltaLam,VecDeltaMu = rk->VecDeltaMu,*VecsSensiTemp = rk->VecsSensiTemp;
866:   Vec              *VecsDeltaLam2 = rk->VecsDeltaLam2,VecDeltaMu2 = rk->VecDeltaMu2,*VecsSensi2Temp = rk->VecsSensi2Temp;
867:   Vec              VecDRDUTransCol = ts->vec_drdu_col,VecDRDPTransCol = ts->vec_drdp_col;
868:   PetscInt         i,j,nadj;
869:   PetscReal        t = ts->ptime;
870:   PetscReal        h = ts->time_step;

872:   rk->status = TS_STEP_INCOMPLETE;

874:   TSGetRHSJacobian(ts,&J,&Jpre,NULL,NULL);
875:   if (quadts) {
876:     TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);
877:   }
878:   for (i=s-1; i>=0; i--) {
879:     if (tab->FSAL && i == s-1) {
880:       /* VecsDeltaLam[nadj*s+s-1] are initialized with zeros and the values never change.*/
881:       continue;
882:     }
883:     rk->stage_time = t + h*(1.0-c[i]);
884:     TSComputeSNESJacobian(ts,Y[i],J,Jpre);
885:     if (quadts) {
886:       TSComputeRHSJacobian(quadts,rk->stage_time,Y[i],Jquad,Jquad); /* get r_u^T */
887:     }
888:     if (ts->vecs_sensip) {
889:       TSComputeRHSJacobianP(ts,rk->stage_time,Y[i],ts->Jacprhs); /* get f_p */
890:       if (quadts) {
891:         TSComputeRHSJacobianP(quadts,rk->stage_time,Y[i],quadts->Jacprhs); /* get f_p for the quadrature */
892:       }
893:     }

895:     if (b[i]) {
896:       for (j=i+1; j<s; j++) w[j-i-1] = A[j*s+i]/b[i]; /* coefficients for computing VecsSensiTemp */
897:     } else {
898:       for (j=i+1; j<s; j++) w[j-i-1] = A[j*s+i]; /* coefficients for computing VecsSensiTemp */
899:     }

901:     for (nadj=0; nadj<ts->numcost; nadj++) {
902:       /* Stage values of lambda */
903:       if (b[i]) {
904:         /* lambda_{n+1} + \sum_{j=i+1}^s a_{ji}/b[i]*lambda_{s,j} */
905:         VecCopy(ts->vecs_sensi[nadj],VecsSensiTemp[nadj]); /* VecDeltaLam is an vec array of size s by numcost */
906:         VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);
907:         MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]); /* VecsSensiTemp will be reused by 2nd-order adjoint */
908:         VecScale(VecsDeltaLam[nadj*s+i],-h*b[i]);
909:         if (quadts) {
910:           MatDenseGetColumn(Jquad,nadj,&xarr);
911:           VecPlaceArray(VecDRDUTransCol,xarr);
912:           VecAXPY(VecsDeltaLam[nadj*s+i],-h*b[i],VecDRDUTransCol);
913:           VecResetArray(VecDRDUTransCol);
914:           MatDenseRestoreColumn(Jquad,&xarr);
915:         }
916:       } else {
917:         /* \sum_{j=i+1}^s a_{ji}*lambda_{s,j} */
918:         VecSet(VecsSensiTemp[nadj],0);
919:         VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);
920:         MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]);
921:         VecScale(VecsDeltaLam[nadj*s+i],-h);
922:       }

924:       /* Stage values of mu */
925:       if (ts->vecs_sensip) {
926:         if (b[i]) {
927:           MatMultTranspose(ts->Jacprhs,VecsSensiTemp[nadj],VecDeltaMu);
928:           VecScale(VecDeltaMu,-h*b[i]);
929:           if (quadts) {
930:             MatDenseGetColumn(quadts->Jacprhs,nadj,&xarr);
931:             VecPlaceArray(VecDRDPTransCol,xarr);
932:             VecAXPY(VecDeltaMu,-h*b[i],VecDRDPTransCol);
933:             VecResetArray(VecDRDPTransCol);
934:             MatDenseRestoreColumn(quadts->Jacprhs,&xarr);
935:           }
936:         } else {
937:           VecScale(VecDeltaMu,-h);
938:         }
939:         VecAXPY(ts->vecs_sensip[nadj],1.,VecDeltaMu); /* update sensip for each stage */
940:       }
941:     }

943:     if (ts->vecs_sensi2 && ts->forward_solve) { /* 2nd-order adjoint, TLM mode has to be turned on */
944:       /* Get w1 at t_{n+1} from TLM matrix */
945:       MatDenseGetColumn(rk->MatsFwdStageSensip[i],0,&xarr);
946:       VecPlaceArray(ts->vec_sensip_col,xarr);
947:       /* lambda_s^T F_UU w_1 */
948:       TSComputeRHSHessianProductFunctionUU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_guu);
949:       if (quadts)  {
950:         /* R_UU w_1 */
951:         TSComputeRHSHessianProductFunctionUU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_guu);
952:       }
953:       if (ts->vecs_sensip) {
954:         /* lambda_s^T F_UP w_2 */
955:         TSComputeRHSHessianProductFunctionUP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gup);
956:         if (quadts)  {
957:           /* R_UP w_2 */
958:           TSComputeRHSHessianProductFunctionUP(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gup);
959:         }
960:       }
961:       if (ts->vecs_sensi2p) {
962:         /* lambda_s^T F_PU w_1 */
963:         TSComputeRHSHessianProductFunctionPU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_gpu);
964:         /* lambda_s^T F_PP w_2 */
965:         TSComputeRHSHessianProductFunctionPP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gpp);
966:         if (b[i] && quadts) {
967:           /* R_PU w_1 */
968:           TSComputeRHSHessianProductFunctionPU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gpu);
969:           /* R_PP w_2 */
970:           TSComputeRHSHessianProductFunctionPP(quadts,rk->stage_time,Y[i],NULL,ts->vec_dir,ts->vecs_gpp);
971:         }
972:       }
973:       VecResetArray(ts->vec_sensip_col);
974:       MatDenseRestoreColumn(rk->MatsFwdStageSensip[i],&xarr);

976:       for (nadj=0; nadj<ts->numcost; nadj++) {
977:         /* Stage values of lambda */
978:         if (b[i]) {
979:           /* J_i^T*(Lambda_{n+1}+\sum_{j=i+1}^s a_{ji}/b_i*Lambda_{s,j} */
980:           VecCopy(ts->vecs_sensi2[nadj],VecsSensi2Temp[nadj]);
981:           VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);
982:           MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);
983:           VecScale(VecsDeltaLam2[nadj*s+i],-h*b[i]);
984:           VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_guu[nadj]);
985:           if (ts->vecs_sensip) {
986:             VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_gup[nadj]);
987:           }
988:         } else {
989:           /* \sum_{j=i+1}^s a_{ji}*Lambda_{s,j} */
990:           VecSet(VecsDeltaLam2[nadj*s+i],0);
991:           VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);
992:           MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);
993:           VecScale(VecsDeltaLam2[nadj*s+i],-h);
994:           VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_guu[nadj]);
995:           if (ts->vecs_sensip) {
996:             VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_gup[nadj]);
997:           }
998:         }
999:         if (ts->vecs_sensi2p) { /* 2nd-order adjoint for parameters */
1000:           MatMultTranspose(ts->Jacprhs,VecsSensi2Temp[nadj],VecDeltaMu2);
1001:           if (b[i]) {
1002:             VecScale(VecDeltaMu2,-h*b[i]);
1003:             VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpu[nadj]);
1004:             VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpp[nadj]);
1005:           } else {
1006:             VecScale(VecDeltaMu2,-h);
1007:             VecAXPY(VecDeltaMu2,-h,ts->vecs_gpu[nadj]);
1008:             VecAXPY(VecDeltaMu2,-h,ts->vecs_gpp[nadj]);
1009:           }
1010:           VecAXPY(ts->vecs_sensi2p[nadj],1,VecDeltaMu2); /* update sensi2p for each stage */
1011:         }
1012:       }
1013:     }
1014:   }

1016:   for (j=0; j<s; j++) w[j] = 1.0;
1017:   for (nadj=0; nadj<ts->numcost; nadj++) { /* no need to do this for mu's */
1018:     VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecsDeltaLam[nadj*s]);
1019:     if (ts->vecs_sensi2) {
1020:       VecMAXPY(ts->vecs_sensi2[nadj],s,w,&VecsDeltaLam2[nadj*s]);
1021:     }
1022:   }
1023:   rk->status = TS_STEP_COMPLETE;
1024:   return 0;
1025: }

1027: static PetscErrorCode TSAdjointReset_RK(TS ts)
1028: {
1029:   TS_RK          *rk = (TS_RK*)ts->data;
1030:   RKTableau      tab = rk->tableau;

1032:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam);
1033:   VecDestroyVecs(ts->numcost,&rk->VecsSensiTemp);
1034:   VecDestroy(&rk->VecDeltaMu);
1035:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam2);
1036:   VecDestroy(&rk->VecDeltaMu2);
1037:   VecDestroyVecs(ts->numcost,&rk->VecsSensi2Temp);
1038:   return 0;
1039: }

1041: static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X)
1042: {
1043:   TS_RK            *rk = (TS_RK*)ts->data;
1044:   PetscInt         s  = rk->tableau->s,p = rk->tableau->p,i,j;
1045:   PetscReal        h;
1046:   PetscReal        tt,t;
1047:   PetscScalar      *b;
1048:   const PetscReal  *B = rk->tableau->binterp;


1052:   switch (rk->status) {
1053:     case TS_STEP_INCOMPLETE:
1054:     case TS_STEP_PENDING:
1055:       h = ts->time_step;
1056:       t = (itime - ts->ptime)/h;
1057:       break;
1058:     case TS_STEP_COMPLETE:
1059:       h = ts->ptime - ts->ptime_prev;
1060:       t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
1061:       break;
1062:     default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
1063:   }
1064:   PetscMalloc1(s,&b);
1065:   for (i=0; i<s; i++) b[i] = 0;
1066:   for (j=0,tt=t; j<p; j++,tt*=t) {
1067:     for (i=0; i<s; i++) {
1068:       b[i]  += h * B[i*p+j] * tt;
1069:     }
1070:   }
1071:   VecCopy(rk->Y[0],X);
1072:   VecMAXPY(X,s,b,rk->YdotRHS);
1073:   PetscFree(b);
1074:   return 0;
1075: }

1077: /*------------------------------------------------------------*/

1079: static PetscErrorCode TSRKTableauReset(TS ts)
1080: {
1081:   TS_RK          *rk = (TS_RK*)ts->data;
1082:   RKTableau      tab = rk->tableau;

1084:   if (!tab) return 0;
1085:   PetscFree(rk->work);
1086:   VecDestroyVecs(tab->s,&rk->Y);
1087:   VecDestroyVecs(tab->s,&rk->YdotRHS);
1088:   return 0;
1089: }

1091: static PetscErrorCode TSReset_RK(TS ts)
1092: {
1093:   TSRKTableauReset(ts);
1094:   if (ts->use_splitrhsfunction) {
1095:     PetscTryMethod(ts,"TSReset_RK_MultirateSplit_C",(TS),(ts));
1096:   } else {
1097:     PetscTryMethod(ts,"TSReset_RK_MultirateNonsplit_C",(TS),(ts));
1098:   }
1099:   return 0;
1100: }

1102: static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx)
1103: {
1104:   return 0;
1105: }

1107: static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
1108: {
1109:   return 0;
1110: }

1112: static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx)
1113: {
1114:   return 0;
1115: }

1117: static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
1118: {
1119:   return 0;
1120: }

1122: static PetscErrorCode TSRKTableauSetUp(TS ts)
1123: {
1124:   TS_RK          *rk  = (TS_RK*)ts->data;
1125:   RKTableau      tab = rk->tableau;

1127:   PetscMalloc1(tab->s,&rk->work);
1128:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->Y);
1129:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->YdotRHS);
1130:   return 0;
1131: }

1133: static PetscErrorCode TSSetUp_RK(TS ts)
1134: {
1135:   TS             quadts = ts->quadraturets;
1136:   DM             dm;

1138:   TSCheckImplicitTerm(ts);
1139:   TSRKTableauSetUp(ts);
1140:   if (quadts && ts->costintegralfwd) {
1141:     Mat Jquad;
1142:     TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);
1143:   }
1144:   TSGetDM(ts,&dm);
1145:   DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
1146:   DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
1147:   if (ts->use_splitrhsfunction) {
1148:     PetscTryMethod(ts,"TSSetUp_RK_MultirateSplit_C",(TS),(ts));
1149:   } else {
1150:     PetscTryMethod(ts,"TSSetUp_RK_MultirateNonsplit_C",(TS),(ts));
1151:   }
1152:   return 0;
1153: }

1155: static PetscErrorCode TSSetFromOptions_RK(PetscOptionItems *PetscOptionsObject,TS ts)
1156: {
1157:   TS_RK          *rk = (TS_RK*)ts->data;

1160:   PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");
1161:   {
1162:     RKTableauLink link;
1163:     PetscInt      count,choice;
1164:     PetscBool     flg,use_multirate = PETSC_FALSE;
1165:     const char    **namelist;

1167:     for (link=RKTableauList,count=0; link; link=link->next,count++) ;
1168:     PetscMalloc1(count,(char***)&namelist);
1169:     for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
1170:     PetscOptionsBool("-ts_rk_multirate","Use interpolation-based multirate RK method","TSRKSetMultirate",rk->use_multirate,&use_multirate,&flg);
1171:     if (flg) {
1172:       TSRKSetMultirate(ts,use_multirate);
1173:     }
1174:     PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rk->tableau->name,&choice,&flg);
1175:     if (flg) TSRKSetType(ts,namelist[choice]);
1176:     PetscFree(namelist);
1177:   }
1178:   PetscOptionsTail();
1179:   PetscOptionsBegin(PetscObjectComm((PetscObject)ts),NULL,"Multirate methods options","");
1180:   PetscOptionsInt("-ts_rk_dtratio","time step ratio between slow and fast","",rk->dtratio,&rk->dtratio,NULL);
1181:   PetscOptionsEnd();
1182:   return 0;
1183: }

1185: static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer)
1186: {
1187:   TS_RK          *rk = (TS_RK*)ts->data;
1188:   PetscBool      iascii;

1190:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1191:   if (iascii) {
1192:     RKTableau       tab  = rk->tableau;
1193:     TSRKType        rktype;
1194:     const PetscReal *c;
1195:     PetscInt        s;
1196:     char            buf[512];
1197:     PetscBool       FSAL;

1199:     TSRKGetType(ts,&rktype);
1200:     TSRKGetTableau(ts,&s,NULL,NULL,&c,NULL,NULL,NULL,&FSAL);
1201:     PetscViewerASCIIPrintf(viewer,"  RK type %s\n",rktype);
1202:     PetscViewerASCIIPrintf(viewer,"  Order: %D\n",tab->order);
1203:     PetscViewerASCIIPrintf(viewer,"  FSAL property: %s\n",FSAL ? "yes" : "no");
1204:     PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",s,c);
1205:     PetscViewerASCIIPrintf(viewer,"  Abscissa c = %s\n",buf);
1206:   }
1207:   return 0;
1208: }

1210: static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer)
1211: {
1212:   TSAdapt        adapt;

1214:   TSGetAdapt(ts,&adapt);
1215:   TSAdaptLoad(adapt,viewer);
1216:   return 0;
1217: }

1219: /*@
1220:   TSRKGetOrder - Get the order of RK scheme

1222:   Not collective

1224:   Input Parameter:
1225: .  ts - timestepping context

1227:   Output Parameter:
1228: .  order - order of RK-scheme

1230:   Level: intermediate

1232: .seealso: TSRKGetType()
1233: @*/
1234: PetscErrorCode TSRKGetOrder(TS ts,PetscInt *order)
1235: {
1238:   PetscUseMethod(ts,"TSRKGetOrder_C",(TS,PetscInt*),(ts,order));
1239:   return 0;
1240: }

1242: /*@C
1243:   TSRKSetType - Set the type of RK scheme

1245:   Logically collective

1247:   Input Parameters:
1248: +  ts - timestepping context
1249: -  rktype - type of RK-scheme

1251:   Options Database:
1252: .   -ts_rk_type - <1fe,2a,3,3bs,4,5f,5dp,5bs>

1254:   Level: intermediate

1256: .seealso: TSRKGetType(), TSRK, TSRKType, TSRK1FE, TSRK2A, TSRK2B, TSRK3, TSRK3BS, TSRK4, TSRK5F, TSRK5DP, TSRK5BS, TSRK6VR, TSRK7VR, TSRK8VR
1257: @*/
1258: PetscErrorCode TSRKSetType(TS ts,TSRKType rktype)
1259: {
1262:   PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));
1263:   return 0;
1264: }

1266: /*@C
1267:   TSRKGetType - Get the type of RK scheme

1269:   Not collective

1271:   Input Parameter:
1272: .  ts - timestepping context

1274:   Output Parameter:
1275: .  rktype - type of RK-scheme

1277:   Level: intermediate

1279: .seealso: TSRKSetType()
1280: @*/
1281: PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype)
1282: {
1284:   PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));
1285:   return 0;
1286: }

1288: static PetscErrorCode TSRKGetOrder_RK(TS ts,PetscInt *order)
1289: {
1290:   TS_RK *rk = (TS_RK*)ts->data;

1292:   *order = rk->tableau->order;
1293:   return 0;
1294: }

1296: static PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype)
1297: {
1298:   TS_RK *rk = (TS_RK*)ts->data;

1300:   *rktype = rk->tableau->name;
1301:   return 0;
1302: }

1304: static PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype)
1305: {
1306:   TS_RK          *rk = (TS_RK*)ts->data;
1307:   PetscBool      match;
1308:   RKTableauLink  link;

1310:   if (rk->tableau) {
1311:     PetscStrcmp(rk->tableau->name,rktype,&match);
1312:     if (match) return 0;
1313:   }
1314:   for (link = RKTableauList; link; link=link->next) {
1315:     PetscStrcmp(link->tab.name,rktype,&match);
1316:     if (match) {
1317:       if (ts->setupcalled) TSRKTableauReset(ts);
1318:       rk->tableau = &link->tab;
1319:       if (ts->setupcalled) TSRKTableauSetUp(ts);
1320:       ts->default_adapt_type = rk->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1321:       return 0;
1322:     }
1323:   }
1324:   SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype);
1325: }

1327: static PetscErrorCode  TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y)
1328: {
1329:   TS_RK *rk = (TS_RK*)ts->data;

1331:   if (ns) *ns = rk->tableau->s;
1332:   if (Y)   *Y = rk->Y;
1333:   return 0;
1334: }

1336: static PetscErrorCode TSDestroy_RK(TS ts)
1337: {
1338:   TSReset_RK(ts);
1339:   if (ts->dm) {
1340:     DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
1341:     DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
1342:   }
1343:   PetscFree(ts->data);
1344:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetOrder_C",NULL);
1345:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);
1346:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);
1347:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetTableau_C",NULL);
1348:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",NULL);
1349:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",NULL);
1350:   return 0;
1351: }

1353: /*
1354:   This defines the nonlinear equation that is to be solved with SNES
1355:   We do not need to solve the equation; we just use SNES to approximate the Jacobian
1356: */
1357: static PetscErrorCode SNESTSFormFunction_RK(SNES snes,Vec x,Vec y,TS ts)
1358: {
1359:   TS_RK          *rk = (TS_RK*)ts->data;
1360:   DM             dm,dmsave;

1362:   SNESGetDM(snes,&dm);
1363:   /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
1364:   dmsave = ts->dm;
1365:   ts->dm = dm;
1366:   TSComputeRHSFunction(ts,rk->stage_time,x,y);
1367:   ts->dm = dmsave;
1368:   return 0;
1369: }

1371: static PetscErrorCode SNESTSFormJacobian_RK(SNES snes,Vec x,Mat A,Mat B,TS ts)
1372: {
1373:   TS_RK          *rk = (TS_RK*)ts->data;
1374:   DM             dm,dmsave;

1376:   SNESGetDM(snes,&dm);
1377:   dmsave = ts->dm;
1378:   ts->dm = dm;
1379:   TSComputeRHSJacobian(ts,rk->stage_time,x,A,B);
1380:   ts->dm = dmsave;
1381:   return 0;
1382: }

1384: /*@C
1385:   TSRKSetMultirate - Use the interpolation-based multirate RK method

1387:   Logically collective

1389:   Input Parameters:
1390: +  ts - timestepping context
1391: -  use_multirate - PETSC_TRUE enables the multirate RK method, sets the basic method to be RK2A and sets the ratio between slow stepsize and fast stepsize to be 2

1393:   Options Database:
1394: .   -ts_rk_multirate - <true,false>

1396:   Notes:
1397:   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 coeffcients (binterp).

1399:   Level: intermediate

1401: .seealso: TSRKGetMultirate()
1402: @*/
1403: PetscErrorCode TSRKSetMultirate(TS ts,PetscBool use_multirate)
1404: {
1405:   PetscTryMethod(ts,"TSRKSetMultirate_C",(TS,PetscBool),(ts,use_multirate));
1406:   return 0;
1407: }

1409: /*@C
1410:   TSRKGetMultirate - Gets whether to Use the interpolation-based multirate RK method

1412:   Not collective

1414:   Input Parameter:
1415: .  ts - timestepping context

1417:   Output Parameter:
1418: .  use_multirate - PETSC_TRUE if the multirate RK method is enabled, PETSC_FALSE otherwise

1420:   Level: intermediate

1422: .seealso: TSRKSetMultirate()
1423: @*/
1424: PetscErrorCode TSRKGetMultirate(TS ts,PetscBool *use_multirate)
1425: {
1426:   PetscUseMethod(ts,"TSRKGetMultirate_C",(TS,PetscBool*),(ts,use_multirate));
1427:   return 0;
1428: }

1430: /*MC
1431:       TSRK - ODE and DAE solver using Runge-Kutta schemes

1433:   The user should provide the right hand side of the equation
1434:   using TSSetRHSFunction().

1436:   Notes:
1437:   The default is TSRK3BS, it can be changed with TSRKSetType() or -ts_rk_type

1439:   Level: beginner

1441: .seealso:  TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRK2D, TTSRK2E, TSRK3,
1442:            TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister(), TSRKSetMultirate(), TSRKGetMultirate()

1444: M*/
1445: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
1446: {
1447:   TS_RK          *rk;

1449:   TSRKInitializePackage();

1451:   ts->ops->reset          = TSReset_RK;
1452:   ts->ops->destroy        = TSDestroy_RK;
1453:   ts->ops->view           = TSView_RK;
1454:   ts->ops->load           = TSLoad_RK;
1455:   ts->ops->setup          = TSSetUp_RK;
1456:   ts->ops->interpolate    = TSInterpolate_RK;
1457:   ts->ops->step           = TSStep_RK;
1458:   ts->ops->evaluatestep   = TSEvaluateStep_RK;
1459:   ts->ops->rollback       = TSRollBack_RK;
1460:   ts->ops->setfromoptions = TSSetFromOptions_RK;
1461:   ts->ops->getstages      = TSGetStages_RK;

1463:   ts->ops->snesfunction    = SNESTSFormFunction_RK;
1464:   ts->ops->snesjacobian    = SNESTSFormJacobian_RK;
1465:   ts->ops->adjointintegral = TSAdjointCostIntegral_RK;
1466:   ts->ops->adjointsetup    = TSAdjointSetUp_RK;
1467:   ts->ops->adjointstep     = TSAdjointStep_RK;
1468:   ts->ops->adjointreset    = TSAdjointReset_RK;

1470:   ts->ops->forwardintegral = TSForwardCostIntegral_RK;
1471:   ts->ops->forwardsetup    = TSForwardSetUp_RK;
1472:   ts->ops->forwardreset    = TSForwardReset_RK;
1473:   ts->ops->forwardstep     = TSForwardStep_RK;
1474:   ts->ops->forwardgetstages= TSForwardGetStages_RK;

1476:   PetscNewLog(ts,&rk);
1477:   ts->data = (void*)rk;

1479:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetOrder_C",TSRKGetOrder_RK);
1480:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);
1481:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);
1482:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetTableau_C",TSRKGetTableau_RK);
1483:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",TSRKSetMultirate_RK);
1484:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",TSRKGetMultirate_RK);

1486:   TSRKSetType(ts,TSRKDefault);
1487:   rk->dtratio = 1;
1488:   return 0;
1489: }