Actual source code: rk.c

petsc-3.12.1 2019-10-22
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  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

 30:      Level: advanced

 32: .seealso: TSRK, TSRKType, TSRKSetType()
 33: M*/
 34: /*MC
 35:      TSRK2A - Second order RK scheme.

 37:      This method has two stages.

 39:      Options database:
 40: .     -ts_rk_type 2a

 42:      Level: advanced

 44: .seealso: TSRK, TSRKType, TSRKSetType()
 45: M*/
 46: /*MC
 47:      TSRK3 - Third order RK scheme.

 49:      This method has three stages.

 51:      Options database:
 52: .     -ts_rk_type 3

 54:      Level: advanced

 56: .seealso: TSRK, TSRKType, TSRKSetType()
 57: M*/
 58: /*MC
 59:      TSRK3BS - Third order RK scheme of Bogacki-Shampine with 2nd order embedded method.

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

 63:      Options database:
 64: .     -ts_rk_type 3bs

 66:      Level: advanced

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

 70: .seealso: TSRK, TSRKType, TSRKSetType()
 71: M*/
 72: /*MC
 73:      TSRK4 - Fourth order RK scheme.

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

 77:      Options database:
 78: .     -ts_rk_type 4

 80:      Level: advanced

 82: .seealso: TSRK, TSRKType, TSRKSetType()
 83: M*/
 84: /*MC
 85:      TSRK5F - Fifth order Fehlberg RK scheme with a 4th order embedded method.

 87:      This method has six stages.

 89:      Options database:
 90: .     -ts_rk_type 5f

 92:      Level: advanced

 94: .seealso: TSRK, TSRKType, TSRKSetType()
 95: M*/
 96: /*MC
 97:      TSRK5DP - Fifth order Dormand-Prince RK scheme with the 4th order embedded method.

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

101:      Options database:
102: .     -ts_rk_type 5dp

104:      Level: advanced

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

108: .seealso: TSRK, TSRKType, TSRKSetType()
109: M*/
110: /*MC
111:      TSRK5BS - Fifth order Bogacki-Shampine RK scheme with 4th order embedded method.

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

115:      Options database:
116: .     -ts_rk_type 5bs

118:      Level: advanced

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

122: .seealso: TSRK, TSRKType, TSRKSetType()
123: M*/
124: /*MC
125:      TSRK6VR - Sixth order robust Verner RK scheme with fifth order embedded method.

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

129:      Options database:
130: .     -ts_rk_type 6vr

132:      Level: advanced

134:      References: http://people.math.sfu.ca/~jverner/RKV65.IIIXb.Robust.00010102836.081204.CoeffsOnlyRAT

136: .seealso: TSRK, TSRKType, TSRKSetType()
137: M*/
138: /*MC
139:      TSRK7VR - Seventh order robust Verner RK scheme with sixth order embedded method.

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

143:      Options database:
144: .     -ts_rk_type 7vr

146:      Level: advanced

148:      References: http://people.math.sfu.ca/~jverner/RKV76.IIa.Robust.000027015646.081206.CoeffsOnlyRAT

150: .seealso: TSRK, TSRKType, TSRKSetType()
151: M*/
152: /*MC
153:      TSRK8VR - Eigth order robust Verner RK scheme with seventh order embedded method.

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

157:      Options database:
158: .     -ts_rk_type 8vr

160:      Level: advanced

162:      References: http://people.math.sfu.ca/~jverner/RKV87.IIa.Robust.00000754677.081208.CoeffsOnlyRATandFLOAT

164: .seealso: TSRK, TSRKType, TSRKSetType()
165: M*/

167: /*@C
168:   TSRKRegisterAll - Registers all of the Runge-Kutta explicit methods in TSRK

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

172:   Level: advanced

174: .seealso:  TSRKRegisterDestroy()
175: @*/
176: PetscErrorCode TSRKRegisterAll(void)
177: {

181:   if (TSRKRegisterAllCalled) return(0);
182:   TSRKRegisterAllCalled = PETSC_TRUE;

184: #define RC PetscRealConstant
185:   {
186:     const PetscReal
187:       A[1][1] = {{0}},
188:       b[1]    = {RC(1.0)};
189:     TSRKRegister(TSRK1FE,1,1,&A[0][0],b,NULL,NULL,0,NULL);
190:   }
191:   {
192:     const PetscReal
193:       A[2][2]   = {{0,0},
194:                    {RC(1.0),0}},
195:       b[2]      =  {RC(0.5),RC(0.5)},
196:       bembed[2] =  {RC(1.0),0};
197:     TSRKRegister(TSRK2A,2,2,&A[0][0],b,NULL,bembed,0,NULL);
198:   }
199:   {
200:     const PetscReal
201:       A[3][3] = {{0,0,0},
202:                  {RC(2.0)/RC(3.0),0,0},
203:                  {RC(-1.0)/RC(3.0),RC(1.0),0}},
204:       b[3]    =  {RC(0.25),RC(0.5),RC(0.25)};
205:     TSRKRegister(TSRK3,3,3,&A[0][0],b,NULL,NULL,0,NULL);
206:   }
207:   {
208:     const PetscReal
209:       A[4][4]   = {{0,0,0,0},
210:                    {RC(1.0)/RC(2.0),0,0,0},
211:                    {0,RC(3.0)/RC(4.0),0,0},
212:                    {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0}},
213:       b[4]      =  {RC(2.0)/RC(9.0),RC(1.0)/RC(3.0),RC(4.0)/RC(9.0),0},
214:       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)};
215:     TSRKRegister(TSRK3BS,3,4,&A[0][0],b,NULL,bembed,0,NULL);
216:   }
217:   {
218:     const PetscReal
219:       A[4][4] = {{0,0,0,0},
220:                  {RC(0.5),0,0,0},
221:                  {0,RC(0.5),0,0},
222:                  {0,0,RC(1.0),0}},
223:       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)};
224:     TSRKRegister(TSRK4,4,4,&A[0][0],b,NULL,NULL,0,NULL);
225:   }
226:   {
227:     const PetscReal
228:       A[6][6]   = {{0,0,0,0,0,0},
229:                    {RC(0.25),0,0,0,0,0},
230:                    {RC(3.0)/RC(32.0),RC(9.0)/RC(32.0),0,0,0,0},
231:                    {RC(1932.0)/RC(2197.0),RC(-7200.0)/RC(2197.0),RC(7296.0)/RC(2197.0),0,0,0},
232:                    {RC(439.0)/RC(216.0),RC(-8.0),RC(3680.0)/RC(513.0),RC(-845.0)/RC(4104.0),0,0},
233:                    {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}},
234:       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)},
235:       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};
236:     TSRKRegister(TSRK5F,5,6,&A[0][0],b,NULL,bembed,0,NULL);
237:   }
238:   {
239:     const PetscReal
240:       A[7][7]   = {{0,0,0,0,0,0,0},
241:                    {RC(1.0)/RC(5.0),0,0,0,0,0,0},
242:                    {RC(3.0)/RC(40.0),RC(9.0)/RC(40.0),0,0,0,0,0},
243:                    {RC(44.0)/RC(45.0),RC(-56.0)/RC(15.0),RC(32.0)/RC(9.0),0,0,0,0},
244:                    {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},
245:                    {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},
246:                    {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}},
247:       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},
248:         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)},
249:         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)},
250:                     {0,0,0,0,0},
251:                     {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)},
252:                     {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)},
253:                     {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)},
254:                     {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)},
255:                     {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)}};

257:         TSRKRegister(TSRK5DP,5,7,&A[0][0],b,NULL,bembed,5,binterp[0]);
258:   }
259:   {
260:     const PetscReal
261:       A[8][8]   = {{0,0,0,0,0,0,0,0},
262:                    {RC(1.0)/RC(6.0),0,0,0,0,0,0,0},
263:                    {RC(2.0)/RC(27.0),RC(4.0)/RC(27.0),0,0,0,0,0,0},
264:                    {RC(183.0)/RC(1372.0),RC(-162.0)/RC(343.0),RC(1053.0)/RC(1372.0),0,0,0,0,0},
265:                    {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},
266:                    {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},
267:                    {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},
268:                    {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}},
269:       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},
270:       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)};
271:     TSRKRegister(TSRK5BS,5,8,&A[0][0],b,NULL,bembed,0,NULL);
272:   }
273:   {
274:     const PetscReal
275:       A[9][9]   = {{0,0,0,0,0,0,0,0,0},
276:                    {RC(1.8000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0},
277:                    {RC(8.9506172839506172839506172839506172839506e-02),RC(7.7160493827160493827160493827160493827160e-02),0,0,0,0,0,0,0},
278:                    {RC(6.2500000000000000000000000000000000000000e-02),0,RC(1.8750000000000000000000000000000000000000e-01),0,0,0,0,0,0},
279:                    {RC(3.1651600000000000000000000000000000000000e-01),0,RC(-1.0449480000000000000000000000000000000000e+00),RC(1.2584320000000000000000000000000000000000e+00),0,0,0,0,0},
280:                    {RC(2.7232612736485626257225065566674305502508e-01),0,RC(-8.2513360323886639676113360323886639676113e-01),RC(1.0480917678812415654520917678812415654521e+00),RC(1.0471570799276856873679117969088177628396e-01),0,0,0,0},
281:                    {RC(-1.6699418599716514314329607278961797333198e-01),0,RC(6.3170850202429149797570850202429149797571e-01),RC(1.7461044552773876082146758838488161796432e-01),RC(-1.0665356459086066122525194734018680677781e+00),RC(1.2272108843537414965986394557823129251701e+00),0,0,0},
282:                    {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},
283:                    {RC(7.6388888888888888888888888888888888888889e-02),0,0,RC(3.6940836940836940836940836940836940836941e-01),0,RC(2.4801587301587301587301587301587301587302e-01),RC(2.3674242424242424242424242424242424242424e-01),RC(6.9444444444444444444444444444444444444444e-02),0}},
284:       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},
285:       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)};
286:     TSRKRegister(TSRK6VR,6,9,&A[0][0],b,NULL,bembed,0,NULL);
287:   }
288:   {
289:     const PetscReal
290:       A[10][10]  = {{0,0,0,0,0,0,0,0,0,0},
291:                     {RC(5.0000000000000000000000000000000000000000e-03),0,0,0,0,0,0,0,0,0},
292:                     {RC(-1.0767901234567901234567901234567901234568e+00),RC(1.1856790123456790123456790123456790123457e+00),0,0,0,0,0,0,0,0},
293:                     {RC(4.0833333333333333333333333333333333333333e-02),0,RC(1.2250000000000000000000000000000000000000e-01),0,0,0,0,0,0,0},
294:                     {RC(6.3607142857142857142857142857142857142857e-01),0,RC(-2.4444642857142857142857142857142857142857e+00),RC(2.2633928571428571428571428571428571428571e+00),0,0,0,0,0,0},
295:                     {RC(-2.5351211079349245229256383554660215487207e+00),0,RC(1.0299374654449267920438514460756024913612e+01),RC(-7.9513032885990579949493217458266876536482e+00),RC(7.9301148923100592201226014271115261823800e-01),0,0,0,0,0},
296:                     {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},
297:                     {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},
298:                     {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},
299:                     {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}},
300:       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},
301:       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)};
302:     TSRKRegister(TSRK7VR,7,10,&A[0][0],b,NULL,bembed,0,NULL);
303:   }
304:   {
305:     const PetscReal
306:       A[13][13]  = {{0,0,0,0,0,0,0,0,0,0,0,0,0},
307:                     {RC(2.5000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0,0,0,0,0},
308:                     {RC(8.7400846504915232052686327594877411977046e-02),RC(2.5487604938654321753087950620345685135815e-02),0,0,0,0,0,0,0,0,0,0,0},
309:                     {RC(4.2333169291338582677165354330708661417323e-02),0,RC(1.2699950787401574803149606299212598425197e-01),0,0,0,0,0,0,0,0,0,0},
310:                     {RC(4.2609505888742261494881445237572274090942e-01),0,RC(-1.5987952846591523265427733230657181117089e+00),RC(1.5967002257717297115939588706899953707994e+00),0,0,0,0,0,0,0,0,0},
311:                     {RC(5.0719337296713929515090618138513639239329e-02),0,0,RC(2.5433377264600407582754714408877778031369e-01),RC(2.0394689005728199465736223777270858044698e-01),0,0,0,0,0,0,0,0},
312:                     {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},
313:                     {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},
314:                     {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},
315:                     {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},
316:                     {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},
317:                     {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},
318:                     {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}},
319:       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},
320:       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)};
321:     TSRKRegister(TSRK8VR,8,13,&A[0][0],b,NULL,bembed,0,NULL);
322:   }
323: #undef RC
324:   return(0);
325: }

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

330:    Not Collective

332:    Level: advanced

334: .seealso: TSRKRegister(), TSRKRegisterAll()
335: @*/
336: PetscErrorCode TSRKRegisterDestroy(void)
337: {
339:   RKTableauLink  link;

342:   while ((link = RKTableauList)) {
343:     RKTableau t = &link->tab;
344:     RKTableauList = link->next;
345:     PetscFree3(t->A,t->b,t->c);
346:     PetscFree (t->bembed);
347:     PetscFree (t->binterp);
348:     PetscFree (t->name);
349:     PetscFree (link);
350:   }
351:   TSRKRegisterAllCalled = PETSC_FALSE;
352:   return(0);
353: }

355: /*@C
356:   TSRKInitializePackage - This function initializes everything in the TSRK package. It is called
357:   from TSInitializePackage().

359:   Level: developer

361: .seealso: PetscInitialize()
362: @*/
363: PetscErrorCode TSRKInitializePackage(void)
364: {

368:   if (TSRKPackageInitialized) return(0);
369:   TSRKPackageInitialized = PETSC_TRUE;
370:   TSRKRegisterAll();
371:   PetscRegisterFinalize(TSRKFinalizePackage);
372:   return(0);
373: }

375: /*@C
376:   TSRKFinalizePackage - This function destroys everything in the TSRK package. It is
377:   called from PetscFinalize().

379:   Level: developer

381: .seealso: PetscFinalize()
382: @*/
383: PetscErrorCode TSRKFinalizePackage(void)
384: {

388:   TSRKPackageInitialized = PETSC_FALSE;
389:   TSRKRegisterDestroy();
390:   return(0);
391: }

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

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

398:    Input Parameters:
399: +  name - identifier for method
400: .  order - approximation order of method
401: .  s - number of stages, this is the dimension of the matrices below
402: .  A - stage coefficients (dimension s*s, row-major)
403: .  b - step completion table (dimension s; NULL to use last row of A)
404: .  c - abscissa (dimension s; NULL to use row sums of A)
405: .  bembed - completion table for embedded method (dimension s; NULL if not available)
406: .  p - Order of the interpolation scheme, equal to the number of columns of binterp
407: -  binterp - Coefficients of the interpolation formula (dimension s*p; NULL to reuse b with p=1)

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

412:    Level: advanced

414: .seealso: TSRK
415: @*/
416: PetscErrorCode TSRKRegister(TSRKType name,PetscInt order,PetscInt s,
417:                             const PetscReal A[],const PetscReal b[],const PetscReal c[],
418:                             const PetscReal bembed[],PetscInt p,const PetscReal binterp[])
419: {
420:   PetscErrorCode  ierr;
421:   RKTableauLink   link;
422:   RKTableau       t;
423:   PetscInt        i,j;


433:   TSRKInitializePackage();
434:   PetscNew(&link);
435:   t = &link->tab;

437:   PetscStrallocpy(name,&t->name);
438:   t->order = order;
439:   t->s = s;
440:   PetscMalloc3(s*s,&t->A,s,&t->b,s,&t->c);
441:   PetscArraycpy(t->A,A,s*s);
442:   if (b)  { PetscArraycpy(t->b,b,s); }
443:   else for (i=0; i<s; i++) t->b[i] = A[(s-1)*s+i];
444:   if (c)  { PetscArraycpy(t->c,c,s); }
445:   else for (i=0; i<s; i++) for (j=0,t->c[i]=0; j<s; j++) t->c[i] += A[i*s+j];
446:   t->FSAL = PETSC_TRUE;
447:   for (i=0; i<s; i++) if (t->A[(s-1)*s+i] != t->b[i]) t->FSAL = PETSC_FALSE;

449:   if (bembed) {
450:     PetscMalloc1(s,&t->bembed);
451:     PetscArraycpy(t->bembed,bembed,s);
452:   }

454:   if (!binterp) { p = 1; binterp = t->b; }
455:   t->p = p;
456:   PetscMalloc1(s*p,&t->binterp);
457:   PetscArraycpy(t->binterp,binterp,s*p);

459:   link->next = RKTableauList;
460:   RKTableauList = link;
461:   return(0);
462: }

464: /*
465:  This is for single-step RK method
466:  The step completion formula is

468:  x1 = x0 + h b^T YdotRHS

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

474:  x1e = x0 + h be^T YdotRHS
475:      = x1 - h b^T YdotRHS + h be^T YdotRHS
476:      = x1 + h (be - b)^T YdotRHS

478:  so we can evaluate the method with different order even after the step has been optimistically completed.
479: */
480: static PetscErrorCode TSEvaluateStep_RK(TS ts,PetscInt order,Vec X,PetscBool *done)
481: {
482:   TS_RK          *rk   = (TS_RK*)ts->data;
483:   RKTableau      tab  = rk->tableau;
484:   PetscScalar    *w    = rk->work;
485:   PetscReal      h;
486:   PetscInt       s    = tab->s,j;

490:   switch (rk->status) {
491:   case TS_STEP_INCOMPLETE:
492:   case TS_STEP_PENDING:
493:     h = ts->time_step; break;
494:   case TS_STEP_COMPLETE:
495:     h = ts->ptime - ts->ptime_prev; break;
496:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
497:   }
498:   if (order == tab->order) {
499:     if (rk->status == TS_STEP_INCOMPLETE) {
500:       VecCopy(ts->vec_sol,X);
501:       for (j=0; j<s; j++) w[j] = h*tab->b[j]/rk->dtratio;
502:       VecMAXPY(X,s,w,rk->YdotRHS);
503:     } else {VecCopy(ts->vec_sol,X);}
504:     return(0);
505:   } else if (order == tab->order-1) {
506:     if (!tab->bembed) goto unavailable;
507:     if (rk->status == TS_STEP_INCOMPLETE) { /*Complete with the embedded method (be)*/
508:       VecCopy(ts->vec_sol,X);
509:       for (j=0; j<s; j++) w[j] = h*tab->bembed[j];
510:       VecMAXPY(X,s,w,rk->YdotRHS);
511:     } else {  /*Rollback and re-complete using (be-b) */
512:       VecCopy(ts->vec_sol,X);
513:       for (j=0; j<s; j++) w[j] = h*(tab->bembed[j] - tab->b[j]);
514:       VecMAXPY(X,s,w,rk->YdotRHS);
515:     }
516:     if (done) *done = PETSC_TRUE;
517:     return(0);
518:   }
519: unavailable:
520:   if (done) *done = PETSC_FALSE;
521:   else SETERRQ3(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);
522:   return(0);
523: }

525: static PetscErrorCode TSForwardCostIntegral_RK(TS ts)
526: {
527:   TS_RK           *rk = (TS_RK*)ts->data;
528:   TS              quadts = ts->quadraturets;
529:   RKTableau       tab = rk->tableau;
530:   const PetscInt  s = tab->s;
531:   const PetscReal *b = tab->b,*c = tab->c;
532:   Vec             *Y = rk->Y;
533:   PetscInt        i;
534:   PetscErrorCode  ierr;

537:   /* No need to backup quadts->vec_sol since it can be reverted in TSRollBack_RK */
538:   for (i=s-1; i>=0; i--) {
539:     /* Evolve quadrature TS solution to compute integrals */
540:     TSComputeRHSFunction(quadts,rk->ptime+rk->time_step*c[i],Y[i],ts->vec_costintegrand);
541:     VecAXPY(quadts->vec_sol,rk->time_step*b[i],ts->vec_costintegrand);
542:   }
543:   return(0);
544: }

546: static PetscErrorCode TSAdjointCostIntegral_RK(TS ts)
547: {
548:   TS_RK           *rk = (TS_RK*)ts->data;
549:   RKTableau       tab = rk->tableau;
550:   TS              quadts = ts->quadraturets;
551:   const PetscInt  s = tab->s;
552:   const PetscReal *b = tab->b,*c = tab->c;
553:   Vec             *Y = rk->Y;
554:   PetscInt        i;
555:   PetscErrorCode  ierr;

558:   for (i=s-1; i>=0; i--) {
559:     /* Evolve quadrature TS solution to compute integrals */
560:     TSComputeRHSFunction(quadts,ts->ptime+ts->time_step*(1.0-c[i]),Y[i],ts->vec_costintegrand);
561:     VecAXPY(quadts->vec_sol,-ts->time_step*b[i],ts->vec_costintegrand);
562:   }
563:   return(0);
564: }

566: static PetscErrorCode TSRollBack_RK(TS ts)
567: {
568:   TS_RK           *rk = (TS_RK*)ts->data;
569:   TS              quadts = ts->quadraturets;
570:   RKTableau       tab = rk->tableau;
571:   const PetscInt  s  = tab->s;
572:   const PetscReal *b = tab->b,*c = tab->c;
573:   PetscScalar     *w = rk->work;
574:   Vec             *Y = rk->Y,*YdotRHS = rk->YdotRHS;
575:   PetscInt        j;
576:   PetscReal       h;
577:   PetscErrorCode  ierr;

580:   switch (rk->status) {
581:   case TS_STEP_INCOMPLETE:
582:   case TS_STEP_PENDING:
583:     h = ts->time_step; break;
584:   case TS_STEP_COMPLETE:
585:     h = ts->ptime - ts->ptime_prev; break;
586:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
587:   }
588:   for (j=0; j<s; j++) w[j] = -h*b[j];
589:   VecMAXPY(ts->vec_sol,s,w,YdotRHS);
590:   if (quadts && ts->costintegralfwd) {
591:     for (j=0; j<s; j++) {
592:       /* Revert the quadrature TS solution */
593:       TSComputeRHSFunction(quadts,rk->ptime+h*c[j],Y[j],ts->vec_costintegrand);
594:       VecAXPY(quadts->vec_sol,-h*b[j],ts->vec_costintegrand);
595:     }
596:   }
597:   return(0);
598: }

600: static PetscErrorCode TSForwardStep_RK(TS ts)
601: {
602:   TS_RK           *rk = (TS_RK*)ts->data;
603:   RKTableau       tab = rk->tableau;
604:   Mat             J,*MatsFwdSensipTemp = rk->MatsFwdSensipTemp;
605:   const PetscInt  s = tab->s;
606:   const PetscReal *A = tab->A,*c = tab->c,*b = tab->b;
607:   Vec             *Y = rk->Y;
608:   PetscInt        i,j;
609:   PetscReal       stage_time,h = ts->time_step;
610:   PetscBool       zero;
611:   PetscErrorCode  ierr;

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

617:   for (i=0; i<s; i++) {
618:     stage_time = ts->ptime + h*c[i];
619:     zero = PETSC_FALSE;
620:     if (b[i] == 0 && i == s-1) zero = PETSC_TRUE;
621:     /* TLM Stage values */
622:     if(!i) {
623:       MatCopy(ts->mat_sensip,rk->MatsFwdStageSensip[i],SAME_NONZERO_PATTERN);
624:     } else if (!zero) {
625:       MatZeroEntries(rk->MatsFwdStageSensip[i]);
626:       for (j=0; j<i; j++) {
627:         MatAXPY(rk->MatsFwdStageSensip[i],h*A[i*s+j],MatsFwdSensipTemp[j],SAME_NONZERO_PATTERN);
628:       }
629:       MatAXPY(rk->MatsFwdStageSensip[i],1.,ts->mat_sensip,SAME_NONZERO_PATTERN);
630:     } else {
631:       MatZeroEntries(rk->MatsFwdStageSensip[i]);
632:     }

634:     TSComputeRHSJacobian(ts,stage_time,Y[i],J,J);
635:     MatMatMult(J,rk->MatsFwdStageSensip[i],MAT_REUSE_MATRIX,PETSC_DEFAULT,&MatsFwdSensipTemp[i]);
636:     if (ts->Jacprhs) {
637:       TSComputeRHSJacobianP(ts,stage_time,Y[i],ts->Jacprhs); /* get f_p */
638:       if (ts->vecs_sensi2p) { /* TLM used for 2nd-order adjoint */
639:         PetscScalar *xarr;
640:         MatDenseGetColumn(MatsFwdSensipTemp[i],0,&xarr);
641:         VecPlaceArray(rk->VecDeltaFwdSensipCol,xarr);
642:         MatMultAdd(ts->Jacprhs,ts->vec_dir,rk->VecDeltaFwdSensipCol,rk->VecDeltaFwdSensipCol);
643:         VecResetArray(rk->VecDeltaFwdSensipCol);
644:         MatDenseRestoreColumn(MatsFwdSensipTemp[i],&xarr);
645:       } else {
646:         MatAXPY(MatsFwdSensipTemp[i],1.,ts->Jacprhs,SUBSET_NONZERO_PATTERN);
647:       }
648:     }
649:   }

651:   for (i=0; i<s; i++) {
652:     MatAXPY(ts->mat_sensip,h*b[i],rk->MatsFwdSensipTemp[i],SAME_NONZERO_PATTERN);
653:   }
654:   rk->status = TS_STEP_COMPLETE;
655:   return(0);
656: }

658: static PetscErrorCode TSForwardGetStages_RK(TS ts,PetscInt *ns,Mat **stagesensip)
659: {
660:   TS_RK     *rk = (TS_RK*)ts->data;
661:   RKTableau tab  = rk->tableau;

664:   if (ns) *ns = tab->s;
665:   if (stagesensip) *stagesensip = rk->MatsFwdStageSensip;
666:   return(0);
667: }

669: static PetscErrorCode TSForwardSetUp_RK(TS ts)
670: {
671:   TS_RK          *rk = (TS_RK*)ts->data;
672:   RKTableau      tab  = rk->tableau;
673:   PetscInt       i;

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

680:   PetscMalloc1(tab->s,&rk->MatsFwdStageSensip);
681:   PetscMalloc1(tab->s,&rk->MatsFwdSensipTemp);
682:   for(i=0; i<tab->s; i++) {
683:     MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdStageSensip[i]);
684:     MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdSensipTemp[i]);
685:   }
686:   VecDuplicate(ts->vec_sol,&rk->VecDeltaFwdSensipCol);
687:   return(0);
688: }

690: static PetscErrorCode TSForwardReset_RK(TS ts)
691: {
692:   TS_RK          *rk = (TS_RK*)ts->data;
693:   RKTableau      tab  = rk->tableau;
694:   PetscInt       i;

698:   MatDestroy(&rk->MatFwdSensip0);
699:   if (rk->MatsFwdStageSensip) {
700:     for (i=0; i<tab->s; i++) {
701:       MatDestroy(&rk->MatsFwdStageSensip[i]);
702:     }
703:     PetscFree(rk->MatsFwdStageSensip);
704:   }
705:   if (rk->MatsFwdSensipTemp) {
706:     for (i=0; i<tab->s; i++) {
707:       MatDestroy(&rk->MatsFwdSensipTemp[i]);
708:     }
709:     PetscFree(rk->MatsFwdSensipTemp);
710:   }
711:   VecDestroy(&rk->VecDeltaFwdSensipCol);
712:   return(0);
713: }

715: static PetscErrorCode TSStep_RK(TS ts)
716: {
717:   TS_RK           *rk  = (TS_RK*)ts->data;
718:   RKTableau       tab  = rk->tableau;
719:   const PetscInt  s = tab->s;
720:   const PetscReal *A = tab->A,*c = tab->c;
721:   PetscScalar     *w = rk->work;
722:   Vec             *Y = rk->Y,*YdotRHS = rk->YdotRHS;
723:   PetscBool       FSAL = tab->FSAL;
724:   TSAdapt         adapt;
725:   PetscInt        i,j;
726:   PetscInt        rejections = 0;
727:   PetscBool       stageok,accept = PETSC_TRUE;
728:   PetscReal       next_time_step = ts->time_step;
729:   PetscErrorCode  ierr;

732:   if (ts->steprollback || ts->steprestart) FSAL = PETSC_FALSE;
733:   if (FSAL) { VecCopy(YdotRHS[s-1],YdotRHS[0]); }

735:   rk->status = TS_STEP_INCOMPLETE;
736:   while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
737:     PetscReal t = ts->ptime;
738:     PetscReal h = ts->time_step;
739:     for (i=0; i<s; i++) {
740:       rk->stage_time = t + h*c[i];
741:       TSPreStage(ts,rk->stage_time);
742:       VecCopy(ts->vec_sol,Y[i]);
743:       for (j=0; j<i; j++) w[j] = h*A[i*s+j];
744:       VecMAXPY(Y[i],i,w,YdotRHS);
745:       TSPostStage(ts,rk->stage_time,i,Y);
746:       TSGetAdapt(ts,&adapt);
747:       TSAdaptCheckStage(adapt,ts,rk->stage_time,Y[i],&stageok);
748:       if (!stageok) goto reject_step;
749:       if (FSAL && !i) continue;
750:       TSComputeRHSFunction(ts,t+h*c[i],Y[i],YdotRHS[i]);
751:     }

753:     rk->status = TS_STEP_INCOMPLETE;
754:     TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);
755:     rk->status = TS_STEP_PENDING;
756:     TSGetAdapt(ts,&adapt);
757:     TSAdaptCandidatesClear(adapt);
758:     TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,(PetscReal)tab->s,PETSC_TRUE);
759:     TSAdaptChoose(adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
760:     rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
761:     if (!accept) { /* Roll back the current step */
762:       TSRollBack_RK(ts);
763:       ts->time_step = next_time_step;
764:       goto reject_step;
765:     }

767:     if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */
768:       rk->ptime     = ts->ptime;
769:       rk->time_step = ts->time_step;
770:     }

772:     ts->ptime += ts->time_step;
773:     ts->time_step = next_time_step;
774:     break;

776:     reject_step:
777:     ts->reject++; accept = PETSC_FALSE;
778:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
779:       ts->reason = TS_DIVERGED_STEP_REJECTED;
780:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
781:     }
782:   }
783:   return(0);
784: }

786: static PetscErrorCode TSAdjointSetUp_RK(TS ts)
787: {
788:   TS_RK          *rk  = (TS_RK*)ts->data;
789:   RKTableau      tab = rk->tableau;
790:   PetscInt       s   = tab->s;

794:   if (ts->adjointsetupcalled++) return(0);
795:   VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam);
796:   VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&rk->VecsSensiTemp);
797:   if(ts->vecs_sensip) {
798:     VecDuplicate(ts->vecs_sensip[0],&rk->VecDeltaMu);
799:   }
800:   if (ts->vecs_sensi2) {
801:     VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam2);
802:     VecDuplicateVecs(ts->vecs_sensi2[0],ts->numcost,&rk->VecsSensi2Temp);
803:   }
804:   if (ts->vecs_sensi2p) {
805:     VecDuplicate(ts->vecs_sensi2p[0],&rk->VecDeltaMu2);
806:   }
807:   return(0);
808: }

810: /*
811:   Assumptions:
812:     - TSStep_RK() always evaluates the step with b, not bembed.
813: */
814: static PetscErrorCode TSAdjointStep_RK(TS ts)
815: {
816:   TS_RK            *rk = (TS_RK*)ts->data;
817:   TS               quadts = ts->quadraturets;
818:   RKTableau        tab = rk->tableau;
819:   Mat              J,Jpre,Jquad;
820:   const PetscInt   s = tab->s;
821:   const PetscReal  *A = tab->A,*b = tab->b,*c = tab->c;
822:   PetscScalar      *w = rk->work,*xarr;
823:   Vec              *Y = rk->Y,*VecsDeltaLam = rk->VecsDeltaLam,VecDeltaMu = rk->VecDeltaMu,*VecsSensiTemp = rk->VecsSensiTemp;
824:   Vec              *VecsDeltaLam2 = rk->VecsDeltaLam2,VecDeltaMu2 = rk->VecDeltaMu2,*VecsSensi2Temp = rk->VecsSensi2Temp;
825:   Vec              VecDRDUTransCol = ts->vec_drdu_col,VecDRDPTransCol = ts->vec_drdp_col;
826:   PetscInt         i,j,nadj;
827:   PetscReal        t = ts->ptime;
828:   PetscReal        h = ts->time_step;
829:   PetscErrorCode   ierr;

832:   rk->status = TS_STEP_INCOMPLETE;

834:   TSGetRHSJacobian(ts,&J,&Jpre,NULL,NULL);
835:   if (quadts) {
836:     TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);
837:   }
838:   for (i=s-1; i>=0; i--) {
839:     if (tab->FSAL && i == s-1) {
840:       /* VecsDeltaLam[nadj*s+s-1] are initialized with zeros and the values never change.*/
841:       continue;
842:     }
843:     rk->stage_time = t + h*(1.0-c[i]);
844:     TSComputeSNESJacobian(ts,Y[i],J,Jpre);
845:     if (quadts) {
846:       TSComputeRHSJacobian(quadts,rk->stage_time,Y[i],Jquad,Jquad); /* get r_u^T */
847:     }
848:     if (ts->vecs_sensip) {
849:       TSComputeRHSJacobianP(ts,rk->stage_time,Y[i],ts->Jacprhs); /* get f_p */
850:       if (quadts) {
851:         TSComputeRHSJacobianP(quadts,rk->stage_time,Y[i],quadts->Jacprhs); /* get f_p for the quadrature */
852:       }
853:     }

855:     if (b[i]) {
856:       for (j=i+1; j<s; j++) w[j-i-1] = A[j*s+i]/b[i]; /* coefficients for computing VecsSensiTemp */
857:     } else {
858:       for (j=i+1; j<s; j++) w[j-i-1] = A[j*s+i]; /* coefficients for computing VecsSensiTemp */
859:     }

861:     for (nadj=0; nadj<ts->numcost; nadj++) {
862:       /* Stage values of lambda */
863:       if (b[i]) {
864:         /* lambda_{n+1} + \sum_{j=i+1}^s a_{ji}/b[i]*lambda_{s,j} */
865:         VecCopy(ts->vecs_sensi[nadj],VecsSensiTemp[nadj]); /* VecDeltaLam is an vec array of size s by numcost */
866:         VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);
867:         MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]); /* VecsSensiTemp will be reused by 2nd-order adjoint */
868:         VecScale(VecsDeltaLam[nadj*s+i],-h*b[i]);
869:         if (quadts) {
870:           MatDenseGetColumn(Jquad,nadj,&xarr);
871:           VecPlaceArray(VecDRDUTransCol,xarr);
872:           VecAXPY(VecsDeltaLam[nadj*s+i],-h*b[i],VecDRDUTransCol);
873:           VecResetArray(VecDRDUTransCol);
874:           MatDenseRestoreColumn(Jquad,&xarr);
875:         }
876:       } else {
877:         /* \sum_{j=i+1}^s a_{ji}*lambda_{s,j} */
878:         VecSet(VecsSensiTemp[nadj],0);
879:         VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);
880:         MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]);
881:         VecScale(VecsDeltaLam[nadj*s+i],-h);
882:       }

884:       /* Stage values of mu */
885:       if (ts->vecs_sensip) {
886:         MatMultTranspose(ts->Jacprhs,VecsSensiTemp[nadj],VecDeltaMu);
887:         if (b[i]) {
888:           VecScale(VecDeltaMu,-h*b[i]);
889:           if (quadts) {
890:             MatDenseGetColumn(quadts->Jacprhs,nadj,&xarr);
891:             VecPlaceArray(VecDRDPTransCol,xarr);
892:             VecAXPY(VecDeltaMu,-h*b[i],VecDRDPTransCol);
893:             VecResetArray(VecDRDPTransCol);
894:             MatDenseRestoreColumn(quadts->Jacprhs,&xarr);
895:           }
896:         } else {
897:           VecScale(VecDeltaMu,-h);
898:         }
899:         VecAXPY(ts->vecs_sensip[nadj],1.,VecDeltaMu); /* update sensip for each stage */
900:       }
901:     }

903:     if (ts->vecs_sensi2 && ts->forward_solve) { /* 2nd-order adjoint, TLM mode has to be turned on */
904:       /* Get w1 at t_{n+1} from TLM matrix */
905:       MatDenseGetColumn(rk->MatsFwdStageSensip[i],0,&xarr);
906:       VecPlaceArray(ts->vec_sensip_col,xarr);
907:       /* lambda_s^T F_UU w_1 */
908:       TSComputeRHSHessianProductFunctionUU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_guu);
909:       if (quadts)  {
910:         /* R_UU w_1 */
911:         TSComputeRHSHessianProductFunctionUU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_guu);
912:       }
913:       if (ts->vecs_sensip) {
914:         /* lambda_s^T F_UP w_2 */
915:         TSComputeRHSHessianProductFunctionUP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gup);
916:         if (quadts)  {
917:           /* R_UP w_2 */
918:           TSComputeRHSHessianProductFunctionUP(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gup);
919:         }
920:       }
921:       if (ts->vecs_sensi2p) {
922:         /* lambda_s^T F_PU w_1 */
923:         TSComputeRHSHessianProductFunctionPU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_gpu);
924:         /* lambda_s^T F_PP w_2 */
925:         TSComputeRHSHessianProductFunctionPP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gpp);
926:         if (b[i] && quadts) {
927:           /* R_PU w_1 */
928:           TSComputeRHSHessianProductFunctionPU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gpu);
929:           /* R_PP w_2 */
930:           TSComputeRHSHessianProductFunctionPP(quadts,rk->stage_time,Y[i],NULL,ts->vec_dir,ts->vecs_gpp);
931:         }
932:       }
933:       VecResetArray(ts->vec_sensip_col);
934:       MatDenseRestoreColumn(rk->MatsFwdStageSensip[i],&xarr);

936:       for (nadj=0; nadj<ts->numcost; nadj++) {
937:         /* Stage values of lambda */
938:         if (b[i]) {
939:           /* J_i^T*(Lambda_{n+1}+\sum_{j=i+1}^s a_{ji}/b_i*Lambda_{s,j} */
940:           VecCopy(ts->vecs_sensi2[nadj],VecsSensi2Temp[nadj]);
941:           VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);
942:           MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);
943:           VecScale(VecsDeltaLam2[nadj*s+i],-h*b[i]);
944:           VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_guu[nadj]);
945:           if (ts->vecs_sensip) {
946:             VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_gup[nadj]);
947:           }
948:         } else {
949:           /* \sum_{j=i+1}^s a_{ji}*Lambda_{s,j} */
950:           VecSet(VecsDeltaLam2[nadj*s+i],0);
951:           VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);
952:           MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);
953:           VecScale(VecsDeltaLam2[nadj*s+i],-h);
954:           VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_guu[nadj]);
955:           if (ts->vecs_sensip) {
956:             VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_gup[nadj]);
957:           }
958:         }
959:         if (ts->vecs_sensi2p) { /* 2nd-order adjoint for parameters */
960:           MatMultTranspose(ts->Jacprhs,VecsSensi2Temp[nadj],VecDeltaMu2);
961:           if (b[i]) {
962:             VecScale(VecDeltaMu2,-h*b[i]);
963:             VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpu[nadj]);
964:             VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpp[nadj]);
965:           } else {
966:             VecScale(VecDeltaMu2,-h);
967:             VecAXPY(VecDeltaMu2,-h,ts->vecs_gpu[nadj]);
968:             VecAXPY(VecDeltaMu2,-h,ts->vecs_gpp[nadj]);
969:           }
970:           VecAXPY(ts->vecs_sensi2p[nadj],1,VecDeltaMu2); /* update sensi2p for each stage */
971:         }
972:       }
973:     }
974:   }

976:   for (j=0; j<s; j++) w[j] = 1.0;
977:   for (nadj=0; nadj<ts->numcost; nadj++) { /* no need to do this for mu's */
978:     VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecsDeltaLam[nadj*s]);
979:     if (ts->vecs_sensi2) {
980:       VecMAXPY(ts->vecs_sensi2[nadj],s,w,&VecsDeltaLam2[nadj*s]);
981:     }
982:   }
983:   rk->status = TS_STEP_COMPLETE;
984:   return(0);
985: }

987: static PetscErrorCode TSAdjointReset_RK(TS ts)
988: {
989:   TS_RK          *rk = (TS_RK*)ts->data;
990:   RKTableau      tab = rk->tableau;

994:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam);
995:   VecDestroyVecs(ts->numcost,&rk->VecsSensiTemp);
996:   VecDestroy(&rk->VecDeltaMu);
997:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam2);
998:   VecDestroy(&rk->VecDeltaMu2);
999:   VecDestroyVecs(ts->numcost,&rk->VecsSensi2Temp);
1000:   return(0);
1001: }

1003: static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X)
1004: {
1005:   TS_RK            *rk = (TS_RK*)ts->data;
1006:   PetscInt         s  = rk->tableau->s,p = rk->tableau->p,i,j;
1007:   PetscReal        h;
1008:   PetscReal        tt,t;
1009:   PetscScalar      *b;
1010:   const PetscReal  *B = rk->tableau->binterp;
1011:   PetscErrorCode   ierr;

1014:   if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRK %s does not have an interpolation formula",rk->tableau->name);

1016:   switch (rk->status) {
1017:     case TS_STEP_INCOMPLETE:
1018:     case TS_STEP_PENDING:
1019:       h = ts->time_step;
1020:       t = (itime - ts->ptime)/h;
1021:       break;
1022:     case TS_STEP_COMPLETE:
1023:       h = ts->ptime - ts->ptime_prev;
1024:       t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
1025:       break;
1026:     default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
1027:   }
1028:   PetscMalloc1(s,&b);
1029:   for (i=0; i<s; i++) b[i] = 0;
1030:   for (j=0,tt=t; j<p; j++,tt*=t) {
1031:     for (i=0; i<s; i++) {
1032:       b[i]  += h * B[i*p+j] * tt;
1033:     }
1034:   }
1035:   VecCopy(rk->Y[0],X);
1036:   VecMAXPY(X,s,b,rk->YdotRHS);
1037:   PetscFree(b);
1038:   return(0);
1039: }

1041: /*------------------------------------------------------------*/

1043: static PetscErrorCode TSRKTableauReset(TS ts)
1044: {
1045:   TS_RK          *rk = (TS_RK*)ts->data;
1046:   RKTableau      tab = rk->tableau;

1050:   if (!tab) return(0);
1051:   PetscFree(rk->work);
1052:   VecDestroyVecs(tab->s,&rk->Y);
1053:   VecDestroyVecs(tab->s,&rk->YdotRHS);
1054:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam);
1055:   VecDestroyVecs(ts->numcost,&rk->VecsSensiTemp);
1056:   VecDestroy(&rk->VecDeltaMu);
1057:   return(0);
1058: }

1060: static PetscErrorCode TSReset_RK(TS ts)
1061: {

1065:   TSRKTableauReset(ts);
1066:   if (ts->use_splitrhsfunction) {
1067:     PetscTryMethod(ts,"TSReset_RK_MultirateSplit_C",(TS),(ts));
1068:   } else {
1069:     PetscTryMethod(ts,"TSReset_RK_MultirateNonsplit_C",(TS),(ts));
1070:   }
1071:   return(0);
1072: }

1074: static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx)
1075: {
1077:   return(0);
1078: }

1080: static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
1081: {
1083:   return(0);
1084: }


1087: static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx)
1088: {
1090:   return(0);
1091: }

1093: static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
1094: {

1097:   return(0);
1098: }

1100: static PetscErrorCode TSRKTableauSetUp(TS ts)
1101: {
1102:   TS_RK          *rk  = (TS_RK*)ts->data;
1103:   RKTableau      tab = rk->tableau;

1107:   PetscMalloc1(tab->s,&rk->work);
1108:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->Y);
1109:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->YdotRHS);
1110:   return(0);
1111: }

1113: static PetscErrorCode TSSetUp_RK(TS ts)
1114: {
1115:   TS             quadts = ts->quadraturets;
1117:   DM             dm;

1120:   TSCheckImplicitTerm(ts);
1121:   TSRKTableauSetUp(ts);
1122:   if (quadts && ts->costintegralfwd) {
1123:     Mat Jquad;
1124:     TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);
1125:   }
1126:   TSGetDM(ts,&dm);
1127:   DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
1128:   DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
1129:   if (ts->use_splitrhsfunction) {
1130:     PetscTryMethod(ts,"TSSetUp_RK_MultirateSplit_C",(TS),(ts));
1131:   } else {
1132:     PetscTryMethod(ts,"TSSetUp_RK_MultirateNonsplit_C",(TS),(ts));
1133:   }
1134:   return(0);
1135: }

1137: static PetscErrorCode TSSetFromOptions_RK(PetscOptionItems *PetscOptionsObject,TS ts)
1138: {
1139:   TS_RK          *rk = (TS_RK*)ts->data;

1143:   PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");
1144:   {
1145:     RKTableauLink link;
1146:     PetscInt      count,choice;
1147:     PetscBool     flg,use_multirate = PETSC_FALSE;
1148:     const char    **namelist;

1150:     for (link=RKTableauList,count=0; link; link=link->next,count++) ;
1151:     PetscMalloc1(count,(char***)&namelist);
1152:     for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
1153:     PetscOptionsBool("-ts_rk_multirate","Use interpolation-based multirate RK method","TSRKSetMultirate",rk->use_multirate,&use_multirate,&flg);
1154:     if (flg) {
1155:       TSRKSetMultirate(ts,use_multirate);
1156:     }
1157:     PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rk->tableau->name,&choice,&flg);
1158:     if (flg) {TSRKSetType(ts,namelist[choice]);}
1159:     PetscFree(namelist);
1160:   }
1161:   PetscOptionsTail();
1162:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Multirate methods options","");
1163:   PetscOptionsInt("-ts_rk_dtratio","time step ratio between slow and fast","",rk->dtratio,&rk->dtratio,NULL);
1164:   PetscOptionsEnd();
1165:   return(0);
1166: }

1168: static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer)
1169: {
1170:   TS_RK          *rk = (TS_RK*)ts->data;
1171:   PetscBool      iascii;

1175:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1176:   if (iascii) {
1177:     RKTableau tab  = rk->tableau;
1178:     TSRKType  rktype;
1179:     char      buf[512];
1180:     TSRKGetType(ts,&rktype);
1181:     PetscViewerASCIIPrintf(viewer,"  RK type %s\n",rktype);
1182:     PetscViewerASCIIPrintf(viewer,"  Order: %D\n",tab->order);
1183:     PetscViewerASCIIPrintf(viewer,"  FSAL property: %s\n",tab->FSAL ? "yes" : "no");
1184:     PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",tab->s,tab->c);
1185:     PetscViewerASCIIPrintf(viewer,"  Abscissa c = %s\n",buf);
1186:   }
1187:   return(0);
1188: }

1190: static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer)
1191: {
1193:   TSAdapt        adapt;

1196:   TSGetAdapt(ts,&adapt);
1197:   TSAdaptLoad(adapt,viewer);
1198:   return(0);
1199: }

1201: /*@C
1202:   TSRKSetType - Set the type of RK scheme

1204:   Logically collective

1206:   Input Parameter:
1207: +  ts - timestepping context
1208: -  rktype - type of RK-scheme

1210:   Options Database:
1211: .   -ts_rk_type - <1fe,2a,3,3bs,4,5f,5dp,5bs>

1213:   Level: intermediate

1215: .seealso: TSRKGetType(), TSRK, TSRKType, TSRK1FE, TSRK2A, TSRK3, TSRK3BS, TSRK4, TSRK5F, TSRK5DP, TSRK5BS, TSRK6VR, TSRK7VR, TSRK8VR
1216: @*/
1217: PetscErrorCode TSRKSetType(TS ts,TSRKType rktype)
1218: {

1224:   PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));
1225:   return(0);
1226: }

1228: /*@C
1229:   TSRKGetType - Get the type of RK scheme

1231:   Logically collective

1233:   Input Parameter:
1234: .  ts - timestepping context

1236:   Output Parameter:
1237: .  rktype - type of RK-scheme

1239:   Level: intermediate

1241: .seealso: TSRKGetType()
1242: @*/
1243: PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype)
1244: {

1249:   PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));
1250:   return(0);
1251: }

1253: static PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype)
1254: {
1255:   TS_RK *rk = (TS_RK*)ts->data;

1258:   *rktype = rk->tableau->name;
1259:   return(0);
1260: }

1262: static PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype)
1263: {
1264:   TS_RK          *rk = (TS_RK*)ts->data;
1266:   PetscBool      match;
1267:   RKTableauLink  link;

1270:   if (rk->tableau) {
1271:     PetscStrcmp(rk->tableau->name,rktype,&match);
1272:     if (match) return(0);
1273:   }
1274:   for (link = RKTableauList; link; link=link->next) {
1275:     PetscStrcmp(link->tab.name,rktype,&match);
1276:     if (match) {
1277:       if (ts->setupcalled) {TSRKTableauReset(ts);}
1278:       rk->tableau = &link->tab;
1279:       if (ts->setupcalled) {TSRKTableauSetUp(ts);}
1280:       ts->default_adapt_type = rk->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1281:       return(0);
1282:     }
1283:   }
1284:   SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype);
1285:   return(0);
1286: }

1288: static PetscErrorCode  TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y)
1289: {
1290:   TS_RK *rk = (TS_RK*)ts->data;

1293:   if (ns) *ns = rk->tableau->s;
1294:   if (Y)   *Y = rk->Y;
1295:   return(0);
1296: }

1298: static PetscErrorCode TSDestroy_RK(TS ts)
1299: {

1303:   TSReset_RK(ts);
1304:   if (ts->dm) {
1305:     DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
1306:     DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
1307:   }
1308:   PetscFree(ts->data);
1309:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);
1310:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);
1311:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",NULL);
1312:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",NULL);
1313:   return(0);
1314: }

1316: /*
1317:   This defines the nonlinear equation that is to be solved with SNES
1318:   We do not need to solve the equation; we just use SNES to approximate the Jacobian
1319: */
1320: static PetscErrorCode SNESTSFormFunction_RK(SNES snes,Vec x,Vec y,TS ts)
1321: {
1322:   TS_RK          *rk = (TS_RK*)ts->data;
1323:   DM             dm,dmsave;

1327:   SNESGetDM(snes,&dm);
1328:   /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
1329:   dmsave = ts->dm;
1330:   ts->dm = dm;
1331:   TSComputeRHSFunction(ts,rk->stage_time,x,y);
1332:   ts->dm = dmsave;
1333:   return(0);
1334: }

1336: static PetscErrorCode SNESTSFormJacobian_RK(SNES snes,Vec x,Mat A,Mat B,TS ts)
1337: {
1338:   TS_RK          *rk = (TS_RK*)ts->data;
1339:   DM             dm,dmsave;

1343:   SNESGetDM(snes,&dm);
1344:   dmsave = ts->dm;
1345:   ts->dm = dm;
1346:   TSComputeRHSJacobian(ts,rk->stage_time,x,A,B);
1347:   ts->dm = dmsave;
1348:   return(0);
1349: }

1351: /*@C
1352:   TSRKSetMultirate - Use the interpolation-based multirate RK method

1354:   Logically collective

1356:   Input Parameter:
1357: +  ts - timestepping context
1358: -  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

1360:   Options Database:
1361: .   -ts_rk_multirate - <true,false>

1363:   Notes:
1364:   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).

1366:   Level: intermediate

1368: .seealso: TSRKGetMultirate()
1369: @*/
1370: PetscErrorCode TSRKSetMultirate(TS ts,PetscBool use_multirate)
1371: {

1375:   PetscTryMethod(ts,"TSRKSetMultirate_C",(TS,PetscBool),(ts,use_multirate));
1376:   return(0);
1377: }

1379: /*@C
1380:   TSRKGetMultirate - Gets whether to Use the interpolation-based multirate RK method

1382:   Not collective

1384:   Input Parameter:
1385: .  ts - timestepping context

1387:   Output Parameter:
1388: .  use_multirate - PETSC_TRUE if the multirate RK method is enabled, PETSC_FALSE otherwise

1390:   Level: intermediate

1392: .seealso: TSRKSetMultirate()
1393: @*/
1394: PetscErrorCode TSRKGetMultirate(TS ts,PetscBool *use_multirate)
1395: {

1399:   PetscUseMethod(ts,"TSRKGetMultirate_C",(TS,PetscBool*),(ts,use_multirate));
1400:   return(0);
1401: }

1403: /*MC
1404:       TSRK - ODE and DAE solver using Runge-Kutta schemes

1406:   The user should provide the right hand side of the equation
1407:   using TSSetRHSFunction().

1409:   Notes:
1410:   The default is TSRK3BS, it can be changed with TSRKSetType() or -ts_rk_type

1412:   Level: beginner

1414: .seealso:  TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRKSetFullyImplicit(), TSRK2D, TTSRK2E, TSRK3,
1415:            TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister(), TSRKSetMultirate(), TSRKGetMultirate()

1417: M*/
1418: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
1419: {
1420:   TS_RK          *rk;

1424:   TSRKInitializePackage();

1426:   ts->ops->reset          = TSReset_RK;
1427:   ts->ops->destroy        = TSDestroy_RK;
1428:   ts->ops->view           = TSView_RK;
1429:   ts->ops->load           = TSLoad_RK;
1430:   ts->ops->setup          = TSSetUp_RK;
1431:   ts->ops->interpolate    = TSInterpolate_RK;
1432:   ts->ops->step           = TSStep_RK;
1433:   ts->ops->evaluatestep   = TSEvaluateStep_RK;
1434:   ts->ops->rollback       = TSRollBack_RK;
1435:   ts->ops->setfromoptions = TSSetFromOptions_RK;
1436:   ts->ops->getstages      = TSGetStages_RK;

1438:   ts->ops->snesfunction    = SNESTSFormFunction_RK;
1439:   ts->ops->snesjacobian    = SNESTSFormJacobian_RK;
1440:   ts->ops->adjointintegral = TSAdjointCostIntegral_RK;
1441:   ts->ops->adjointsetup    = TSAdjointSetUp_RK;
1442:   ts->ops->adjointstep     = TSAdjointStep_RK;
1443:   ts->ops->adjointreset    = TSAdjointReset_RK;

1445:   ts->ops->forwardintegral = TSForwardCostIntegral_RK;
1446:   ts->ops->forwardsetup    = TSForwardSetUp_RK;
1447:   ts->ops->forwardreset    = TSForwardReset_RK;
1448:   ts->ops->forwardstep     = TSForwardStep_RK;
1449:   ts->ops->forwardgetstages= TSForwardGetStages_RK;

1451:   PetscNewLog(ts,&rk);
1452:   ts->data = (void*)rk;

1454:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);
1455:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);
1456:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",TSRKSetMultirate_RK);
1457:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",TSRKGetMultirate_RK);

1459:   TSRKSetType(ts,TSRKDefault);
1460:   rk->dtratio = 1;
1461:   return(0);
1462: }