Actual source code: rk.c

petsc-master 2020-05-31
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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)}};
256:       TSRKRegister(TSRK5DP,5,7,&A[0][0],b,NULL,bembed,5,binterp[0]);
257:   }
258:   {
259:     const PetscReal
260:       A[8][8]   = {{0,0,0,0,0,0,0,0},
261:                    {RC(1.0)/RC(6.0),0,0,0,0,0,0,0},
262:                    {RC(2.0)/RC(27.0),RC(4.0)/RC(27.0),0,0,0,0,0,0},
263:                    {RC(183.0)/RC(1372.0),RC(-162.0)/RC(343.0),RC(1053.0)/RC(1372.0),0,0,0,0,0},
264:                    {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},
265:                    {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},
266:                    {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},
267:                    {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}},
268:       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},
269:       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)};
270:     TSRKRegister(TSRK5BS,5,8,&A[0][0],b,NULL,bembed,0,NULL);
271:   }
272:   {
273:     const PetscReal
274:       A[9][9]   = {{0,0,0,0,0,0,0,0,0},
275:                    {RC(1.8000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0},
276:                    {RC(8.9506172839506172839506172839506172839506e-02),RC(7.7160493827160493827160493827160493827160e-02),0,0,0,0,0,0,0},
277:                    {RC(6.2500000000000000000000000000000000000000e-02),0,RC(1.8750000000000000000000000000000000000000e-01),0,0,0,0,0,0},
278:                    {RC(3.1651600000000000000000000000000000000000e-01),0,RC(-1.0449480000000000000000000000000000000000e+00),RC(1.2584320000000000000000000000000000000000e+00),0,0,0,0,0},
279:                    {RC(2.7232612736485626257225065566674305502508e-01),0,RC(-8.2513360323886639676113360323886639676113e-01),RC(1.0480917678812415654520917678812415654521e+00),RC(1.0471570799276856873679117969088177628396e-01),0,0,0,0},
280:                    {RC(-1.6699418599716514314329607278961797333198e-01),0,RC(6.3170850202429149797570850202429149797571e-01),RC(1.7461044552773876082146758838488161796432e-01),RC(-1.0665356459086066122525194734018680677781e+00),RC(1.2272108843537414965986394557823129251701e+00),0,0,0},
281:                    {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},
282:                    {RC(7.6388888888888888888888888888888888888889e-02),0,0,RC(3.6940836940836940836940836940836940836941e-01),0,RC(2.4801587301587301587301587301587301587302e-01),RC(2.3674242424242424242424242424242424242424e-01),RC(6.9444444444444444444444444444444444444444e-02),0}},
283:       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},
284:       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)};
285:     TSRKRegister(TSRK6VR,6,9,&A[0][0],b,NULL,bembed,0,NULL);
286:   }
287:   {
288:     const PetscReal
289:       A[10][10]  = {{0,0,0,0,0,0,0,0,0,0},
290:                     {RC(5.0000000000000000000000000000000000000000e-03),0,0,0,0,0,0,0,0,0},
291:                     {RC(-1.0767901234567901234567901234567901234568e+00),RC(1.1856790123456790123456790123456790123457e+00),0,0,0,0,0,0,0,0},
292:                     {RC(4.0833333333333333333333333333333333333333e-02),0,RC(1.2250000000000000000000000000000000000000e-01),0,0,0,0,0,0,0},
293:                     {RC(6.3607142857142857142857142857142857142857e-01),0,RC(-2.4444642857142857142857142857142857142857e+00),RC(2.2633928571428571428571428571428571428571e+00),0,0,0,0,0,0},
294:                     {RC(-2.5351211079349245229256383554660215487207e+00),0,RC(1.0299374654449267920438514460756024913612e+01),RC(-7.9513032885990579949493217458266876536482e+00),RC(7.9301148923100592201226014271115261823800e-01),0,0,0,0,0},
295:                     {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},
296:                     {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},
297:                     {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},
298:                     {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}},
299:       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},
300:       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)};
301:     TSRKRegister(TSRK7VR,7,10,&A[0][0],b,NULL,bembed,0,NULL);
302:   }
303:   {
304:     const PetscReal
305:       A[13][13]  = {{0,0,0,0,0,0,0,0,0,0,0,0,0},
306:                     {RC(2.5000000000000000000000000000000000000000e-01),0,0,0,0,0,0,0,0,0,0,0,0},
307:                     {RC(8.7400846504915232052686327594877411977046e-02),RC(2.5487604938654321753087950620345685135815e-02),0,0,0,0,0,0,0,0,0,0,0},
308:                     {RC(4.2333169291338582677165354330708661417323e-02),0,RC(1.2699950787401574803149606299212598425197e-01),0,0,0,0,0,0,0,0,0,0},
309:                     {RC(4.2609505888742261494881445237572274090942e-01),0,RC(-1.5987952846591523265427733230657181117089e+00),RC(1.5967002257717297115939588706899953707994e+00),0,0,0,0,0,0,0,0,0},
310:                     {RC(5.0719337296713929515090618138513639239329e-02),0,0,RC(2.5433377264600407582754714408877778031369e-01),RC(2.0394689005728199465736223777270858044698e-01),0,0,0,0,0,0,0,0},
311:                     {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},
312:                     {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},
313:                     {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},
314:                     {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},
315:                     {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},
316:                     {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},
317:                     {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}},
318:       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},
319:       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)};
320:     TSRKRegister(TSRK8VR,8,13,&A[0][0],b,NULL,bembed,0,NULL);
321:   }
322: #undef RC
323:   return(0);
324: }

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

329:    Not Collective

331:    Level: advanced

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

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

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

358:   Level: developer

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

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

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

378:   Level: developer

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

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

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

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

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

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

411:    Level: advanced

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


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

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

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

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

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

463: PetscErrorCode TSRKGetTableau_RK(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed,
464:                                         PetscInt *p, const PetscReal **binterp, PetscBool *FSAL)
465: {
466:   TS_RK     *rk   = (TS_RK*)ts->data;
467:   RKTableau tab  = rk->tableau;

470:   if (s) *s = tab->s;
471:   if (A) *A = tab->A;
472:   if (b) *b = tab->b;
473:   if (c) *c = tab->c;
474:   if (bembed) *bembed = tab->bembed;
475:   if (p) *p = tab->p;
476:   if (binterp) *binterp = tab->binterp;
477:   if (FSAL) *FSAL = tab->FSAL;
478:   return(0);
479: }

481: /*@C
482:    TSRKGetTableau - Get info on the RK tableau

484:    Not Collective

486:    Input Parameters:
487: .  ts - timestepping context

489:    Output Parameters:
490: +  s - number of stages, this is the dimension of the matrices below
491: .  A - stage coefficients (dimension s*s, row-major)
492: .  b - step completion table (dimension s)
493: .  c - abscissa (dimension s)
494: .  bembed - completion table for embedded method (dimension s; NULL if not available)
495: .  p - Order of the interpolation scheme, equal to the number of columns of binterp
496: .  binterp - Coefficients of the interpolation formula (dimension s*p)
497: -  FSAL - wheather or not the scheme has the First Same As Last property

499:    Level: developer

501: .seealso: TSRK
502: @*/
503: PetscErrorCode TSRKGetTableau(TS ts, PetscInt *s, const PetscReal **A, const PetscReal **b, const PetscReal **c, const PetscReal **bembed,
504:                                      PetscInt *p, const PetscReal **binterp, PetscBool *FSAL)
505: {

510:   PetscUseMethod(ts,"TSRKGetTableau_C",(TS,PetscInt*,const PetscReal**,const PetscReal**,const PetscReal**,const PetscReal**,
511:                                                   PetscInt*,const PetscReal**,PetscBool*),(ts,s,A,b,c,bembed,p,binterp,FSAL));
512:   return(0);
513: }

515: /*
516:  This is for single-step RK method
517:  The step completion formula is

519:  x1 = x0 + h b^T YdotRHS

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

525:  x1e = x0 + h be^T YdotRHS
526:      = x1 - h b^T YdotRHS + h be^T YdotRHS
527:      = x1 + h (be - b)^T YdotRHS

529:  so we can evaluate the method with different order even after the step has been optimistically completed.
530: */
531: static PetscErrorCode TSEvaluateStep_RK(TS ts,PetscInt order,Vec X,PetscBool *done)
532: {
533:   TS_RK          *rk   = (TS_RK*)ts->data;
534:   RKTableau      tab  = rk->tableau;
535:   PetscScalar    *w    = rk->work;
536:   PetscReal      h;
537:   PetscInt       s    = tab->s,j;

541:   switch (rk->status) {
542:   case TS_STEP_INCOMPLETE:
543:   case TS_STEP_PENDING:
544:     h = ts->time_step; break;
545:   case TS_STEP_COMPLETE:
546:     h = ts->ptime - ts->ptime_prev; break;
547:   default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
548:   }
549:   if (order == tab->order) {
550:     if (rk->status == TS_STEP_INCOMPLETE) {
551:       VecCopy(ts->vec_sol,X);
552:       for (j=0; j<s; j++) w[j] = h*tab->b[j]/rk->dtratio;
553:       VecMAXPY(X,s,w,rk->YdotRHS);
554:     } else {VecCopy(ts->vec_sol,X);}
555:     return(0);
556:   } else if (order == tab->order-1) {
557:     if (!tab->bembed) goto unavailable;
558:     if (rk->status == TS_STEP_INCOMPLETE) { /*Complete with the embedded method (be)*/
559:       VecCopy(ts->vec_sol,X);
560:       for (j=0; j<s; j++) w[j] = h*tab->bembed[j];
561:       VecMAXPY(X,s,w,rk->YdotRHS);
562:     } else {  /*Rollback and re-complete using (be-b) */
563:       VecCopy(ts->vec_sol,X);
564:       for (j=0; j<s; j++) w[j] = h*(tab->bembed[j] - tab->b[j]);
565:       VecMAXPY(X,s,w,rk->YdotRHS);
566:     }
567:     if (done) *done = PETSC_TRUE;
568:     return(0);
569:   }
570: unavailable:
571:   if (done) *done = PETSC_FALSE;
572:   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);
573:   return(0);
574: }

576: static PetscErrorCode TSForwardCostIntegral_RK(TS ts)
577: {
578:   TS_RK           *rk = (TS_RK*)ts->data;
579:   TS              quadts = ts->quadraturets;
580:   RKTableau       tab = rk->tableau;
581:   const PetscInt  s = tab->s;
582:   const PetscReal *b = tab->b,*c = tab->c;
583:   Vec             *Y = rk->Y;
584:   PetscInt        i;
585:   PetscErrorCode  ierr;

588:   /* No need to backup quadts->vec_sol since it can be reverted in TSRollBack_RK */
589:   for (i=s-1; i>=0; i--) {
590:     /* Evolve quadrature TS solution to compute integrals */
591:     TSComputeRHSFunction(quadts,rk->ptime+rk->time_step*c[i],Y[i],ts->vec_costintegrand);
592:     VecAXPY(quadts->vec_sol,rk->time_step*b[i],ts->vec_costintegrand);
593:   }
594:   return(0);
595: }

597: static PetscErrorCode TSAdjointCostIntegral_RK(TS ts)
598: {
599:   TS_RK           *rk = (TS_RK*)ts->data;
600:   RKTableau       tab = rk->tableau;
601:   TS              quadts = ts->quadraturets;
602:   const PetscInt  s = tab->s;
603:   const PetscReal *b = tab->b,*c = tab->c;
604:   Vec             *Y = rk->Y;
605:   PetscInt        i;
606:   PetscErrorCode  ierr;

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

617: static PetscErrorCode TSRollBack_RK(TS ts)
618: {
619:   TS_RK           *rk = (TS_RK*)ts->data;
620:   TS              quadts = ts->quadraturets;
621:   RKTableau       tab = rk->tableau;
622:   const PetscInt  s  = tab->s;
623:   const PetscReal *b = tab->b,*c = tab->c;
624:   PetscScalar     *w = rk->work;
625:   Vec             *Y = rk->Y,*YdotRHS = rk->YdotRHS;
626:   PetscInt        j;
627:   PetscReal       h;
628:   PetscErrorCode  ierr;

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

651: static PetscErrorCode TSForwardStep_RK(TS ts)
652: {
653:   TS_RK           *rk = (TS_RK*)ts->data;
654:   RKTableau       tab = rk->tableau;
655:   Mat             J,*MatsFwdSensipTemp = rk->MatsFwdSensipTemp;
656:   const PetscInt  s = tab->s;
657:   const PetscReal *A = tab->A,*c = tab->c,*b = tab->b;
658:   Vec             *Y = rk->Y;
659:   PetscInt        i,j;
660:   PetscReal       stage_time,h = ts->time_step;
661:   PetscBool       zero;
662:   PetscErrorCode  ierr;

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;

715:   if (ns) *ns = tab->s;
716:   if (stagesensip) *stagesensip = rk->MatsFwdStageSensip;
717:   return(0);
718: }

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

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

731:   PetscMalloc1(tab->s,&rk->MatsFwdStageSensip);
732:   PetscMalloc1(tab->s,&rk->MatsFwdSensipTemp);
733:   for(i=0; i<tab->s; i++) {
734:     MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdStageSensip[i]);
735:     MatDuplicate(ts->mat_sensip,MAT_DO_NOT_COPY_VALUES,&rk->MatsFwdSensipTemp[i]);
736:   }
737:   VecDuplicate(ts->vec_sol,&rk->VecDeltaFwdSensipCol);
738:   return(0);
739: }

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

749:   MatDestroy(&rk->MatFwdSensip0);
750:   if (rk->MatsFwdStageSensip) {
751:     for (i=0; i<tab->s; i++) {
752:       MatDestroy(&rk->MatsFwdStageSensip[i]);
753:     }
754:     PetscFree(rk->MatsFwdStageSensip);
755:   }
756:   if (rk->MatsFwdSensipTemp) {
757:     for (i=0; i<tab->s; i++) {
758:       MatDestroy(&rk->MatsFwdSensipTemp[i]);
759:     }
760:     PetscFree(rk->MatsFwdSensipTemp);
761:   }
762:   VecDestroy(&rk->VecDeltaFwdSensipCol);
763:   return(0);
764: }

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

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

786:   rk->status = TS_STEP_INCOMPLETE;
787:   while (!ts->reason && rk->status != TS_STEP_COMPLETE) {
788:     PetscReal t = ts->ptime;
789:     PetscReal h = ts->time_step;
790:     for (i=0; i<s; i++) {
791:       rk->stage_time = t + h*c[i];
792:       TSPreStage(ts,rk->stage_time); 
793:       VecCopy(ts->vec_sol,Y[i]);
794:       for (j=0; j<i; j++) w[j] = h*A[i*s+j];
795:       VecMAXPY(Y[i],i,w,YdotRHS);
796:       TSPostStage(ts,rk->stage_time,i,Y); 
797:       TSGetAdapt(ts,&adapt);
798:       TSAdaptCheckStage(adapt,ts,rk->stage_time,Y[i],&stageok);
799:       if (!stageok) goto reject_step;
800:       if (FSAL && !i) continue;
801:       TSComputeRHSFunction(ts,t+h*c[i],Y[i],YdotRHS[i]);
802:     }

804:     rk->status = TS_STEP_INCOMPLETE;
805:     TSEvaluateStep(ts,tab->order,ts->vec_sol,NULL);
806:     rk->status = TS_STEP_PENDING;
807:     TSGetAdapt(ts,&adapt);
808:     TSAdaptCandidatesClear(adapt);
809:     TSAdaptCandidateAdd(adapt,tab->name,tab->order,1,tab->ccfl,(PetscReal)tab->s,PETSC_TRUE);
810:     TSAdaptChoose(adapt,ts,ts->time_step,NULL,&next_time_step,&accept);
811:     rk->status = accept ? TS_STEP_COMPLETE : TS_STEP_INCOMPLETE;
812:     if (!accept) { /* Roll back the current step */
813:       TSRollBack_RK(ts);
814:       ts->time_step = next_time_step;
815:       goto reject_step;
816:     }

818:     if (ts->costintegralfwd) { /* Save the info for the later use in cost integral evaluation */
819:       rk->ptime     = ts->ptime;
820:       rk->time_step = ts->time_step;
821:     }

823:     ts->ptime += ts->time_step;
824:     ts->time_step = next_time_step;
825:     break;

827:     reject_step:
828:     ts->reject++; accept = PETSC_FALSE;
829:     if (!ts->reason && ++rejections > ts->max_reject && ts->max_reject >= 0) {
830:       ts->reason = TS_DIVERGED_STEP_REJECTED;
831:       PetscInfo2(ts,"Step=%D, step rejections %D greater than current TS allowed, stopping solve\n",ts->steps,rejections);
832:     }
833:   }
834:   return(0);
835: }

837: static PetscErrorCode TSAdjointSetUp_RK(TS ts)
838: {
839:   TS_RK          *rk  = (TS_RK*)ts->data;
840:   RKTableau      tab = rk->tableau;
841:   PetscInt       s   = tab->s;

845:   if (ts->adjointsetupcalled++) return(0);
846:   VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam);
847:   VecDuplicateVecs(ts->vecs_sensi[0],ts->numcost,&rk->VecsSensiTemp);
848:   if(ts->vecs_sensip) {
849:     VecDuplicate(ts->vecs_sensip[0],&rk->VecDeltaMu);
850:   }
851:   if (ts->vecs_sensi2) {
852:     VecDuplicateVecs(ts->vecs_sensi[0],s*ts->numcost,&rk->VecsDeltaLam2);
853:     VecDuplicateVecs(ts->vecs_sensi2[0],ts->numcost,&rk->VecsSensi2Temp);
854:   }
855:   if (ts->vecs_sensi2p) {
856:     VecDuplicate(ts->vecs_sensi2p[0],&rk->VecDeltaMu2);
857:   }
858:   return(0);
859: }

861: /*
862:   Assumptions:
863:     - TSStep_RK() always evaluates the step with b, not bembed.
864: */
865: static PetscErrorCode TSAdjointStep_RK(TS ts)
866: {
867:   TS_RK            *rk = (TS_RK*)ts->data;
868:   TS               quadts = ts->quadraturets;
869:   RKTableau        tab = rk->tableau;
870:   Mat              J,Jpre,Jquad;
871:   const PetscInt   s = tab->s;
872:   const PetscReal  *A = tab->A,*b = tab->b,*c = tab->c;
873:   PetscScalar      *w = rk->work,*xarr;
874:   Vec              *Y = rk->Y,*VecsDeltaLam = rk->VecsDeltaLam,VecDeltaMu = rk->VecDeltaMu,*VecsSensiTemp = rk->VecsSensiTemp;
875:   Vec              *VecsDeltaLam2 = rk->VecsDeltaLam2,VecDeltaMu2 = rk->VecDeltaMu2,*VecsSensi2Temp = rk->VecsSensi2Temp;
876:   Vec              VecDRDUTransCol = ts->vec_drdu_col,VecDRDPTransCol = ts->vec_drdp_col;
877:   PetscInt         i,j,nadj;
878:   PetscReal        t = ts->ptime;
879:   PetscReal        h = ts->time_step;
880:   PetscErrorCode   ierr;

883:   rk->status = TS_STEP_INCOMPLETE;

885:   TSGetRHSJacobian(ts,&J,&Jpre,NULL,NULL);
886:   if (quadts) {
887:     TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);
888:   }
889:   for (i=s-1; i>=0; i--) {
890:     if (tab->FSAL && i == s-1) {
891:       /* VecsDeltaLam[nadj*s+s-1] are initialized with zeros and the values never change.*/
892:       continue;
893:     }
894:     rk->stage_time = t + h*(1.0-c[i]);
895:     TSComputeSNESJacobian(ts,Y[i],J,Jpre);
896:     if (quadts) {
897:       TSComputeRHSJacobian(quadts,rk->stage_time,Y[i],Jquad,Jquad); /* get r_u^T */
898:     }
899:     if (ts->vecs_sensip) {
900:       TSComputeRHSJacobianP(ts,rk->stage_time,Y[i],ts->Jacprhs); /* get f_p */
901:       if (quadts) {
902:         TSComputeRHSJacobianP(quadts,rk->stage_time,Y[i],quadts->Jacprhs); /* get f_p for the quadrature */
903:       }
904:     }

906:     if (b[i]) {
907:       for (j=i+1; j<s; j++) w[j-i-1] = A[j*s+i]/b[i]; /* coefficients for computing VecsSensiTemp */
908:     } else {
909:       for (j=i+1; j<s; j++) w[j-i-1] = A[j*s+i]; /* coefficients for computing VecsSensiTemp */
910:     }

912:     for (nadj=0; nadj<ts->numcost; nadj++) {
913:       /* Stage values of lambda */
914:       if (b[i]) {
915:         /* lambda_{n+1} + \sum_{j=i+1}^s a_{ji}/b[i]*lambda_{s,j} */
916:         VecCopy(ts->vecs_sensi[nadj],VecsSensiTemp[nadj]); /* VecDeltaLam is an vec array of size s by numcost */
917:         VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);
918:         MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]); /* VecsSensiTemp will be reused by 2nd-order adjoint */
919:         VecScale(VecsDeltaLam[nadj*s+i],-h*b[i]);
920:         if (quadts) {
921:           MatDenseGetColumn(Jquad,nadj,&xarr);
922:           VecPlaceArray(VecDRDUTransCol,xarr);
923:           VecAXPY(VecsDeltaLam[nadj*s+i],-h*b[i],VecDRDUTransCol);
924:           VecResetArray(VecDRDUTransCol);
925:           MatDenseRestoreColumn(Jquad,&xarr);
926:         }
927:       } else {
928:         /* \sum_{j=i+1}^s a_{ji}*lambda_{s,j} */
929:         VecSet(VecsSensiTemp[nadj],0);
930:         VecMAXPY(VecsSensiTemp[nadj],s-i-1,w,&VecsDeltaLam[nadj*s+i+1]);
931:         MatMultTranspose(J,VecsSensiTemp[nadj],VecsDeltaLam[nadj*s+i]);
932:         VecScale(VecsDeltaLam[nadj*s+i],-h);
933:       }

935:       /* Stage values of mu */
936:       if (ts->vecs_sensip) {
937:         MatMultTranspose(ts->Jacprhs,VecsSensiTemp[nadj],VecDeltaMu);
938:         if (b[i]) {
939:           VecScale(VecDeltaMu,-h*b[i]);
940:           if (quadts) {
941:             MatDenseGetColumn(quadts->Jacprhs,nadj,&xarr);
942:             VecPlaceArray(VecDRDPTransCol,xarr);
943:             VecAXPY(VecDeltaMu,-h*b[i],VecDRDPTransCol);
944:             VecResetArray(VecDRDPTransCol);
945:             MatDenseRestoreColumn(quadts->Jacprhs,&xarr);
946:           }
947:         } else {
948:           VecScale(VecDeltaMu,-h);
949:         }
950:         VecAXPY(ts->vecs_sensip[nadj],1.,VecDeltaMu); /* update sensip for each stage */
951:       }
952:     }

954:     if (ts->vecs_sensi2 && ts->forward_solve) { /* 2nd-order adjoint, TLM mode has to be turned on */
955:       /* Get w1 at t_{n+1} from TLM matrix */
956:       MatDenseGetColumn(rk->MatsFwdStageSensip[i],0,&xarr);
957:       VecPlaceArray(ts->vec_sensip_col,xarr);
958:       /* lambda_s^T F_UU w_1 */
959:       TSComputeRHSHessianProductFunctionUU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_guu);
960:       if (quadts)  {
961:         /* R_UU w_1 */
962:         TSComputeRHSHessianProductFunctionUU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_guu);
963:       }
964:       if (ts->vecs_sensip) {
965:         /* lambda_s^T F_UP w_2 */
966:         TSComputeRHSHessianProductFunctionUP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gup);
967:         if (quadts)  {
968:           /* R_UP w_2 */
969:           TSComputeRHSHessianProductFunctionUP(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gup);
970:         }
971:       }
972:       if (ts->vecs_sensi2p) {
973:         /* lambda_s^T F_PU w_1 */
974:         TSComputeRHSHessianProductFunctionPU(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_sensip_col,ts->vecs_gpu);
975:         /* lambda_s^T F_PP w_2 */
976:         TSComputeRHSHessianProductFunctionPP(ts,rk->stage_time,Y[i],VecsSensiTemp,ts->vec_dir,ts->vecs_gpp);
977:         if (b[i] && quadts) {
978:           /* R_PU w_1 */
979:           TSComputeRHSHessianProductFunctionPU(quadts,rk->stage_time,Y[i],NULL,ts->vec_sensip_col,ts->vecs_gpu);
980:           /* R_PP w_2 */
981:           TSComputeRHSHessianProductFunctionPP(quadts,rk->stage_time,Y[i],NULL,ts->vec_dir,ts->vecs_gpp);
982:         }
983:       }
984:       VecResetArray(ts->vec_sensip_col);
985:       MatDenseRestoreColumn(rk->MatsFwdStageSensip[i],&xarr);

987:       for (nadj=0; nadj<ts->numcost; nadj++) {
988:         /* Stage values of lambda */
989:         if (b[i]) {
990:           /* J_i^T*(Lambda_{n+1}+\sum_{j=i+1}^s a_{ji}/b_i*Lambda_{s,j} */
991:           VecCopy(ts->vecs_sensi2[nadj],VecsSensi2Temp[nadj]);
992:           VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);
993:           MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);
994:           VecScale(VecsDeltaLam2[nadj*s+i],-h*b[i]);
995:           VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_guu[nadj]);
996:           if (ts->vecs_sensip) {
997:             VecAXPY(VecsDeltaLam2[nadj*s+i],-h*b[i],ts->vecs_gup[nadj]);
998:           }
999:         } else {
1000:           /* \sum_{j=i+1}^s a_{ji}*Lambda_{s,j} */
1001:           VecSet(VecsDeltaLam2[nadj*s+i],0);
1002:           VecMAXPY(VecsSensi2Temp[nadj],s-i-1,w,&VecsDeltaLam2[nadj*s+i+1]);
1003:           MatMultTranspose(J,VecsSensi2Temp[nadj],VecsDeltaLam2[nadj*s+i]);
1004:           VecScale(VecsDeltaLam2[nadj*s+i],-h);
1005:           VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_guu[nadj]);
1006:           if (ts->vecs_sensip) {
1007:             VecAXPY(VecsDeltaLam2[nadj*s+i],-h,ts->vecs_gup[nadj]);
1008:           }
1009:         }
1010:         if (ts->vecs_sensi2p) { /* 2nd-order adjoint for parameters */
1011:           MatMultTranspose(ts->Jacprhs,VecsSensi2Temp[nadj],VecDeltaMu2);
1012:           if (b[i]) {
1013:             VecScale(VecDeltaMu2,-h*b[i]);
1014:             VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpu[nadj]);
1015:             VecAXPY(VecDeltaMu2,-h*b[i],ts->vecs_gpp[nadj]);
1016:           } else {
1017:             VecScale(VecDeltaMu2,-h);
1018:             VecAXPY(VecDeltaMu2,-h,ts->vecs_gpu[nadj]);
1019:             VecAXPY(VecDeltaMu2,-h,ts->vecs_gpp[nadj]);
1020:           }
1021:           VecAXPY(ts->vecs_sensi2p[nadj],1,VecDeltaMu2); /* update sensi2p for each stage */
1022:         }
1023:       }
1024:     }
1025:   }

1027:   for (j=0; j<s; j++) w[j] = 1.0;
1028:   for (nadj=0; nadj<ts->numcost; nadj++) { /* no need to do this for mu's */
1029:     VecMAXPY(ts->vecs_sensi[nadj],s,w,&VecsDeltaLam[nadj*s]);
1030:     if (ts->vecs_sensi2) {
1031:       VecMAXPY(ts->vecs_sensi2[nadj],s,w,&VecsDeltaLam2[nadj*s]);
1032:     }
1033:   }
1034:   rk->status = TS_STEP_COMPLETE;
1035:   return(0);
1036: }

1038: static PetscErrorCode TSAdjointReset_RK(TS ts)
1039: {
1040:   TS_RK          *rk = (TS_RK*)ts->data;
1041:   RKTableau      tab = rk->tableau;

1045:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam);
1046:   VecDestroyVecs(ts->numcost,&rk->VecsSensiTemp);
1047:   VecDestroy(&rk->VecDeltaMu);
1048:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam2);
1049:   VecDestroy(&rk->VecDeltaMu2);
1050:   VecDestroyVecs(ts->numcost,&rk->VecsSensi2Temp);
1051:   return(0);
1052: }

1054: static PetscErrorCode TSInterpolate_RK(TS ts,PetscReal itime,Vec X)
1055: {
1056:   TS_RK            *rk = (TS_RK*)ts->data;
1057:   PetscInt         s  = rk->tableau->s,p = rk->tableau->p,i,j;
1058:   PetscReal        h;
1059:   PetscReal        tt,t;
1060:   PetscScalar      *b;
1061:   const PetscReal  *B = rk->tableau->binterp;
1062:   PetscErrorCode   ierr;

1065:   if (!B) SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_SUP,"TSRK %s does not have an interpolation formula",rk->tableau->name);

1067:   switch (rk->status) {
1068:     case TS_STEP_INCOMPLETE:
1069:     case TS_STEP_PENDING:
1070:       h = ts->time_step;
1071:       t = (itime - ts->ptime)/h;
1072:       break;
1073:     case TS_STEP_COMPLETE:
1074:       h = ts->ptime - ts->ptime_prev;
1075:       t = (itime - ts->ptime)/h + 1; /* In the interval [0,1] */
1076:       break;
1077:     default: SETERRQ(PetscObjectComm((PetscObject)ts),PETSC_ERR_PLIB,"Invalid TSStepStatus");
1078:   }
1079:   PetscMalloc1(s,&b);
1080:   for (i=0; i<s; i++) b[i] = 0;
1081:   for (j=0,tt=t; j<p; j++,tt*=t) {
1082:     for (i=0; i<s; i++) {
1083:       b[i]  += h * B[i*p+j] * tt;
1084:     }
1085:   }
1086:   VecCopy(rk->Y[0],X);
1087:   VecMAXPY(X,s,b,rk->YdotRHS);
1088:   PetscFree(b);
1089:   return(0);
1090: }

1092: /*------------------------------------------------------------*/

1094: static PetscErrorCode TSRKTableauReset(TS ts)
1095: {
1096:   TS_RK          *rk = (TS_RK*)ts->data;
1097:   RKTableau      tab = rk->tableau;

1101:   if (!tab) return(0);
1102:   PetscFree(rk->work);
1103:   VecDestroyVecs(tab->s,&rk->Y);
1104:   VecDestroyVecs(tab->s,&rk->YdotRHS);
1105:   VecDestroyVecs(tab->s*ts->numcost,&rk->VecsDeltaLam);
1106:   VecDestroyVecs(ts->numcost,&rk->VecsSensiTemp);
1107:   VecDestroy(&rk->VecDeltaMu);
1108:   return(0);
1109: }

1111: static PetscErrorCode TSReset_RK(TS ts)
1112: {

1116:   TSRKTableauReset(ts);
1117:   if (ts->use_splitrhsfunction) {
1118:     PetscTryMethod(ts,"TSReset_RK_MultirateSplit_C",(TS),(ts));
1119:   } else {
1120:     PetscTryMethod(ts,"TSReset_RK_MultirateNonsplit_C",(TS),(ts));
1121:   }
1122:   return(0);
1123: }

1125: static PetscErrorCode DMCoarsenHook_TSRK(DM fine,DM coarse,void *ctx)
1126: {
1128:   return(0);
1129: }

1131: static PetscErrorCode DMRestrictHook_TSRK(DM fine,Mat restrct,Vec rscale,Mat inject,DM coarse,void *ctx)
1132: {
1134:   return(0);
1135: }


1138: static PetscErrorCode DMSubDomainHook_TSRK(DM dm,DM subdm,void *ctx)
1139: {
1141:   return(0);
1142: }

1144: static PetscErrorCode DMSubDomainRestrictHook_TSRK(DM dm,VecScatter gscat,VecScatter lscat,DM subdm,void *ctx)
1145: {

1148:   return(0);
1149: }

1151: static PetscErrorCode TSRKTableauSetUp(TS ts)
1152: {
1153:   TS_RK          *rk  = (TS_RK*)ts->data;
1154:   RKTableau      tab = rk->tableau;

1158:   PetscMalloc1(tab->s,&rk->work);
1159:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->Y);
1160:   VecDuplicateVecs(ts->vec_sol,tab->s,&rk->YdotRHS);
1161:   return(0);
1162: }

1164: static PetscErrorCode TSSetUp_RK(TS ts)
1165: {
1166:   TS             quadts = ts->quadraturets;
1168:   DM             dm;

1171:   TSCheckImplicitTerm(ts);
1172:   TSRKTableauSetUp(ts);
1173:   if (quadts && ts->costintegralfwd) {
1174:     Mat Jquad;
1175:     TSGetRHSJacobian(quadts,&Jquad,NULL,NULL,NULL);
1176:   }
1177:   TSGetDM(ts,&dm);
1178:   DMCoarsenHookAdd(dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
1179:   DMSubDomainHookAdd(dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
1180:   if (ts->use_splitrhsfunction) {
1181:     PetscTryMethod(ts,"TSSetUp_RK_MultirateSplit_C",(TS),(ts));
1182:   } else {
1183:     PetscTryMethod(ts,"TSSetUp_RK_MultirateNonsplit_C",(TS),(ts));
1184:   }
1185:   return(0);
1186: }

1188: static PetscErrorCode TSSetFromOptions_RK(PetscOptionItems *PetscOptionsObject,TS ts)
1189: {
1190:   TS_RK          *rk = (TS_RK*)ts->data;

1194:   PetscOptionsHead(PetscOptionsObject,"RK ODE solver options");
1195:   {
1196:     RKTableauLink link;
1197:     PetscInt      count,choice;
1198:     PetscBool     flg,use_multirate = PETSC_FALSE;
1199:     const char    **namelist;

1201:     for (link=RKTableauList,count=0; link; link=link->next,count++) ;
1202:     PetscMalloc1(count,(char***)&namelist);
1203:     for (link=RKTableauList,count=0; link; link=link->next,count++) namelist[count] = link->tab.name;
1204:     PetscOptionsBool("-ts_rk_multirate","Use interpolation-based multirate RK method","TSRKSetMultirate",rk->use_multirate,&use_multirate,&flg);
1205:     if (flg) {
1206:       TSRKSetMultirate(ts,use_multirate);
1207:     }
1208:     PetscOptionsEList("-ts_rk_type","Family of RK method","TSRKSetType",(const char*const*)namelist,count,rk->tableau->name,&choice,&flg);
1209:     if (flg) {TSRKSetType(ts,namelist[choice]);}
1210:     PetscFree(namelist);
1211:   }
1212:   PetscOptionsTail();
1213:   PetscOptionsBegin(PetscObjectComm((PetscObject)ts),NULL,"Multirate methods options","");
1214:   PetscOptionsInt("-ts_rk_dtratio","time step ratio between slow and fast","",rk->dtratio,&rk->dtratio,NULL);
1215:   PetscOptionsEnd();
1216:   return(0);
1217: }

1219: static PetscErrorCode TSView_RK(TS ts,PetscViewer viewer)
1220: {
1221:   TS_RK          *rk = (TS_RK*)ts->data;
1222:   PetscBool      iascii;

1226:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1227:   if (iascii) {
1228:     RKTableau       tab  = rk->tableau;
1229:     TSRKType        rktype;
1230:     const PetscReal *c;
1231:     PetscInt        s;
1232:     char            buf[512];
1233:     PetscBool       FSAL;

1235:     TSRKGetType(ts,&rktype);
1236:     TSRKGetTableau(ts,&s,NULL,NULL,&c,NULL,NULL,NULL,&FSAL);
1237:     PetscViewerASCIIPrintf(viewer,"  RK type %s\n",rktype);
1238:     PetscViewerASCIIPrintf(viewer,"  Order: %D\n",tab->order);
1239:     PetscViewerASCIIPrintf(viewer,"  FSAL property: %s\n",FSAL ? "yes" : "no");
1240:     PetscFormatRealArray(buf,sizeof(buf),"% 8.6f",s,c);
1241:     PetscViewerASCIIPrintf(viewer,"  Abscissa c = %s\n",buf);
1242:   }
1243:   return(0);
1244: }

1246: static PetscErrorCode TSLoad_RK(TS ts,PetscViewer viewer)
1247: {
1249:   TSAdapt        adapt;

1252:   TSGetAdapt(ts,&adapt);
1253:   TSAdaptLoad(adapt,viewer);
1254:   return(0);
1255: }

1257: /*@
1258:   TSRKGetOrder - Get the order of RK scheme

1260:   Not collective

1262:   Input Parameter:
1263: .  ts - timestepping context

1265:   Output Parameter:
1266: .  order - order of RK-scheme

1268:   Level: intermediate

1270: .seealso: TSRKGetType()
1271: @*/
1272: PetscErrorCode TSRKGetOrder(TS ts,PetscInt *order)
1273: {

1279:   PetscUseMethod(ts,"TSRKGetOrder_C",(TS,PetscInt*),(ts,order));
1280:   return(0);
1281: }

1283: /*@C
1284:   TSRKSetType - Set the type of RK scheme

1286:   Logically collective

1288:   Input Parameter:
1289: +  ts - timestepping context
1290: -  rktype - type of RK-scheme

1292:   Options Database:
1293: .   -ts_rk_type - <1fe,2a,3,3bs,4,5f,5dp,5bs>

1295:   Level: intermediate

1297: .seealso: TSRKGetType(), TSRK, TSRKType, TSRK1FE, TSRK2A, TSRK3, TSRK3BS, TSRK4, TSRK5F, TSRK5DP, TSRK5BS, TSRK6VR, TSRK7VR, TSRK8VR
1298: @*/
1299: PetscErrorCode TSRKSetType(TS ts,TSRKType rktype)
1300: {

1306:   PetscTryMethod(ts,"TSRKSetType_C",(TS,TSRKType),(ts,rktype));
1307:   return(0);
1308: }

1310: /*@C
1311:   TSRKGetType - Get the type of RK scheme

1313:   Not collective

1315:   Input Parameter:
1316: .  ts - timestepping context

1318:   Output Parameter:
1319: .  rktype - type of RK-scheme

1321:   Level: intermediate

1323: .seealso: TSRKSetType()
1324: @*/
1325: PetscErrorCode TSRKGetType(TS ts,TSRKType *rktype)
1326: {

1331:   PetscUseMethod(ts,"TSRKGetType_C",(TS,TSRKType*),(ts,rktype));
1332:   return(0);
1333: }

1335: static PetscErrorCode TSRKGetOrder_RK(TS ts,PetscInt *order)
1336: {
1337:   TS_RK *rk = (TS_RK*)ts->data;

1340:   *order = rk->tableau->order;
1341:   return(0);
1342: }

1344: static PetscErrorCode TSRKGetType_RK(TS ts,TSRKType *rktype)
1345: {
1346:   TS_RK *rk = (TS_RK*)ts->data;

1349:   *rktype = rk->tableau->name;
1350:   return(0);
1351: }

1353: static PetscErrorCode TSRKSetType_RK(TS ts,TSRKType rktype)
1354: {
1355:   TS_RK          *rk = (TS_RK*)ts->data;
1357:   PetscBool      match;
1358:   RKTableauLink  link;

1361:   if (rk->tableau) {
1362:     PetscStrcmp(rk->tableau->name,rktype,&match);
1363:     if (match) return(0);
1364:   }
1365:   for (link = RKTableauList; link; link=link->next) {
1366:     PetscStrcmp(link->tab.name,rktype,&match);
1367:     if (match) {
1368:       if (ts->setupcalled) {TSRKTableauReset(ts);}
1369:       rk->tableau = &link->tab;
1370:       if (ts->setupcalled) {TSRKTableauSetUp(ts);}
1371:       ts->default_adapt_type = rk->tableau->bembed ? TSADAPTBASIC : TSADAPTNONE;
1372:       return(0);
1373:     }
1374:   }
1375:   SETERRQ1(PetscObjectComm((PetscObject)ts),PETSC_ERR_ARG_UNKNOWN_TYPE,"Could not find '%s'",rktype);
1376:   return(0);
1377: }

1379: static PetscErrorCode  TSGetStages_RK(TS ts,PetscInt *ns,Vec **Y)
1380: {
1381:   TS_RK *rk = (TS_RK*)ts->data;

1384:   if (ns) *ns = rk->tableau->s;
1385:   if (Y)   *Y = rk->Y;
1386:   return(0);
1387: }

1389: static PetscErrorCode TSDestroy_RK(TS ts)
1390: {

1394:   TSReset_RK(ts);
1395:   if (ts->dm) {
1396:     DMCoarsenHookRemove(ts->dm,DMCoarsenHook_TSRK,DMRestrictHook_TSRK,ts);
1397:     DMSubDomainHookRemove(ts->dm,DMSubDomainHook_TSRK,DMSubDomainRestrictHook_TSRK,ts);
1398:   }
1399:   PetscFree(ts->data);
1400:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetOrder_C",NULL);
1401:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",NULL);
1402:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",NULL);
1403:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetTableau_C",NULL);
1404:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",NULL);
1405:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",NULL);
1406:   return(0);
1407: }

1409: /*
1410:   This defines the nonlinear equation that is to be solved with SNES
1411:   We do not need to solve the equation; we just use SNES to approximate the Jacobian
1412: */
1413: static PetscErrorCode SNESTSFormFunction_RK(SNES snes,Vec x,Vec y,TS ts)
1414: {
1415:   TS_RK          *rk = (TS_RK*)ts->data;
1416:   DM             dm,dmsave;

1420:   SNESGetDM(snes,&dm);
1421:   /* DM monkey-business allows user code to call TSGetDM() inside of functions evaluated on levels of FAS */
1422:   dmsave = ts->dm;
1423:   ts->dm = dm;
1424:   TSComputeRHSFunction(ts,rk->stage_time,x,y);
1425:   ts->dm = dmsave;
1426:   return(0);
1427: }

1429: static PetscErrorCode SNESTSFormJacobian_RK(SNES snes,Vec x,Mat A,Mat B,TS ts)
1430: {
1431:   TS_RK          *rk = (TS_RK*)ts->data;
1432:   DM             dm,dmsave;

1436:   SNESGetDM(snes,&dm);
1437:   dmsave = ts->dm;
1438:   ts->dm = dm;
1439:   TSComputeRHSJacobian(ts,rk->stage_time,x,A,B);
1440:   ts->dm = dmsave;
1441:   return(0);
1442: }

1444: /*@C
1445:   TSRKSetMultirate - Use the interpolation-based multirate RK method

1447:   Logically collective

1449:   Input Parameter:
1450: +  ts - timestepping context
1451: -  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

1453:   Options Database:
1454: .   -ts_rk_multirate - <true,false>

1456:   Notes:
1457:   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).

1459:   Level: intermediate

1461: .seealso: TSRKGetMultirate()
1462: @*/
1463: PetscErrorCode TSRKSetMultirate(TS ts,PetscBool use_multirate)
1464: {

1468:   PetscTryMethod(ts,"TSRKSetMultirate_C",(TS,PetscBool),(ts,use_multirate));
1469:   return(0);
1470: }

1472: /*@C
1473:   TSRKGetMultirate - Gets whether to Use the interpolation-based multirate RK method

1475:   Not collective

1477:   Input Parameter:
1478: .  ts - timestepping context

1480:   Output Parameter:
1481: .  use_multirate - PETSC_TRUE if the multirate RK method is enabled, PETSC_FALSE otherwise

1483:   Level: intermediate

1485: .seealso: TSRKSetMultirate()
1486: @*/
1487: PetscErrorCode TSRKGetMultirate(TS ts,PetscBool *use_multirate)
1488: {

1492:   PetscUseMethod(ts,"TSRKGetMultirate_C",(TS,PetscBool*),(ts,use_multirate));
1493:   return(0);
1494: }

1496: /*MC
1497:       TSRK - ODE and DAE solver using Runge-Kutta schemes

1499:   The user should provide the right hand side of the equation
1500:   using TSSetRHSFunction().

1502:   Notes:
1503:   The default is TSRK3BS, it can be changed with TSRKSetType() or -ts_rk_type

1505:   Level: beginner

1507: .seealso:  TSCreate(), TS, TSSetType(), TSRKSetType(), TSRKGetType(), TSRK2D, TTSRK2E, TSRK3,
1508:            TSRK4, TSRK5, TSRKPRSSP2, TSRKBPR3, TSRKType, TSRKRegister(), TSRKSetMultirate(), TSRKGetMultirate()

1510: M*/
1511: PETSC_EXTERN PetscErrorCode TSCreate_RK(TS ts)
1512: {
1513:   TS_RK          *rk;

1517:   TSRKInitializePackage();

1519:   ts->ops->reset          = TSReset_RK;
1520:   ts->ops->destroy        = TSDestroy_RK;
1521:   ts->ops->view           = TSView_RK;
1522:   ts->ops->load           = TSLoad_RK;
1523:   ts->ops->setup          = TSSetUp_RK;
1524:   ts->ops->interpolate    = TSInterpolate_RK;
1525:   ts->ops->step           = TSStep_RK;
1526:   ts->ops->evaluatestep   = TSEvaluateStep_RK;
1527:   ts->ops->rollback       = TSRollBack_RK;
1528:   ts->ops->setfromoptions = TSSetFromOptions_RK;
1529:   ts->ops->getstages      = TSGetStages_RK;

1531:   ts->ops->snesfunction    = SNESTSFormFunction_RK;
1532:   ts->ops->snesjacobian    = SNESTSFormJacobian_RK;
1533:   ts->ops->adjointintegral = TSAdjointCostIntegral_RK;
1534:   ts->ops->adjointsetup    = TSAdjointSetUp_RK;
1535:   ts->ops->adjointstep     = TSAdjointStep_RK;
1536:   ts->ops->adjointreset    = TSAdjointReset_RK;

1538:   ts->ops->forwardintegral = TSForwardCostIntegral_RK;
1539:   ts->ops->forwardsetup    = TSForwardSetUp_RK;
1540:   ts->ops->forwardreset    = TSForwardReset_RK;
1541:   ts->ops->forwardstep     = TSForwardStep_RK;
1542:   ts->ops->forwardgetstages= TSForwardGetStages_RK;

1544:   PetscNewLog(ts,&rk);
1545:   ts->data = (void*)rk;

1547:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetOrder_C",TSRKGetOrder_RK);
1548:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetType_C",TSRKGetType_RK);
1549:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetType_C",TSRKSetType_RK);
1550:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetTableau_C",TSRKGetTableau_RK);
1551:   PetscObjectComposeFunction((PetscObject)ts,"TSRKSetMultirate_C",TSRKSetMultirate_RK);
1552:   PetscObjectComposeFunction((PetscObject)ts,"TSRKGetMultirate_C",TSRKGetMultirate_RK);

1554:   TSRKSetType(ts,TSRKDefault);
1555:   rk->dtratio = 1;
1556:   return(0);
1557: }