Actual source code: adaptdsp.c

      1: #include <petsc/private/tsimpl.h>
      2: #include <petscdm.h>

      4: static const char *citation[] = {
      5:   "@article{Soderlind2003,\n"
      6:   " author = {S\"{o}derlind, Gustaf},\n"
      7:   " title = {Digital Filters in Adaptive Time-stepping},\n"
      8:   " journal = {ACM Transactions on Mathematical Software},\n"
      9:   " volume = {29},\n"
     10:   " number = {1},\n"
     11:   " pages = {1--26},\n"
     12:   " year = {2003},\n"
     13:   " issn = {0098-3500},\n"
     14:   " doi = {http://dx.doi.org/10.1145/641876.641877},\n"
     15:   "}\n",
     16:   "@article{Soderlind2006,\n"
     17:   " author = {Gustaf S\"{o}derlind and Lina Wang},\n"
     18:   " title = {Adaptive time-stepping and computational stability},\n"
     19:   " journal = {Journal of Computational and Applied Mathematics},\n"
     20:   " volume = {185},\n"
     21:   " number = {2},\n"
     22:   " pages = {225--243},\n"
     23:   " year = {2006},\n"
     24:   " issn = {0377-0427},\n"
     25:   " doi = {http://dx.doi.org/10.1016/j.cam.2005.03.008},\n"
     26:   "}\n",
     27: };
     28: static PetscBool cited[] = {PETSC_FALSE,PETSC_FALSE};

     30: typedef struct {
     31:   PetscReal kBeta[3];  /* filter parameters */
     32:   PetscReal Alpha[2];  /* filter parameters */
     33:   PetscReal cerror[3]; /* control error (controller input) history */
     34:   PetscReal hratio[3]; /* stepsize ratio (controller output) history */
     35:   PetscBool rollback;
     36: } TSAdapt_DSP;

     38: static PetscReal Limiter(PetscReal value,PetscReal kappa)
     39: {
     40:   return 1 + kappa*PetscAtanReal((value - 1)/kappa);
     41: }

     43: static PetscErrorCode TSAdaptRestart_DSP(TSAdapt adapt)
     44: {
     45:   TSAdapt_DSP *dsp = (TSAdapt_DSP*)adapt->data;
     47:   dsp->cerror[0] = dsp->hratio[0] = 1.0;
     48:   dsp->cerror[1] = dsp->hratio[1] = 1.0;
     49:   dsp->cerror[2] = dsp->hratio[2] = 1.0;
     50:   return(0);
     51: }

     53: static PetscErrorCode TSAdaptRollBack_DSP(TSAdapt adapt)
     54: {
     55:   TSAdapt_DSP *dsp = (TSAdapt_DSP*)adapt->data;
     57:   dsp->cerror[0] = dsp->cerror[1];
     58:   dsp->cerror[1] = dsp->cerror[2];
     59:   dsp->cerror[2] = 1.0;
     60:   dsp->hratio[0] = dsp->hratio[1];
     61:   dsp->hratio[1] = dsp->hratio[2];
     62:   dsp->hratio[2] = 1.0;
     63:   return(0);
     64: }

     66: static PetscErrorCode TSAdaptChoose_DSP(TSAdapt adapt,TS ts,PetscReal h,PetscInt *next_sc,PetscReal *next_h,PetscBool *accept,PetscReal *wlte,PetscReal *wltea,PetscReal *wlter)
     67: {
     68:   TSAdapt_DSP    *dsp = (TSAdapt_DSP*)adapt->data;
     69:   PetscInt       order = PETSC_DECIDE;
     70:   PetscReal      enorm = -1;
     71:   PetscReal      enorma,enormr;
     72:   PetscReal      safety = adapt->safety * (PetscReal)0.9;
     73:   PetscReal      hnew,hfac = PETSC_INFINITY;
     74:   PetscReal      hmin = adapt->dt_min*(1 + PETSC_SQRT_MACHINE_EPSILON);

     78:   *next_sc = 0;   /* Reuse the same order scheme */
     79:   *wltea   = -1;  /* Weighted absolute local truncation error is not used */
     80:   *wlter   = -1;  /* Weighted relative local truncation error is not used */

     82:   if (ts->ops->evaluatewlte) {
     83:     TSEvaluateWLTE(ts,adapt->wnormtype,&order,&enorm);
     84:     if (enorm >= 0 && order < 1) SETERRQ1(PetscObjectComm((PetscObject)adapt),PETSC_ERR_ARG_OUTOFRANGE,"Computed error order %D must be positive",order);
     85:   } else if (ts->ops->evaluatestep) {
     86:     DM  dm;
     87:     Vec Y;

     89:     if (adapt->candidates.n < 1) SETERRQ(PetscObjectComm((PetscObject)adapt),PETSC_ERR_ARG_WRONGSTATE,"No candidate has been registered");
     90:     if (!adapt->candidates.inuse_set) SETERRQ1(PetscObjectComm((PetscObject)adapt),PETSC_ERR_ARG_WRONGSTATE,"The current in-use scheme is not among the %D candidates",adapt->candidates.n);
     91:     order = adapt->candidates.order[0];
     92:     TSGetDM(ts,&dm);
     93:     DMGetGlobalVector(dm,&Y);
     94:     TSEvaluateStep(ts,order-1,Y,NULL);
     95:     TSErrorWeightedNorm(ts,ts->vec_sol,Y,adapt->wnormtype,&enorm,&enorma,&enormr);
     96:     DMRestoreGlobalVector(dm,&Y);
     97:   }
     98:   if (enorm < 0) {
     99:     TSAdaptRestart_DSP(adapt);
    100:     *accept = PETSC_TRUE;  /* Accept the step */
    101:     *next_h = h;           /* Reuse the old step size */
    102:     *wlte   = -1;          /* Weighted local truncation error was not evaluated */
    103:     return(0);
    104:   }

    106:   PetscCitationsRegister(citation[0],&cited[0]);
    107:   PetscCitationsRegister(citation[1],&cited[1]);

    109:   /* Update history after rollback */
    110:   if (!ts->steprollback)
    111:     dsp->rollback = PETSC_FALSE;
    112:   else if (!dsp->rollback) {
    113:     dsp->rollback = PETSC_TRUE;
    114:     TSAdaptRollBack_DSP(adapt);
    115:   }
    116:   /* Reset history after restart */
    117:   if (ts->steprestart) {
    118:     TSAdaptRestart_DSP(adapt);
    119:   }

    121:   {
    122:     PetscReal k = (PetscReal)order;
    123:     PetscReal b1 = dsp->kBeta[0];
    124:     PetscReal b2 = dsp->kBeta[1];
    125:     PetscReal b3 = dsp->kBeta[2];
    126:     PetscReal a2 = dsp->Alpha[0];
    127:     PetscReal a3 = dsp->Alpha[1];

    129:     PetscReal ctr0;
    130:     PetscReal ctr1 = dsp->cerror[0];
    131:     PetscReal ctr2 = dsp->cerror[1];
    132:     PetscReal rho0;
    133:     PetscReal rho1 = dsp->hratio[0];
    134:     PetscReal rho2 = dsp->hratio[1];

    136:     /* Compute the step size ratio */
    137:     enorm = PetscMax(enorm,PETSC_SMALL);
    138:     ctr0  = PetscPowReal(1/enorm,1/k);
    139:     rho0  = PetscPowReal(ctr0,b1);
    140:     rho0 *= PetscPowReal(ctr1,b2);
    141:     rho0 *= PetscPowReal(ctr2,b3);
    142:     rho0 *= PetscPowReal(rho1,-a2);
    143:     rho0 *= PetscPowReal(rho2,-a3);
    144:     rho0  = Limiter(rho0,1);

    146:     /* Determine whether the step is accepted or rejected */
    147:     if (rho0 >= safety)
    148:       *accept = PETSC_TRUE;
    149:     else if (adapt->always_accept)
    150:       *accept = PETSC_TRUE;
    151:     else if (h < hmin)
    152:       *accept = PETSC_TRUE;
    153:     else
    154:       *accept = PETSC_FALSE;

    156:     /* Update history after accept */
    157:     if (*accept) {
    158:       dsp->cerror[2] = dsp->cerror[1];
    159:       dsp->cerror[1] = dsp->cerror[0];
    160:       dsp->cerror[0] = ctr0;
    161:       dsp->hratio[2] = dsp->hratio[1];
    162:       dsp->hratio[1] = dsp->hratio[0];
    163:       dsp->hratio[0] = rho0;
    164:       dsp->rollback  = PETSC_FALSE;
    165:     }

    167:     hfac = rho0;
    168:   }

    170:   hnew    = h * PetscClipInterval(hfac,adapt->clip[0],adapt->clip[1]);
    171:   *next_h = PetscClipInterval(hnew,adapt->dt_min,adapt->dt_max);
    172:   *wlte   = enorm;
    173:   return(0);
    174: }

    176: static PetscErrorCode TSAdaptDestroy_DSP(TSAdapt adapt)
    177: {

    181:   PetscObjectComposeFunction((PetscObject)adapt,"TSAdaptDSPSetFilter_C",NULL);
    182:   PetscObjectComposeFunction((PetscObject)adapt,"TSAdaptDSPSetPID_C",NULL);
    183:   PetscFree(adapt->data);
    184:   return(0);
    185: }

    187: static PetscErrorCode TSAdaptView_DSP(TSAdapt adapt,PetscViewer viewer)
    188: {
    189:   TSAdapt_DSP    *dsp = (TSAdapt_DSP*)adapt->data;
    190:   PetscBool      iascii;

    194:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    195:   if (iascii) {
    196:     double a2 = (double)dsp->Alpha[0], a3 = (double)dsp->Alpha[1];
    197:     double b1 = (double)dsp->kBeta[0], b2 = (double)dsp->kBeta[1], b3 = (double)dsp->kBeta[2];
    198:     PetscViewerASCIIPrintf(viewer,"filter parameters kBeta=[%g,%g,%g] Alpha=[%g,%g]\n",b1,b2,b3,a2,a3);
    199:   }
    200:   return(0);
    201: }

    203: struct FilterTab {
    204:   const char *name;
    205:   PetscReal scale;
    206:   PetscReal kBeta[3];
    207:   PetscReal Alpha[2];
    208: };

    210: static struct FilterTab filterlist[] = {
    211:   {"basic",    1, {  1,  0,  0 }, {   0,  0 }},

    213:   {"PI30",     3, {  1,  0,  0 }, {   0,  0 }},
    214:   {"PI42",     5, {  3, -1,  0 }, {   0,  0 }},
    215:   {"PI33",     3, {  2, -1,  0 }, {   0,  0 }},
    216:   {"PI34",    10, {  7, -4,  0 }, {   0,  0 }},

    218:   {"PC11",     1, {  2, -1,  0 }, {  -1,  0 }},
    219:   {"PC47",    10, { 11, -7,  0 }, { -10,  0 }},
    220:   {"PC36",    10, {  9, -6,  0 }, { -10,  0 }},

    222:   {"H0211",    2, {  1,  1,  0 }, {   1,  0 }},
    223:   {"H211b",    4, {  1,  1,  0 }, {   1,  0 }},
    224:   {"H211PI",   6, {  1,  1,  0 }, {   0,  0 }},

    226:   {"H0312",    4, {  1,  2,  1 }, {   3,  1 }},
    227:   {"H312b",    8, {  1,  2,  1 }, {   3,  1 }},
    228:   {"H312PID", 18, {  1,  2,  1 }, {   0,  0 }},

    230:   {"H0321",    4, {  5,  2, -3 }, {  -1, -3 }},
    231:   {"H321",    18, {  6,  1, -5 }, { -15, -3 }},
    232: };

    234: static PetscErrorCode TSAdaptDSPSetFilter_DSP(TSAdapt adapt,const char *name)
    235: {
    236:   TSAdapt_DSP       *dsp = (TSAdapt_DSP*)adapt->data;
    237:   PetscInt          i,count = (PetscInt)(sizeof(filterlist)/sizeof(filterlist[0]));
    238:   struct FilterTab* tab = NULL;
    239:   PetscBool         match;
    240:   PetscErrorCode    ierr;

    243:   for (i=0; i<count; i++) {
    244:     PetscStrcasecmp(name,filterlist[i].name,&match);
    245:     if (match) { tab = &filterlist[i]; break; }
    246:   }
    247:   if (!tab) SETERRQ1(PetscObjectComm((PetscObject)adapt),PETSC_ERR_ARG_UNKNOWN_TYPE,"Filter name %s not found",name);
    248:   dsp->kBeta[0] = tab->kBeta[0]/tab->scale;
    249:   dsp->kBeta[1] = tab->kBeta[1]/tab->scale;
    250:   dsp->kBeta[2] = tab->kBeta[2]/tab->scale;
    251:   dsp->Alpha[0] = tab->Alpha[0]/tab->scale;
    252:   dsp->Alpha[1] = tab->Alpha[1]/tab->scale;
    253:   return(0);
    254: }

    256: static PetscErrorCode TSAdaptDSPSetPID_DSP(TSAdapt adapt,PetscReal kkI,PetscReal kkP,PetscReal kkD)
    257: {
    258:   TSAdapt_DSP    *dsp = (TSAdapt_DSP*)adapt->data;

    261:   dsp->kBeta[0] = kkI + kkP + kkD;
    262:   dsp->kBeta[1] = -(kkP + 2*kkD);
    263:   dsp->kBeta[2] = kkD;
    264:   dsp->Alpha[0] = 0;
    265:   dsp->Alpha[1] = 0;
    266:   return(0);
    267: }

    269: static PetscErrorCode TSAdaptSetFromOptions_DSP(PetscOptionItems *PetscOptionsObject,TSAdapt adapt)
    270: {
    271:   TSAdapt_DSP    *dsp = (TSAdapt_DSP*)adapt->data;
    272:   const char     *names[sizeof(filterlist)/sizeof(filterlist[0])];
    273:   PetscInt       count = (PetscInt)(sizeof(filterlist)/sizeof(filterlist[0]));
    274:   PetscInt       index = 2; /* PI42 */
    275:   PetscReal      pid[3] = {1,0,0};
    276:   PetscInt       i,n;
    277:   PetscBool      set;

    281:   for (i=0; i<count; i++) names[i] = filterlist[i].name;
    282:   PetscOptionsHead(PetscOptionsObject,"DSP adaptive controller options");

    284:   PetscOptionsEList("-ts_adapt_dsp_filter","Filter name","TSAdaptDSPSetFilter",names,count,names[index],&index,&set);
    285:   if (set) { TSAdaptDSPSetFilter(adapt,names[index]);}

    287:   PetscOptionsRealArray("-ts_adapt_dsp_pid","PID parameters <kkI,kkP,kkD>","TSAdaptDSPSetPID",pid,(n=3,&n),&set);
    288:   if (set && !n) SETERRQ(PetscObjectComm((PetscObject)adapt),PETSC_ERR_ARG_WRONG,"Must provide at least one value for PID parameters");
    289:   if (set) {TSAdaptDSPSetPID(adapt,pid[0],pid[1],pid[2]);}

    291:   PetscOptionsRealArray("-ts_adapt_dsp_kbeta","Filter parameters","",dsp->kBeta,(n=3,&n),&set);
    292:   if (set && !n) SETERRQ(PetscObjectComm((PetscObject)adapt),PETSC_ERR_ARG_WRONG,"Must provide at least one value for parameter kbeta");
    293:   if (set) for (i=n; i<3; i++) dsp->kBeta[i] = 0;

    295:   PetscOptionsRealArray("-ts_adapt_dsp_alpha","Filter parameters","",dsp->Alpha,(n=2,&n),&set);
    296:   if (set && !n) SETERRQ(PetscObjectComm((PetscObject)adapt),PETSC_ERR_ARG_WRONG,"Must provide at least one value for parameter alpha");
    297:   if (set) for (i=n; i<2; i++) dsp->Alpha[i] = 0;

    299:   PetscOptionsTail();
    300:   return(0);
    301: }

    303: /*@C
    304:    TSAdaptDSPSetFilter - Sets internal parameters corresponding to the named filter

    306:    Collective on TSAdapt

    308:    Input Arguments:
    309: +  adapt - adaptive controller context
    310: -  name - filter name

    312:    Level: intermediate

    314:    References: http://dx.doi.org/10.1145/641876.641877

    316:    Notes:
    317:     Valid filter names are
    318: +  "basic" - similar to TSADAPTBASIC but with different criteria for step rejections.
    319: .  "PI30", "PI42", "PI33", "PI34" - PI controllers.
    320: .  "PC11", "PC47", "PC36" - predictive controllers.
    321: .  "H0211", "H211b", "H211PI" - digital filters with orders dynamics=2, adaptivity=1, filter=1.
    322: .  "H0312", "H312b", "H312PID" - digital filters with orders dynamics=3, adaptivity=1, filter=2.
    323: -  "H0321", "H321" - digital filters with orders dynamics=3, adaptivity=2, filter=1.

    325:    Options Database:
    326: .   -ts_adapt_dsp_filter <name> - Sets predefined controller by name; use -help for a list of available controllers

    328: .seealso: TS, TSAdapt, TSGetAdapt(), TSAdaptDSPSetPID()
    329: @*/
    330: PetscErrorCode TSAdaptDSPSetFilter(TSAdapt adapt,const char *name)
    331: {
    336:   PetscTryMethod(adapt,"TSAdaptDSPSetFilter_C",(TSAdapt,const char*),(adapt,name));
    337:   return(0);
    338: }

    340: /*@
    341:    TSAdaptDSPSetPID - Set the PID controller parameters

    343:    Input Arguments:
    344: +  adapt - adaptive controller context
    345: .  kkI - Integral parameter
    346: .  kkP - Proportional parameter
    347: -  kkD - Derivative parameter

    349:    Level: intermediate

    351:    References: http://dx.doi.org/10.1016/j.cam.2005.03.008

    353:    Options Database:
    354: .   -ts_adapt_dsp_pid <kkI,kkP,kkD> - Sets PID controller parameters

    356: .seealso: TS, TSAdapt, TSGetAdapt(), TSAdaptDSPSetFilter()
    357: @*/
    358: PetscErrorCode TSAdaptDSPSetPID(TSAdapt adapt,PetscReal kkI,PetscReal kkP,PetscReal kkD)
    359: {
    366:   PetscTryMethod(adapt,"TSAdaptDSPSetPID_C",(TSAdapt,PetscReal,PetscReal,PetscReal),(adapt,kkI,kkP,kkD));
    367:   return(0);
    368: }

    370: /*MC
    371:    TSADAPTDSP - Adaptive controller for time-stepping based on digital signal processing (DSP)

    373:    Level: intermediate

    375:    References: http://dx.doi.org/10.1145/641876.641877 and http://dx.doi.org/10.1016/j.cam.2005.03.008

    377:    Options Database:
    378: +   -ts_adapt_dsp_filter <name> - Sets predefined controller by name; use -help for a list of available controllers
    379: .   -ts_adapt_dsp_pid <kkI,kkP,kkD> - Sets PID controller parameters
    380: .   -ts_adapt_dsp_kbeta <b1,b2,b2> - Sets general filter parameters
    381: -   -ts_adapt_dsp_alpha <a2,a3> - Sets general filter parameters

    383: .seealso: TS, TSAdapt, TSGetAdapt(), TSAdaptDSPSetPID(), TSAdaptDSPSetFilter()
    384: M*/
    385: PETSC_EXTERN PetscErrorCode TSAdaptCreate_DSP(TSAdapt adapt)
    386: {
    387:   TSAdapt_DSP    *dsp;

    391:   PetscNewLog(adapt,&dsp);
    392:   adapt->reject_safety = 1.0; /* unused */

    394:   adapt->data                = (void*)dsp;
    395:   adapt->ops->choose         = TSAdaptChoose_DSP;
    396:   adapt->ops->setfromoptions = TSAdaptSetFromOptions_DSP;
    397:   adapt->ops->destroy        = TSAdaptDestroy_DSP;
    398:   adapt->ops->view           = TSAdaptView_DSP;

    400:   PetscObjectComposeFunction((PetscObject)adapt,"TSAdaptDSPSetFilter_C",TSAdaptDSPSetFilter_DSP);
    401:   PetscObjectComposeFunction((PetscObject)adapt,"TSAdaptDSPSetPID_C",TSAdaptDSPSetPID_DSP);

    403:   TSAdaptDSPSetFilter_DSP(adapt,"PI42");
    404:   TSAdaptRestart_DSP(adapt);
    405:   return(0);
    406: }