1: #pragma once

  3: #include <petsc/private/tsimpl.h>

  5: typedef enum {
  6:   TSGLLEERROR_FORWARD,
  7:   TSGLLEERROR_BACKWARD
  8: } TSGLLEErrorDirection;

 10: typedef struct _TSGLLEScheme *TSGLLEScheme;
 11: struct _TSGLLEScheme {
 12:   PetscInt     p;             /* order of the method */
 13:   PetscInt     q;             /* stage-order of the method */
 14:   PetscInt     r;             /* number of items carried between stages */
 15:   PetscInt     s;             /* number of stages */
 16:   PetscScalar *c;             /* location of the stages */
 17:   PetscScalar *a, *b, *u, *v; /* tableau for the method */

 19:   /* For use in rescale & modify */
 20:   PetscScalar *alpha; /* X_n(t_n) - X_{n-1}(t_n) = - alpha^T h^{p+1} x^{(p+1)}(t_n)        */
 21:   PetscScalar *beta;  /*                 - beta^T h^{p+2} x^{(p+2)}(t_n)                   */
 22:   PetscScalar *gamma; /*                 - gamma^T h^{p+2} f' x^{(p+1)}(t_n)  + O(h^{p+3}) */

 24:   /* Error estimates */
 25:   /* h^{p+1}x^{(p+1)}(t_n)     ~= phi[0]*h*Ydot + psi[0]*X[1:] */
 26:   /* h^{p+2}x^{(p+2)}(t_n)     ~= phi[1]*h*Ydot + psi[1]*X[1:] */
 27:   /* h^{p+2}f' x^{(p+1)}(t_n)  ~= phi[2]*h*Ydot + psi[2]*X[1:] */
 28:   PetscScalar *phi; /* dim=[3][s] for estimating higher moments, see B,J,W 2007 */
 29:   PetscScalar *psi; /* dim=[3][r-1], [0 psi^T] of B,J,W 2007 */
 30:   PetscScalar *stage_error;

 32:   /* Desirable properties which enable extra optimizations */
 33:   PetscBool stiffly_accurate; /* Last row of [A U] is equal t first row of [B V]? */
 34:   PetscBool fsal;             /* First Same As Last: X[1] = h*Ydot[s-1] (and stiffly accurate) */
 35: };

 37: typedef struct TS_GLLE {
 38:   TSGLLEAcceptFn *Accept; /* Decides whether to accept a given time step, given estimates of local truncation error */
 39:   TSGLLEAdapt     adapt;

 41:   /* These names are only stored so that they can be printed in TSView_GLLE() without making these schemes full-blown
 42:    objects (the implementations I'm thinking of do not have state and I'm lazy). */
 43:   char accept_name[256];

 45:   /* specific to the family of GL method */
 46:   PetscErrorCode (*EstimateHigherMoments)(TSGLLEScheme, PetscReal, Vec *, Vec *, Vec *); /* Provide local error estimates */
 47:   PetscErrorCode (*CompleteStep)(TSGLLEScheme, PetscReal, TSGLLEScheme, PetscReal, Vec *, Vec *, Vec *);
 48:   PetscErrorCode (*Destroy)(struct TS_GLLE *);
 49:   PetscErrorCode (*View)(struct TS_GLLE *, PetscViewer);
 50:   char          type_name[256];
 51:   PetscInt      nschemes;
 52:   TSGLLEScheme *schemes;

 54:   Vec      *X;     /* Items to carry between steps */
 55:   Vec      *Xold;  /* Values of these items at the last step */
 56:   Vec       W;     /* = 1/(atol+rtol*|X0|), used for WRMS norm */
 57:   Vec      *himom; /* len=3, Estimates of h^{p+1}x^{(p+1)}, h^{p+2}x^{(p+2)}, h^{p+2}(df/dx) x^{(p+1)} */
 58:   PetscReal wrms_atol, wrms_rtol;

 60:   /* Stages (Y,Ydot) are computed sequentially */
 61:   Vec      *Ydot;       /* Derivatives of stage vectors, must be stored */
 62:   Vec       Y;          /* Stage vector, only used while solving the stage so we don't need to store it */
 63:   Vec       Z;          /* Affine vector */
 64:   PetscReal scoeff;     /* Ydot = Z + shift*Y; shift = scoeff/ts->time_step */
 65:   PetscReal stage_time; /* time at current stage */
 66:   PetscInt  stage;      /* index of the stage we are currently solving for */

 68:   /* Runtime options */
 69:   PetscInt             current_scheme;
 70:   PetscInt             max_order, min_order, start_order;
 71:   PetscBool            extrapolate;     /* use extrapolation to produce initial Newton iterate? */
 72:   TSGLLEErrorDirection error_direction; /* TSGLLEERROR_FORWARD or TSGLLEERROR_BACKWARD */

 74:   PetscInt max_step_rejections;

 76:   PetscBool setupcalled;
 77:   void     *data;
 78: } TS_GLLE;