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

  6: typedef enum {TSGLLEERROR_FORWARD,TSGLLEERROR_BACKWARD} TSGLLEErrorDirection;

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

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

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

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

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

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

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

 52:   Vec       *X;                 /* Items to carry between steps */
 53:   Vec       *Xold;              /* Values of these items at the last step */
 54:   Vec       W;                  /* = 1/(atol+rtol*|X0|), used for WRMS norm */
 55:   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)} */
 56:   PetscReal wrms_atol,wrms_rtol;

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

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

 72:   PetscInt max_step_rejections;

 74:   PetscBool setupcalled;
 75:   void      *data;
 76: } TS_GLLE;

 78: #endif