1: typedef struct _ARKTableau *ARKTableau;
  2: struct _ARKTableau {
  3:   char      *name;
  4:   PetscBool  additive;             /* If False, it is a DIRK method */
  5:   PetscInt   order;                /* Classical approximation order of the method */
  6:   PetscInt   s;                    /* Number of stages */
  7:   PetscBool  stiffly_accurate;     /* The implicit part is stiffly accurate */
  8:   PetscBool  FSAL_implicit;        /* The implicit part is FSAL */
  9:   PetscBool  explicit_first_stage; /* The implicit part has an explicit first stage */
 10:   PetscInt   pinterp;              /* Interpolation order */
 11:   PetscReal *At, *bt, *ct;         /* Stiff tableau */
 12:   PetscReal *A, *b, *c;            /* Non-stiff tableau */
 13:   PetscReal *bembedt, *bembed;     /* Embedded formula of order one less (order-1) */
 14:   PetscReal *binterpt, *binterp;   /* Dense output formula */
 15:   PetscReal  ccfl;                 /* Placeholder for CFL coefficient relative to forward Euler */
 16: };
 17: typedef struct _ARKTableauLink *ARKTableauLink;
 18: struct _ARKTableauLink {
 19:   struct _ARKTableau tab;
 20:   ARKTableauLink     next;
 21: };

 23: typedef struct {
 24:   ARKTableau   tableau;
 25:   Vec         *Y;            /* States computed during the step */
 26:   Vec         *YdotI;        /* Time derivatives for the stiff part */
 27:   Vec         *YdotRHS;      /* Function evaluations for the non-stiff part */
 28:   Vec         *Y_prev;       /* States computed during the previous time step */
 29:   Vec         *YdotI_prev;   /* Time derivatives for the stiff part for the previous time step*/
 30:   Vec         *YdotRHS_prev; /* Function evaluations for the non-stiff part for the previous time step*/
 31:   Vec          Ydot0;        /* Holds the slope from the previous step in FSAL case */
 32:   Vec          Ydot;         /* Work vector holding Ydot during residual evaluation */
 33:   Vec          Z;            /* Ydot = shift(Y-Z) */
 34:   IS           alg_is;       /* Index set for algebraic variables, needed when restarting with DIRK */
 35:   PetscScalar *work;         /* Scalar work */
 36:   PetscReal    scoeff;       /* shift = scoeff/dt */
 37:   PetscReal    stage_time;
 38:   PetscBool    imex;
 39:   PetscBool    extrapolate; /* Extrapolate initial guess from previous time-step stage values */
 40:   TSStepStatus status;

 42:   /* context for fast-slow split */
 43:   Vec       Y_snes;       /* Work vector for SNES */
 44:   Vec      *YdotI_fast;   /* Function evaluations for the fast components in YdotI */
 45:   Vec      *YdotRHS_fast; /* Function evaluations for the fast components in YdotRHS */
 46:   Vec      *YdotRHS_slow; /* Function evaluations for the slow components in YdotRHS */
 47:   IS        is_slow, is_fast;
 48:   TS        subts_slow, subts_fast;
 49:   PetscBool fastslowsplit;

 51:   /* context for sensitivity analysis */
 52:   Vec *VecsDeltaLam;   /* Increment of the adjoint sensitivity w.r.t IC at stage */
 53:   Vec *VecsSensiTemp;  /* Vectors to be multiplied with Jacobian transpose */
 54:   Vec *VecsSensiPTemp; /* Temporary Vectors to store JacobianP-transpose-vector product */
 55: } TS_ARKIMEX;