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Module Arkode_bbd

module Arkode_bbd: sig .. end

Parallel band-block-diagonal preconditioners for ARKODE (requires MPI).

type [< `ARKStep | `MRIStep ] parallel_session = (Nvector_parallel.data, Nvector_parallel.kind,
        [< `ARKStep | `MRIStep ] as 'a)
       session

Alias for sessions based on parallel nvectors.

type [< `ARKStep | `MRIStep ] parallel_preconditioner = (Nvector_parallel.data, Nvector_parallel.kind,
        [< `ARKStep | `MRIStep ] as 'a)
       Arkode.Spils.preconditioner

Alias for preconditioners based on parallel nvectors.

type bandwidths = ArkodeBbdTypes.bandwidths = {
   mudq : int; (*

Upper half-bandwidth for the difference quotient Jacobian approximation.

*)
   mldq : int; (*

Lower half-bandwidth for the difference quotient Jacobian approximation.

*)
   mukeep : int; (*

Upper half-bandwidth for the retained banded approximate Jacobian block.

*)
   mlkeep : int; (*

Lower half-bandwidth for the retained banded approximate Jacobian block.

*)
}

The bandwidths for the difference quotient Jacobian operation.

type local_fn = float -> Nvector_parallel.data -> Nvector_parallel.data -> unit

Approximates the right-hand side function using local computations only. That is, it computes the approximation $g(t,y) \approx f_I(t,y)$. In the call gloc t y g, t is the independent variable (time), y is the input vector, and g stores the computed derivatives.

Raising Sundials.RecoverableFailure signals a recoverable error. Other exceptions signal unrecoverable errors.

type comm_fn = float -> Nvector_parallel.data -> unit

Functions that perform the interprocess communication necessary for the execution of Arkode_bbd.local_fn. In the call cfn t y, t is the independent variable (time) and y is the input vector.

Raising Sundials.RecoverableFailure signals a recoverable error. Other exceptions signal unrecoverable errors.

val prec_left : ?dqrely:float ->
       bandwidths ->
       ?comm:comm_fn ->
       local_fn ->
       [< `ARKStep | `MRIStep ] parallel_preconditioner

Left preconditioning using the Parallel Band-Block-Diagonal module. The difference quotient operation is controlled by ?dqrely, which specifies the relative increment in components of y, and Arkode_bbd.bandwidths.

NB: Band-Block-Diagonal preconditioners may not be used for problems involving a non-identity mass matrix.

val prec_right : ?dqrely:float ->
       bandwidths ->
       ?comm:comm_fn ->
       local_fn ->
       [< `ARKStep | `MRIStep ] parallel_preconditioner

Right preconditioning using the Parallel Band-Block-Diagonal module. The difference quotient operation is controlled by ?dqrely, which specifies the relative increment in components of y, and Arkode_bbd.bandwidths.

val prec_both : ?dqrely:float ->
       bandwidths ->
       ?comm:comm_fn ->
       local_fn ->
       [< `ARKStep | `MRIStep ] parallel_preconditioner

Preconditioning from both sides using the Parallel Band-Block-Diagonal module. The difference quotient operation is controlled by ?dqrely, the relative increment in components of y, and Arkode_bbd.bandwidths.

val reinit : [< `ARKStep | `MRIStep ] parallel_session ->
       ?dqrely:float -> int -> int -> unit

Reinitializes some BBD preconditioner parameters. In the call, reinit s ~dqrely:dqrely mudq mldq, dqrely is the relative increment in the components of y, and mudq and mldq are, respectively, the upper-half and lower-half bandwidths of the difference quotient Jacobian approximation.

val get_work_space : [< `ARKStep | `MRIStep ] parallel_session -> int * int

Returns the sizes of the real and integer workspaces used by the BBD preconditioner.

val get_num_gfn_evals : [< `ARKStep | `MRIStep ] parallel_session -> int

Returns the number of calls to the right-hand side function due to finite difference banded Jacobian approximation in the setup function.