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Module Arkode.ARKStep.Spils

module Spils: sig .. end

Scaled Preconditioned Iterative Linear Solvers.

include Sundials_LinearSolver.Iterative
include Arkode.Spils

Preconditioners

val prec_none : ('d, 'k, Arkode.arkstep) preconditioner

No preconditioning.

val prec_left : ?setup:'d prec_setup_fn ->
       'd prec_solve_fn -> ('d, 'k, Arkode.arkstep) preconditioner

Left preconditioning. $(P^{-1}A)x = P^{-1}b$ .

val prec_right : ?setup:'d prec_setup_fn ->
       'd prec_solve_fn -> ('d, 'k, Arkode.arkstep) preconditioner

Right preconditioning. $(AP^{-1})Px = b$ .

val prec_both : ?setup:'d prec_setup_fn ->
       'd prec_solve_fn -> ('d, 'k, Arkode.arkstep) preconditioner

Left and right preconditioning. $(P_L^{-1}AP_R^{-1})P_Rx = P_L^{-1}b$

Solvers

val solver : ('m, 'd, 'k, [> `Iter ]) Sundials.LinearSolver.t ->
       ?jac_times_vec:'d jac_times_setup_fn option * 'd jac_times_vec_fn ->
       ?jac_times_rhs:'d rhsfn ->
       ('d, 'k, Arkode.arkstep) preconditioner ->
       ('d, 'k) Arkode.ARKStep.linear_solver

Create an ARKStep-specific linear solver from a generic iterative linear solver.

The jac_times_rhs argument specifies an alternative right-hand-side function for use in the internal Jacobian-vector product difference quotient approximation. It is incorrect to specify both this argument and jac_times_vec.

NB: a jac_times_setup_fn is not supported in Config.sundials_version < 3.0.0.

NB: a jac_times_rhs function is not supported in Config.sundials_version < 5.3.0.

Solver parameters

val set_jac_eval_frequency : ('d, 'k) Arkode.ARKStep.session -> int -> unit

Sets the maximum number of time steps to wait before recomputation of the Jacobian or recommendation to update the preconditioner. If the integer argument is less than or equal to 0, a default value of 50 is used.

val set_linear_solution_scaling : ('d, 'k) Arkode.ARKStep.session -> bool -> unit

Enables or disables scaling of the linear system solution to account for a change in $\gamma$ in the linear system. Linear solution scaling is enabled by default when a matrix-based linear solver is attached.

val set_eps_lin : ('d, 'k) Arkode.ARKStep.session -> float -> unit

Sets the factor by which the Krylov linear solver's convergence test constant is reduced from the Newton iteration test constant. This factor must be >= 0; passing 0 specifies the default (0.05).

val set_ls_norm_factor : ('d, 'k) Arkode.ARKStep.session -> float -> unit

Sets the factor for converting from the integrator tolerance (WRMS norm) to the linear solver tolerance (L2 norm). That is, $\mathit{tol}_{\mathsf{L2}} = \mathit{fact}\cdot\mathit{tol}_{\mathsf{WRMS}}$ . The given value is used directly if it is greater than zero. If it is zero (the default), then the square root of the state vector length is used. If it is less than zero, then the square root of the dot product of a state vector full of ones with itself is used.

Solver statistics

val get_work_space : ('d, 'k) Arkode.ARKStep.session -> int * int

Returns the sizes of the real and integer workspaces used by the spils linear solver.

val get_num_lin_iters : ('d, 'k) Arkode.ARKStep.session -> int

Returns the cumulative number of linear iterations.

val get_num_lin_conv_fails : ('d, 'k) Arkode.ARKStep.session -> int

Returns the cumulative number of linear convergence failures.

val get_num_prec_evals : ('d, 'k) Arkode.ARKStep.session -> int

Returns the cumulative number of calls to the setup function with jok=false.

val get_num_prec_solves : ('d, 'k) Arkode.ARKStep.session -> int

Returns the cumulative number of calls to the preconditioner solve function.

val get_num_jtsetup_evals : ('d, 'k) Arkode.ARKStep.session -> int

Returns the cumulative number of calls to the Jacobian-vector setup function.

val get_num_jtimes_evals : ('d, 'k) Arkode.ARKStep.session -> int

Returns the cumulative number of calls to the Jacobian-vector function.

val get_num_lin_rhs_evals : ('d, 'k) Arkode.ARKStep.session -> int

Returns the number of calls to the right-hand side callback for finite difference Jacobian-vector product approximation. This counter is only updated if the default difference quotient function is used.

Low-level solver manipulation

The Arkode.ARKStep.init and Arkode.ARKStep.reinit functions are the preferred way to set or change preconditioner functions. These low-level functions are provided for experts who want to avoid resetting internal counters and other associated side-effects.

val set_preconditioner : ('d, 'k) Arkode.ARKStep.session ->
       ?setup:'d prec_setup_fn -> 'd prec_solve_fn -> unit

Change the preconditioner functions.

val set_jac_times : ('d, 'k) Arkode.ARKStep.session ->
       ?jac_times_setup:'d jac_times_setup_fn -> 'd jac_times_vec_fn -> unit

Change the Jacobian-times-vector function.

val clear_jac_times : ('d, 'k) Arkode.ARKStep.session -> unit

Remove a Jacobian-times-vector function and use the default implementation.