Previous  Up  Next

Module Arkode.Spils

module Spils: sig .. end

Common definitions for Scaled Preconditioned Iterative Linear Solvers.

Preconditioners

type 'd prec_solve_arg = {
   rhs : 'd; (*

Right-hand side vector of the linear system.

*)
   gamma : float; (*

Scalar $\gamma$ in the Newton matrix given by $A = M - \gamma J$.

*)
   delta : float; (*

Input tolerance for iterative methods.

*)
   left : bool; (*

true for left preconditioning and false for right preconditioning.

*)
}

Arguments passed to the preconditioner solver function.

type 'd prec_solve_fn = (unit, 'd) Arkode.Common.jacobian_arg ->
       'd prec_solve_arg -> 'd -> unit

Callback functions that solve a linear system involving a preconditioner matrix. In the call prec_solve_fn jac arg z, jac is a Arkode.Common.jacobian_arg with one work vector, arg is a Arkode.Spils.prec_solve_arg that specifies the linear system, and z is computed to solve $P\mathtt{z} = \mathtt{arg.rhs}$. $P$ is a preconditioner matrix, which approximates, however crudely, the Newton matrix $A = M - \gamma J$ where $J = \frac{\partial f_I}{\partial y}$.

Raising Sundials.RecoverableFailure indicates a recoverable error. Any other exception is treated as an unrecoverable error.

The elements of jac, arg, and z should not be accessed after the function has returned.

type 'd prec_setup_fn = (unit, 'd) Arkode.Common.jacobian_arg -> bool -> float -> bool

Callback functions that preprocess or evaluate Jacobian-related data needed by Arkode.Spils.prec_solve_fn. In the call prec_setup_fn jac jok gamma, jac is a Arkode.Common.jacobian_arg with three work vectors, jok indicates whether any saved Jacobian-related data can be reused with the current value of gamma, and gamma is the scalar $\gamma$ in the Newton matrix $A = M - \gamma J$ where $J$ is the Jacobian matrix. A function should return true if Jacobian-related data was updated and false if saved data was reused.

Raising Sundials.RecoverableFailure indicates a recoverable error. Any other exception is treated as an unrecoverable error.

The elements of jac should not be accessed after the function has returned.

type ('d, 'k, 's) preconditioner = ('d, 'k, 's) SpilsTypes.preconditioner

Specifies a preconditioner, including the type of preconditioning (none, left, right, or both) and callback functions. The following functions and those in Arkode.Spils.Banded and Arkode_bbd construct preconditioners.

The Arkode.Spils.prec_solve_fn is usually mandatory. The Arkode.Spils.prec_setup_fn can be omitted if not needed.

module Banded: sig .. end

Banded preconditioners.

Solvers

type 'd jac_times_setup_fn = (unit, 'd) Arkode.Common.jacobian_arg -> unit

Callback functions that preprocess or evaluate Jacobian-related data needed by the jac_times_vec_fn. In the call jac_times_setup_fn arg, arg is a Arkode.Common.jacobian_arg with no work vectors.

Raising Sundials.RecoverableFailure indicates a recoverable error. Any other exception is treated as an unrecoverable error.

The elements of arg should not be accessed after the function has returned.

type 'd jac_times_vec_fn = ('d, 'd) Arkode.Common.jacobian_arg -> 'd -> 'd -> unit

Callback functions that compute the Jacobian times a vector. In the call jac_times_vec_fn arg v jv, arg is a Arkode.Common.jacobian_arg with one work vector, v is the vector multiplying the Jacobian, and jv is the vector in which to store the result—$\mathtt{jv} = J\mathtt{v}$.

Raising Sundials.RecoverableFailure indicates a recoverable error. Any other exception is treated as an unrecoverable error.

Neither the elements of arg nor v or jv should be accessed after the function has returned.