regrid_solvers module reference¶

Solvers of linear systems.

Functions/Subroutines¶

`solve_linear_system()`	Solve the linear system AX = R by Gaussian elimination.
`linear_solver()`	Solve the linear system AX = R by Gaussian elimination.
`solve_tridiagonal_system()`	Solve the tridiagonal system AX = R.
`solve_diag_dominant_tridiag()`	Solve the tridiagonal system AX = R.

Detailed Description¶

Date of creation: 2008.06.12 L. White.

This module contains solvers of linear systems. These routines have now been updated for greater efficiency, especially in special cases.

Function/Subroutine Documentation¶

subroutine regrid_solvers/solve_linear_system(A, R, X, N, answer_date)¶

Solve the linear system AX = R by Gaussian elimination.

This routine uses Gauss’s algorithm to transform the system’s original matrix into an upper triangular matrix. Back substitution yields the answer. The matrix A must be square, with the first index varing down the column.

Parameters:

n :: [in] The size of the system
a :: [inout] The matrix being inverted in arbitrary units [A] on input, but internally modified to become nondimensional during the solver.
r :: [inout] system right-hand side in arbitrary units [A B] on input, but internally modified to have units of [B] during the solver
x :: [inout] solution vector in arbitrary units [B]
answer_date :: [in] The vintage of the expressions to use

Call to:

mom_error_handler::mom_error

subroutine regrid_solvers/linear_solver(N, A, R, X)¶

Solve the linear system AX = R by Gaussian elimination.

This routine uses Gauss’s algorithm to transform the system’s original matrix into an upper triangular matrix. Back substitution then yields the answer. The matrix A must be square, with the first index varing along the row.

Parameters:

n :: [in] The size of the system
a :: [inout] The matrix being inverted in arbitrary units [A] on input, but internally modified to become nondimensional during the solver.
r :: [inout] system right-hand side in [A B] on input, but internally modified to have units of [B] during the solver
x :: [inout] solution vector [B]

Call to:

mom_error_handler::mom_error

subroutine regrid_solvers/solve_tridiagonal_system(Al, Ad, Au, R, X, N, answer_date)¶

Solve the tridiagonal system AX = R.

This routine uses Thomas’s algorithm to solve the tridiagonal system AX = R. (A is made up of lower, middle and upper diagonals)

Parameters:

n :: [in] The size of the system
ad :: [in] Matrix center diagonal in arbitrary units [A]
al :: [in] Matrix lower diagonal [A]
au :: [in] Matrix upper diagonal [A]
r :: [in] system right-hand side in arbitrary units [A B]
x :: [out] solution vector in arbitrary units [B]
answer_date :: [in] The vintage of the expressions to use

Called from:

regrid_edge_values::edge_slopes_implicit_h3 regrid_edge_values::edge_slopes_implicit_h5 regrid_edge_values::edge_values_implicit_h4 regrid_edge_values::edge_values_implicit_h6

subroutine regrid_solvers/solve_diag_dominant_tridiag(Al, Ac, Au, R, X, N)¶

Solve the tridiagonal system AX = R.

This routine uses a variant of Thomas’s algorithm to solve the tridiagonal system AX = R, in a form that is guaranteed to avoid dividing by a zero pivot. The matrix A is made up of lower (Al) and upper diagonals (Au) and a central diagonal Ad = Ac+Al+Au, where Al, Au, and Ac are all positive (or negative) definite. However when Ac is smaller than roundoff compared with (Al+Au), the answers are prone to inaccuracy.

Parameters:

n :: [in] The size of the system
ac :: [in] Matrix center diagonal offset from Al + Au in arbitrary units [A]
al :: [in] Matrix lower diagonal [A]
au :: [in] Matrix upper diagonal [A]
r :: [in] system right-hand side in arbitrary units [A B]
x :: [out] solution vector in arbitrary units [B]

Called from:

regrid_edge_values::edge_slopes_implicit_h3 regrid_edge_values::edge_values_implicit_h4