Provides a derived type which representes a finite difference matrix/operator. This can be useful for preconditioning problems which use a spectral discretisation.
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| integer, | private, | parameter | :: | no_extra_derivative | = | -1 |
Build a tridiagonal matrix block for finite differences. See the end of the documentation of the fin_diff_block type for a description of how boundary conditions are treated.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(abstract_field), | intent(in) | :: | template | A scalar field with the same grid as any fields passed as arguments to the solve_for method. |
||
| integer, | intent(in), | optional | dimension(:) | :: | boundary_locs | The locations in the raw representation of |
| integer, | intent(in), | optional | dimension(:) | :: | boundary_types | Integers specifying the type of boundary condition. The type
of boundary condition corresponding to a given integer is
specified in boundary_types_mod. Only Dirichlet and
Neumann conditions are supported. Defaults to Dirichlet. The
order in which they are stored must match that of
|
A new finite difference operator
A data type representing a matrix finite difference operator. It can be useful when preconditioning systems which use a spectral discretisation. It is inherently 1-D in its implementation. Note that multiplication of a field will simply call that field's differentiation operator, which may or may not use a finite difference method.
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| real(kind=r8), | private, | dimension(:), allocatable | :: | diagonal | The diagonal of the tridiagonal matrix representation of this block. |
||
| real(kind=r8), | private, | dimension(:), allocatable | :: | super_diagonal | The super-diagonal of the tridiagonal matrix representation of this block. |
||
| real(kind=r8), | private, | dimension(:), allocatable | :: | sub_diagonal | The sub-diagonal of the tridiagonal matrix representation of this block. |
||
| real(kind=r8), | private, | dimension(:), allocatable | :: | l_multipliers | Multipliers defining the L matrix in the LU factorisation of the tridiagonal matrix representation of this block. |
||
| real(kind=r8), | private, | dimension(:), allocatable | :: | u_diagonal | The diagonal of the U matrix in the LU factorisation of the tridiagonal matrix representation of this block. |
||
| real(kind=r8), | private, | dimension(:), allocatable | :: | u_superdiagonal1 | The first superdiagonal of the U matrix in the LU factorisation of the tridiagonal matrix representation of this block. |
||
| real(kind=r8), | private, | dimension(:), allocatable | :: | u_superdiagonal2 | The second superdiagonal of the U matrix in the LU factorisation of the tridiagonal matrix representation of this block. |
||
| integer, | private, | dimension(:), allocatable | :: | pivots | Pivot indicies from the LU factorisation of the tridiagonal matrix representation of this block. |
||
| integer, | private, | dimension(:), allocatable | :: | boundary_locs | Locations in the raw arrays which are used to specify boundary conditions. |
||
| integer, | private, | dimension(:), allocatable | :: | boundary_types | The types of boundary conditions, specified using the parameters found in boundary_types_mod. |
||
| logical, | private | :: | had_offset | = | .true. | True if the factorisation was computed from a tridiagonal system in which an offset was added to the diagonal. |
| private function constructor(template, boundary_locs, boundary_types) | Build a tridiagonal matrix block for finite differences. See the end of the documentation of the fin_diff_block type for a description of how boundary conditions are treated. |
| procedure, private :: fin_diff_block_solve_scalar | |
| procedure, private :: fin_diff_block_solve_vector | |
| generic, public :: solve_for => fin_diff_block_solve_scalar, fin_diff_block_solve_vector |
Build a tridiagonal matrix block for finite differences. See the end of the documentation of the fin_diff_block type for a description of how boundary conditions are treated.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(abstract_field), | intent(in) | :: | template | A scalar field with the same grid as any fields passed as arguments to the solve_for method. |
||
| integer, | intent(in), | optional | dimension(:) | :: | boundary_locs | The locations in the raw representation of |
| integer, | intent(in), | optional | dimension(:) | :: | boundary_types | Integers specifying the type of boundary condition. The type
of boundary condition corresponding to a given integer is
specified in boundary_types_mod. Only Dirichlet and
Neumann conditions are supported. Defaults to Dirichlet. The
order in which they are stored must match that of
|
A new finite difference operator
Solves the linear(ised) system represented by this finite difference block, for a given right hand side state vector (represented by a scalar field). Optionally, the differential operator can be augmented by adding an offset, i.e. a scalar field which is added to the operator.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(fin_diff_block), | intent(inout) | :: | this | |||
| class(scalar_field), | intent(in) | :: | rhs | The right hand side of the linear(ised) system. |
||
| class(scalar_field), | intent(in), | optional | :: | offset | An offset to add to the differential operator |
Solves the linear(ised) system represented by this finite difference block, for a given right hand side state vector (represented by a vector field). Optionally, the differential operator can be augmented by adding an offset, i.e. a vector field which is added to the operator.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(fin_diff_block), | intent(inout) | :: | this | |||
| class(cheb1d_vector_field), | intent(in) | :: | rhs | The right hand side of the linear(ised) system. |
||
| class(cheb1d_vector_field), | intent(in), | optional | :: | offset | An offset to add to the differential operator |