SetSparsity

Inheritence

This method is inherited from the AbstractMesh class.

SetSparsity

The SetSparsity method sets the sparsity pattern of a CSR matrix based on mesh connectivity. It has four versions for different use cases.

Interface 1

INTERFACE
  MODULE SUBROUTINE obj_SetSparsity1(obj, mat, localNodeNumber, lbound, &
                                     ubound)
    CLASS(AbstractMesh_), INTENT(INOUT) :: obj
    !! [[Mesh_]] class
    TYPE(CSRMatrix_), INTENT(INOUT) :: mat
    !! [[CSRMatrix_]] object
    INTEGER(I4B), INTENT(IN) :: lbound
    INTEGER(I4B), INTENT(IN) :: ubound
    INTEGER(I4B), INTENT(IN) :: localNodeNumber(lbound:ubound)
    !! Global to local node number map
  END SUBROUTINE obj_SetSparsity1
END INTERFACE

• localNodeNumber is used to convert the global node numbers of mesh to local node number in mat
• lbound and ubound are bounds of localNodeNumber

The algorithm is as follows:

1. Start loop of node numbers in mesh
2. Get the global node number of mesh
3. Get the global node numbers around this node
4. Use localNodeNumber to get the local node number of global node number (from step 3)
5. Call SetSparsity on mat from base lib.

Interface 2

INTERFACE
  MODULE SUBROUTINE obj_SetSparsity2(obj, mat)
    CLASS(AbstractMesh_), INTENT(INOUT) :: obj
    !! Mesh_ class
    TYPE(CSRMatrix_), INTENT(INOUT) :: mat
    !! CSRMatrix object
  END SUBROUTINE obj_SetSparsity2
END INTERFACE

Inteface 3

INTERFACE
  MODULE SUBROUTINE obj_SetSparsity3(obj, colMesh, nodeToNode, mat, &
                                     ivar, jvar)
    CLASS(AbstractMesh_), INTENT(INOUT) :: obj
    !! Abstract mesh class
    CLASS(AbstractMesh_), INTENT(INOUT) :: colMesh
    !! Abstract mesh class
    INTEGER(I4B), INTENT(IN) :: nodeToNode(:)
    !! Node to node connectivity between obj and colMesh
    TYPE(CSRMatrix_), INTENT(INOUT) :: mat
    !! [[CSRMatrix_]] object
    INTEGER(I4B), INTENT(IN) :: ivar
    INTEGER(I4B), INTENT(IN) :: jvar
  END SUBROUTINE obj_SetSparsity3
END INTERFACE

Interface 4

INTERFACE
  MODULE SUBROUTINE obj_SetSparsity4(obj, colMesh, nodeToNode, mat, &
                              rowGlobalToLocalNodeNum, rowLBOUND, rowUBOUND, &
                    colGlobalToLocalNodeNum, colLBOUND, colUBOUND, ivar, jvar)
    CLASS(AbstractMesh_), INTENT(INOUT) :: obj
    !! [[Mesh_]] class
    CLASS(AbstractMesh_), INTENT(INOUT) :: colMesh
    !! [[Mesh_]] class
    INTEGER(I4B), INTENT(IN) :: nodeToNode(:)
    !! node to node connectivity between obj and colMesh
    TYPE(CSRMatrix_), INTENT(INOUT) :: mat
    !! [[CSRMatrix_]] object
    INTEGER(I4B), INTENT(IN) :: rowLBOUND
    INTEGER(I4B), INTENT(IN) :: rowUBOUND
    INTEGER(I4B), INTENT(IN) :: rowGlobalToLocalNodeNum( &
      & rowLBOUND:rowUBOUND)
    !! Global to local node number map
    INTEGER(I4B), INTENT(IN) :: colLBOUND
    INTEGER(I4B), INTENT(IN) :: colUBOUND
    INTEGER(I4B), INTENT(IN) :: colGlobalToLocalNodeNum( &
      & colLBOUND:colUBOUND)
    INTEGER(I4B), INTENT(IN) :: ivar
    INTEGER(I4B), INTENT(IN) :: jvar
  END SUBROUTINE obj_SetSparsity4
END INTERFACE

Syntax

! Version 1: Using global-to-local node number mapping
CALL obj%SetSparsity(mat, localNodeNumber, lbound, ubound)

! Version 2: Using mesh connectivity directly
CALL obj%SetSparsity(mat)

! Version 3: For coupled meshes with physical variables
CALL obj%SetSparsity(colMesh, nodeToNode, mat, ivar, jvar)

! Version 4: With custom node mappings for coupled meshes
CALL obj%SetSparsity(colMesh, nodeToNode, mat, rowGlobalToLocalNodeNum, rowLBOUND, rowUBOUND, colGlobalToLocalNodeNum, colLBOUND, colUBOUND, ivar, jvar)

Parameters

Parameters vary by version but generally include:

• obj: The mesh object
• mat: The CSR matrix to set sparsity for
• localNodeNumber: Mapping from global to local node numbers
• Various bounds and indices for node mappings
• For coupled meshes: colMesh, nodeToNode, physical variable indices

Description

SetSparsity establishes the sparsity pattern of a CSR matrix based on mesh connectivity. This is crucial for finite element computations, as it determines which matrix entries can be non-zero.

The different versions accommodate various use cases:

• Version 1: Uses a provided global-to-local node number mapping
• Version 2: Uses mesh connectivity directly
• Version 3: For coupled meshes with physical variables
• Version 4: For complex scenarios with custom node mappings

Implementation Notes

All versions ensure that node-to-node connectivity is available, calling InitiateNodeToNodes if needed. They then iterate through nodes, determine connected nodes, and set the sparsity pattern accordingly.

Example 1

!> author: Vikas Sharma, Ph. D.
! date: 2025-06-05
! summary:  Test for SetSparsity method of FEMesh class

PROGRAM main
USE GlobalData
USE FEMesh_Class
USE HDF5File_Class
USE BaseType, ONLY: DOF_, CSRMatrix_
USE DOF_Method
USE CSRMatrix_Method

IMPLICIT NONE
TYPE(FEMesh_) :: obj
TYPE(HDF5File_) :: meshfile
TYPE(DOF_) :: dofobj
TYPE(CSRMatrix_) :: mat
INTEGER(I4B) :: tNodes(1)

INTEGER(I4B), PARAMETER :: spaceCompo(1) = [1], &
                           timeCompo(1) = [1], &
                           storageFMT = NODES_FMT
CHARACTER(1), PARAMETER :: names(1) = ["K"]

CHARACTER(LEN=*), PARAMETER :: filename = &
                               "./meshdata/small_tri3_mesh.h5"

CALL meshfile%Initiate(FileName=filename, MODE="READ")

CALL meshfile%OPEN()

CALL obj%Initiate(hdf5=meshfile, dim=2)

tNodes = obj%GetTotalNodes()
CALL Initiate(obj=dofobj, tNodes=tNodes, &
              spaceCompo=spaceCompo, timeCompo=timeCompo, &
              names=names, storageFMT=storageFMT)

CALL Initiate(mat, ncol=SIZE(dofobj), nrow=SIZE(dofobj), &
              idof=dofobj, jdof=dofobj)

CALL obj%SetSparsity(mat=mat)

CALL obj%DEALLOCATE()
CALL meshfile%DEALLOCATE()
END PROGRAM main