maspack.solvers

Class FemMatrixGenerator

java.lang.Object

maspack.solvers.FemMatrixGenerator

public class FemMatrixGenerator
extends java.lang.Object

Generates synthetic sparse matrices whose sparsity patterns match those arising from 2D and 3D finite element models on structured grids.

A grid of nx X ny X nz nodes is divided into elements of the requested FemMatrixGenerator.ElemType, and the matrix pattern is formed from the resulting node adjacency: nodes i and j are coupled if and only if they share an element. Each node carries dofsPerNode degrees of freedom (3 for 3D solid mechanics, 2 for 2D), so each node coupling expands into a dense dofsPerNode X dofsPerNode block, exactly as in a real FEM stiffness matrix.

Numeric values are assembled from element matrices of the form

   K_e = k (I - 1/m 1 1^T) (X) A
 

where m is the number of element nodes and A is a fixed random SPD dofsPerNode X dofsPerNode block. Each element matrix is therefore symmetric positive semi-definite, and adding a positive diagonal mass term makes the assembled matrix SPD, with every block entry non-zero.

Matrices are returned in the 1-based upper triangular CRS form accepted by DirectSolver.analyze(double[],int[],int[],int,int). A bordered KKT form, which is symmetric indefinite, may be produced using addConstraints().

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	FemMatrixGenerator.CRSMatrix Sparse symmetric matrix in the 1-based upper triangular CRS form used by DirectSolver.
static class	FemMatrixGenerator.ElemType Element type used to subdivide the grid.

Constructor Summary

Constructors

Constructor and Description
FemMatrixGenerator()

Method Summary

Modifier and Type	Method and Description
FemMatrixGenerator.CRSMatrix	addConstraints(FemMatrixGenerator.CRSMatrix M, int numCons, int nodesPerCon, int dofsPerNode) Creates a bordered KKT matrix
FemMatrixGenerator.CRSMatrix	create(FemMatrixGenerator.ElemType type, int nx, int ny, int nz, int dofsPerNode) Creates a matrix for a grid of nx X ny X nz nodes.
FemMatrixGenerator.CRSMatrix	createForSize(FemMatrixGenerator.ElemType type, int size) Creates a matrix for a cubic (or square) grid with approximately size rows.
int	numElems() Returns the number of elements used by the most recent call to create().
int	numNodes() Returns the number of grid nodes used by the most recent call to create().

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

FemMatrixGenerator

public FemMatrixGenerator()

Method Detail

numNodes

public int numNodes()

Returns the number of grid nodes used by the most recent call to create().

Returns:

number of nodes

numElems

public int numElems()

Returns the number of elements used by the most recent call to create().

Returns:

number of elements

createForSize

public FemMatrixGenerator.CRSMatrix createForSize(FemMatrixGenerator.ElemType type,
                                                  int size)

Creates a matrix for a cubic (or square) grid with approximately size rows. The grid resolution is chosen so that the resulting matrix is as close as possible to the requested size.

Parameters:

type - element type

size - desired matrix size

Returns:

generated matrix

create

public FemMatrixGenerator.CRSMatrix create(FemMatrixGenerator.ElemType type,
                                           int nx,
                                           int ny,
                                           int nz,
                                           int dofsPerNode)

Creates a matrix for a grid of nx X ny X nz nodes. For 2D element types, nz is ignored.

Parameters:

type - element type

nx - number of nodes along x

ny - number of nodes along y

nz - number of nodes along z (3D only)

dofsPerNode - degrees of freedom per node

Returns:

generated matrix

addConstraints

public FemMatrixGenerator.CRSMatrix addConstraints(FemMatrixGenerator.CRSMatrix M,
                                                   int numCons,
                                                   int nodesPerCon,
                                                   int dofsPerNode)

Creates a bordered KKT matrix

   [ M  G^T ]
   [ G   0  ]
 

from a stiffness matrix M, where G is a sparse constraint matrix with numCons rows, each coupling all the degrees of freedom of a small number of randomly selected nodes. The result is symmetric indefinite, and so has type Matrix.SYMMETRIC.

Parameters:

M - stiffness matrix, left unmodified

numCons - number of constraint rows

nodesPerCon - number of nodes coupled by each constraint

dofsPerNode - degrees of freedom per node in M

Returns:

bordered KKT matrix