Finite Element Routines
FEMPACK - Finite Element RoutinesFEMPACK is a collection of some simple routines for implementing the finite element method. The emphasis is on simplicity and clarity. Currently, only the 2D case is handled, with a choice of low order triangular and quadrilateral elements.
Files you may copy include:
fempack.f90, the source code;
fempack_prb.f90, the calling program;
fempack_prb.out, the sample output.
The list of routines includes:
BASIS_Q4 evalutes basis functions for a rectangular bilinear element.
DIV_Q4 estimates the divergence and vorticity of a discrete field.
ELEMENT_CODE returns the code for each element.
GRID returns the grid associated with any available element.
GRID_SHAPE_2D guesses the shape N1 by N2 of a vector of data.
GRID_TEST tests the grid routines.
GRID_WIDTH computes the width of a given grid.
GRID_Q4 produces a grid of 4 node quadrilaterals.
GRID_Q8 produces a grid of 8 node quadrilaterals.
GRID_Q9 produces a grid of 9 node quadrilaterals.
GRID_Q12 produces a grid of 12 node quadrilaterals.
GRID_Q16 produces a grid of 16 node quadrilaterals.
GRID_QL produces a grid of 6 node quadratics/linears.
GRID_T3 produces a grid of pairs of 3 node triangles.
GRID_T6 produces a grid of pairs of 6 node triangles.
GRID_T10 produces a grid of pairs of 10 node triangles.
INTERP interpolates a quantity in an element from basis node values.
LEGENDRE_COM computes abscissas and weights for Gauss-Legendre quadrature.
LEGENDRE_SET sets abscissas and weights for Gauss-Legendre quadrature.
MAP returns the interpolation matrix for any available element.
MAP_TEST tests the map routines.
NODE returns the basis nodes for any available element.
NODE_Q4 returns the basis nodes for a 4 node quadrilateral.
NODE_Q8 returns the basis nodes for an 8 node quadrilateral.
NODE_Q9 returns the basis nodes for a 9 node quadrilateral.
NODE_Q12 returns the basis nodes for a 12 node quadrilateral.
NODE_Q16 returns the basis nodes for a 16 node quadrilateral.
NODE_QL returns the basis nodes for a quadratic/linear.
NODE_T3 returns the basis nodes for the 3 node triangle.
NODE_T6 returns the basis nodes for a 6 node triangle.
NODE_T10 returns the basis nodes for a 10 node triangle.
ORDER_CODE returns the order for each element.
POLY returns the polynomials associated with any available element.
POLY_Q4 returns the polynomials associated with a 4 node quadrilateral.
POLY_Q8 returns the polynomials associated with an 8 node quadrilateral.
POLY_Q9 returns the polynomials associated with a 9 node quadrilateral.
POLY_Q12 returns the polynomials associated with a 12 node quadrilateral.
POLY_Q16 returns the polynomials associated with a 16 node quadrilateral.
POLY_QL returns the polynomials for a quadratic/linear quadrilateral.
POLY_T3 returns the polynomials associated with a 3 node triangle.
POLY_T6 returns the polynomials associated with a 6 node triangle.
POLY_T10 returns the polynomials associated with a 10 node triangle.
R_SWAP switches two real values.
S_L2NORM computes the "big" L2 norm of a scalar function over a region.
SERENE interpolates data using a serendipity quadrilateral.
SGE_CHECK checks the dimensions of a general matrix.
SGE_FA factors a general matrix.
SGE_INV computes the inverse of a matrix factored by SGE_FA.
SHAPE evaluates shape functions for any available element.
SHAPE_TEST verifies the shape function values at the basis nodes.
SHAPE_Q4 evaluates shape functions for a 4 node quadrilateral.
SHAPE_Q8 evaluates shape functions for an 8 node quadrilateral.
SHAPE_Q9 evaluates shape functions for a 9 node quadrilateral.
SHAPE_Q12 evaluates shape functions for a 12 node quadrilateral.
SHAPE_Q16 evaluates shape functions for a 16 node quadrilateral.
SHAPE_QL evaluates shape functions for a 6 node quadratic/linear.
SHAPE_T3 evaluates shape functions for a 3 node triangle.
SHAPE_T6 evaluates shape functions for a 6 node triangle.
SHAPE_T10 evaluates shape functions for a 10 node triangle.
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