FEMPACK - Finite Element Routines

FEMPACK 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.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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