# TET_MESH_QUAD Integral Estimate Over a Region Defined by a Tetrahedral Mesh

TET_MESH_QUAD is a MATLAB program which reads information defining a tetrahedral mesh, and estimates the integral of a function whose values are given at the nodes.

Note that this program only expects to receive values of the function f(x,y,z) at the nodes of the tet mesh, that is, as a simple list of values. No formula for f is expected or used. A much better estimate for the integral might be possible if a formula for f(x,y,z) were available, in which case a higher order quadrature scheme could be employed.

This program should be able to compute exactly the integrals of 1, x, y, z, and any linear combination of these. It will only be able to approximate the integrals of other functions, and the accuracy of the approximation will depend in part on the size of the triangles in the triangulation.

### Usage:

where 'prefix' is the common prefix for the node, element, and value files.
• prefix_nodes.txt, the node coordinates;
• prefix_elements.txt, the elements of the triangulation.
• prefix_values.txt, the value (which may be a scalar or vector) of some function at each node.
• quad is the (scalar or vector) result of the integration estimate.
• volume is the volume of the region covered by the tetrahedral mesh.

### Languages:

TET_MESH_QUAD is available in a C++ version and a FORTRAN90 version and a MATLAB version.

### Related Data and Programs:

TET_MESH, a MATLAB library which carries out various operations on tetrahedral meshes.

TRIANGULATION_QUAD, a MATLAB program which estimates the integral of a function over a triangulated region.

### Examples and Tests:

CUBE_4x4x4 is a set of nodes in the [0,4]x[0,4]x[0,4] cube, which have been arranged into an order 4 tet mesh.

You can go up one level to the MATLAB source codes.

Last revised on 20 December 2012.