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PROGRAMMING OF FINITE ELEMENT METHODS IN MATLAB

PROGRAMMING OF FINITE ELEMENT METHODS IN MATLABLONG CHENWe shall discuss how to implement the linear FINITE ELEMENT method for solving the Pois-son equation. We begin with the data structure to represent the triangulation and boundaryconditions, introduce the sparse matrix, and then discuss the assembling process. Since weuse MATLAB as the PROGRAMMING language, we pay attention to an efficient programmingstyle using sparse matrices in DATASTRUCTURE OFTRIANGULATIONWe shall discuss the data structure to represent triangulations and boundary data matricesnode(1:N,1:d)andelem(1:NT,1:d+1) areused to represent ad-dimensional triangulation embedded inRd, whereNis the numberof vertices andNTis the number of elements . These two matrices represent two differentstructure of a triangulation:elemfor the topology andnodefor the geometric matrixelemrepresents a set of abstract simplices.

two additional integer arrays to store the indices of nonzero entries. An intutive scheme, known as coordinate format, is to store both the row and column indices. In the sequel, we suppose Ais a m nmatrix containing only nnznonzero elements. Let us look at the following simple example: (1) A= 2 6 6 4 1 0 0 0 2 4 0 0 0 0 9 0 3 7 7 5; i= 2 6 6 4 ...

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