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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 .

1.2. Boundarycondition. We use bdFlag(1:NT,1:d+1)to record the type of boundary sides (edges in 2-D and faces in 3-D). The value is the type of boundary condition: 0 for non-boundary sides; 1 for the first type, i.e., Dirichlet boundary; 2 for the second type, i.e., Neumann boundary; 3 for the third type, i.e., Robin boundary. 1

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