Solving Linear Systems of Equations from BEM Codes

In this paper, we compare different methods to solve systems of linear equations in order to determine which one allows us to reduce as much as possible the execution time. We consider contact problems that are solved by applying the Boundary Element Method that involves the resolution of different systems of linear equations. Depending on the kind of problem, thermal and elastic systems of equations have to be solved. The number of equations depends on the number of elements in which solids are discretized. This means that the more realistic are the solids defined, the more number of elements are considered. For this reason, it is really interesting to determine the most efficient method. We compare the Gauss Elimination method with and without pivoting, the Gauss-Jordan method and the LU Factorization method for several elastic and thermoelastic problems. LU Factorization provides an average reduction of a 37% in the execution times, and up to a 41% for some particular problems.

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