Sparse BEM Implementations Using an Application Framework for Discrete Methods

Marco Dondero, Diego Santiago, Adrián P. Cisilino, Santiago Urquiza


A practical strategy to increase the software reliability and to reduce programming effort is to implement the code using Application Frameworks (AF). A strategy for the implementation of a Boundary Element Method (BEM) solver within an AF for discrete methods is presented in this work. The rationale behind this approach is to reuse existing code for the implementation of the BEM solver. Thus, the effort put into the implementation of the BEM code is much less than that required for an ad-hoc development starting from scratch. Two strategies are introduced in order to reduce the memory requirements of the direct BEM . Both approaches consist in iterative procedures in which a number of coefficients of the fully-populated BEM system matrix are moved to the to the right hand side multiplied by the corresponding values of the unknowns in the previous iteration. In the Rapproach the coefficients are selected using a criterion based on the distance between the collocation and field points, while in the N-approach consists in a condensation procedure for clusters of elements. A benchmark problem is used to verify and assess the developed code. Convergence and accuracy is studied for both memory reduction strategies while the performance of the implementations is assessed in terms of execution times and memory requirements. The ability of the proposed methodologies for reducing the memory requirements is demonstrated. The analysis of an example showed that the N-approach has a better convergence behavior than the R-approach.

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