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Fast Boundary Elements Methods and applications

Fast convolution on unstructured grids have been developed for many applications (e.g. electrostatics, magnetostatics, acoustics, electromagnetics, etc.). The goal is to reduce the complexity of matrix-vector products, from O(N2) to O(N log N ). In this presentation, we describe a new efficient numerical method called Sparse Cardinal Sine Decomposition (SCSD), based on a suitable Fourier decomposition of the Green kernel, sparse quadrature formulae and Type-III Non Uniform Fast Fourier Transform (type-III NUFFT). This talk summarizes this new way, provide comparisons between SCSD, FMM and H-Matrix, and gives numerical results from our new Boundary Element solver, MyBEM. 

CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46