SUMMARYThis paper presents a fast approach for rapidly solving problems with multiple load cases using the boundary element method (BEM). The basic idea of this approach is to assemble the BEM matrices separately and to compress them using fast wavelet transforms. Using a technique called 'virtual assembly', the matrices are then combined inside an iterative solver according to the boundary conditions of the problem, with no need for recompression each time a new load case is solved. This technique does not change the condition number of the matrices-up to a small variation introduced by compressionso that previous theoretical convergence estimates are still valid. Substantial savings in computer time are obtained with the present technique.
This paper follows an earlier work by Bucher et al. [1] on the application of wavelet transforms to the boundary element method, which shows how to reuse models stored in compressed form to solve new models with the same geometry but arbitrary load cases-the so-called virtual assembly technique. The extension presented in this paper involves a new computational procedure created to perform the required twodimensional wavelet transforms by blocks, theoretically allowing the compression of matrices of arbitrary size. Details of the computer implementation that allows the use of this methodology for very large models or at high compression ratios are given. A numerical application shows a standard PC being used to solve a 131,072 DOF model, previously compressed, for 100 distinct load cases in less than 1 hour-or 33 seconds for each load case.
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