Parallel iterative solvers involving fast wavelet transforms for the solution of BEM systems

This paper describes the parallelization of a strategy to speed up the convergence of iterative methods applied to boundary element method (BEM) systems arising from problems with non-smooth boundaries and mixed boundary conditions. The aim of the work is the application of fast wavelet transforms as a black box transformation in existing boundary element codes. A new strategy was proposed, applying wavelet transforms on the interval, so it could be used in case of non-smooth coefficient matrices. Here, we describe the parallel iterative scheme and we present some of the results we have obtained.

[1]  Barry Hilary Valentine Topping.  Advances in Engineering Computational Technology , 1998 .

[2]  Tomás F. Pena,et al.  Parallel iterative scheme for solving BEM systems using fast wavelet transforms , 2000 .

[3]  Tomás F. Pena,et al.  Dual BEM for crack growth analysis on distributed-memory multiprocessors , 2000 .

[4]  C. Brebbia,et al.  Boundary Element Techniques , 1984 .

[5]  Stephen A. Vavasis,et al.  Fast Wavelet Transforms for Matrices Arising from Boundary Element Methods , 1994 .

[6]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[7]  Gunnar Peters,et al.  Wavelet probing for compression-based segmentation , 1993, Optics & Photonics.

[8]  R. Bellman,et al.  Proceedings of Symposia in Applied Mathematics. , 1961 .

[9]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[10]  G. Beylkin.  Wavelets and Fast Numerical Algorithms , 1993, comp-gas/9304004.

[11]  Gabriel Fernandez,et al.  LIFTPACK: a software package for wavelet transforms using lifting , 1996, Optics & Photonics.

[12]  Barry Hilary Valentine Topping.  Developments in Engineering Computational Technology , 2000 .

[13]  G. Zack,et al.  Automatic measurement of sister chromatid exchange frequency. , 1977, The journal of histochemistry and cytochemistry : official journal of the Histochemistry Society.

[14]  Wim Sweldens,et al.  Lifting scheme: a new philosophy in biorthogonal wavelet constructions , 1995, Optics + Photonics.

[15]  Michael Unser,et al.  Wavelet Applications in Signal and Image Processing II: 27-29 July 1994, San Diego, California , 1994 .

[16]  Andreas Uhl,et al.  Wavelet Packet Best Basis Selection on Moderate Parallel MIMD Architectures , 1996, Parallel Comput..

[17]  Tomás F. Pena,et al.  Parallel Computation of Wavelet Transforms Using the Lifting Scheme , 2001, The Journal of Supercomputing.

[18]  William Gropp,et al.  Skjellum using mpi: portable parallel programming with the message-passing interface , 1994 .

[19]  Wim Sweldens,et al.  The lifting scheme: a construction of second generation wavelets , 1998 .

[20]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[21]  Steven L. Scott,et al.  Synchronization and communication in the T3E multiprocessor , 1996, ASPLOS VII.

[22]  R. Coifman,et al.  Fast wavelet transforms and numerical algorithms I , 1991 .

[23]  Gilbert Strang,et al.  Wavelets and Dilation Equations: A Brief Introduction , 1989, SIAM Rev..