Xiao, Jinyou; Tausch, Johannes; Hu, Yucai A-posteriori compression of wavelet-BEM matrices. (English) Zbl 1398.74421 Comput. Mech. 44, No. 5, 705-715 (2009). Summary: The success of the wavelet boundary element method (BEM) depends on its matrix compression capability. The wavelet Galerkin BEM (WGBEM) based on non-standard form (NS-form) in [J. Tausch, J. Numer. Math. 12, No. 3, 233–254 (2004; Zbl 1063.65133)] has almost linear memory and time complexity. Recently, wavelets with the quasi-vanishing moments (QVMs) have been used to decrease the constant factors involved in the complexity estimates [J. Xiao et al., Comput. Methods Appl. Mech. Eng. 197, No. 45–48, 4000–4006 (2008; Zbl 1197.65193)]. However, the representations of layer potentials in QVM bases still have much more negligible entries than predicted by a-priori estimates, which are based on the separation of the supports of the source- and test-wavelets. In this paper, we introduce an a-posteriori compression strategy, which is designed to preserve the convergence properties of the underlying Galerkin discretization scheme. We summarize the different compression schemes for the WGBEM and demonstrate their performances on practical problems including Stokes flow, acoustic scattering and capacitance extraction. Numerical results show that memory allocation and CPU time can be reduced several times. Thus the storage for the NS-form is typically less than what is required to store the near-field interactions in the well-known fast multipole method. Cited in 8 Documents MSC: 74S05 Finite element methods applied to problems in solid mechanics 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:wavelet BEM; matrix compression; a-posteriori compression; non-standard form; quasi- vanishing moment; Stokes flow; capacitance Citations:Zbl 1063.65133; Zbl 1197.65193 PDFBibTeX XMLCite \textit{J. Xiao} et al., Comput. Mech. 44, No. 5, 705--715 (2009; Zbl 1398.74421) Full Text: DOI References: [1] Greengard L, Rokhlin V (1987) A fast algorithm for particle simulations. J Comp Phys 73: 325–348 · Zbl 0629.65005 [2] Nishimura N (2002) Fast multipole accelerated boundary integral equation methods. Appl Mech Rev 55(4): 299–324 [3] Tausch J (2004) The variable order fast multipole method for boundary integral equations of the second kind. 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