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• W2126587899 abstract "In general the numerical solution of boundary integral equations leads to full coefficientmatrices. The discrete system can be solved in O(N2) operations by iterative solvers ofthe Conjugate Gradient type. Therefore, we are interested in fast methods such as fastmultipole and wavelets, that reduce the computational cost to O(N lnp N).In this thesis we are concerned with wavelet methods. They have proved to be veryefficient and effective basis functions due to the fact that the coefficients of a wavelet expansiondecay rapidly for a large class of functions. Due to the multiresolution propertyof wavelets they provide accurate local descriptions of functions efficiently. For examplein the presence of corners and edges, the functions can still be approximated with a linearcombination of just a few basis functions. Wavelets are attractive for the numericalsolution of integral equations because their vanishing moments property leads to operatorcompression. However, to obtain wavelets with compact support and high order of vanishingmoments, the length of the support increases as the order of the vanishingmomentsincreases. This causes difficulties with the practical use of wavelets particularly at edgesand corners. However, with multiwavelets, an increase in the order of vanishing momentsis obtained not by increasing the support but by increasing the number of mother wavelets.In chapter 2 we review the methods and techniques required for these reformulations,we also discuss how these boundary integral equations may be discretised by a boundaryelement method. In chapter 3, we discuss wavelet and multiwavelet bases. In chapter4, we consider two boundary element methods, namely, the standard and non-standardGalerkin methods with multiwavelet basis functions. For both methods compressionstrategies are developed which only require the computation of the significant matrix elements.We show that they are O(N logp N) such significant elements. In chapters 5 and6 we apply the standard and non-standard Galerkin methods to several test problems." @default.
• W2126587899 created "2016-06-24" @default.
• W2126587899 creator A5062959497 @default.
• W2126587899 date "2004-06-01" @default.
• W2126587899 modified "2023-09-23" @default.
• W2126587899 title "Theory and applications of the multiwavelets for compression of boundary integral operators" @default.
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• W2126587899 hasPublicationYear "2004" @default.
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