PRECONDITIONING FOR THE p-VERSION BOUNDARY ELEMENT METHOD IN THREE DIMENSIONS WITH TRIANGULAR ELEMENTS

Title & Authors
PRECONDITIONING FOR THE p-VERSION BOUNDARY ELEMENT METHOD IN THREE DIMENSIONS WITH TRIANGULAR ELEMENTS
Cao, Wei-Ming; Guo, Benqi;

Abstract
A preconditioning algorithm is developed in this paper for the iterative solution of the linear system of equations resulting from the p-version boundary element approximation of the three dimensional integral equation with hypersingular operators. The preconditioner is derived by first making the nodal and side basis functions locally orthogonal to the element internal bases, and then by decoupling the nodal and side bases from the internal bases. Its implementation consists of solving a global problem on the wire-basket and a series of local problems defined on a single element. Moreover, the condition number of the preconditioned system is shown to be of order $\small{O((1＋ln/p)^{7})}$. This technique can be applied to discretization with triangular elements and with general basis functions.
Keywords
p-version boundary element method;hypersingular integral equation;iterative methods;preconditioning.;
Language
English
Cited by
1.
ON A FAST ITERATIVE METHOD FOR APPROXIMATE INVERSE OF MATRICES,;

대한수학회논문집, 2013. vol.28. 2, pp.407-418
1.
An iterative substructuring method for thehp-version of the BEM on quasi-uniform triangular meshes, Numerical Methods for Partial Differential Equations, 2007, 23, 4, 879
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An extension theorem for polynomials on triangles, Calcolo, 2008, 45, 2, 69
3.
ON A FAST ITERATIVE METHOD FOR APPROXIMATE INVERSE OF MATRICES, Communications of the Korean Mathematical Society, 2013, 28, 2, 407
4.
Optimal error estimate of a projection based interpolation for the p-version approximation in three dimensions, Computers & Mathematics with Applications, 2005, 50, 3-4, 359
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