Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PRECONDITIONING FOR THE p-VERSION BOUNDARY ELEMENT METHOD IN THREE DIMENSIONS WITH TRIANGULAR ELEMENTS

  • Cao, Wei-Ming (Department of Applied Mathematics The University of Texas at San Antonio) ;
  • Guo, Benqi (Department of Mathematics University of Manitoba Winnipeg)
  • Published : 2004.03.01
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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 $O((1＋ln/p)^{7})$. This technique can be applied to discretization with triangular elements and with general basis functions.

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References

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