Removal of hypersingularity in a direct BEM formulation
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Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like [수식] and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.
Abstract
Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like [수식] and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.
참고문헌 (4)
- J.T. Chen, "Supurious and true eignesolutions of Helmholtz BIEs and BEMs for a multiply connected problem", Proc. R. Soc. Lond. Ser. A, 통권 : 459, pp.1891~1924 (2003)
- Gabriel N. Gatica, "On the coupling of MIXED-FEM and BEM for an exterior Helmholtz problem in the plane", Numer. Math., 100, pp.663~695 (2005)
- Y. Khalighi, "Improved near-wall accuarcy for solutions of the Helmholtz equation using boundary element method", Center for Turbulence Research Annual Research Briefs (2006)
- J.C. Nedelec, "Accoustic and Electromagnetic Equations" (2001), Springe-Verlag