Solution of elastic scattering problems in linear acoustics using h-p boundary element method

Abstract The work is a continuation of [1]. A simplified 3D model problem reduced from the general class of elastic scattering problems is analyzed, focusing attention on such practical details of the 3D implementation as a triangles-based h-p approximation and corresponding data structure, integration of singular integrals and its effect on (theoretically) optimal rates of convergence, a posteriori error estimation and sample adaptive strategies.

[1]  J. Nédélec,et al.  Curved finite element methods for the solution of singular integral equations on surfaces in R3 , 1976 .

[2]  Mark Ainsworth,et al.  Solution of elastic scattering problems in linear acoustics using h-p boundary element methods , 1991 .

[3]  Ernst P. Stephan,et al.  On the Convergence of the p-Version of the Boundary Element Galerkin Method. , 1989 .

[4]  Martin Costabel,et al.  Experimental convergence rates for various couplings of boundary and finite elements , 1991 .

[5]  R. Jeans,et al.  A comparison of numerical collocation and variational procedures to the hypersingular acoustic integral operator , 1992 .

[6]  Leszek Demkowicz,et al.  Toward a universal adaptive finite element strategy part 3. design of meshes , 1989 .

[7]  C. Schwab,et al.  On numerical cubatures of singular surface integrals in boundary element methods , 1992 .

[8]  J. Oden,et al.  Toward a universal h - p adaptive finite element strategy: Part 2 , 1989 .

[9]  Ivo Babuška,et al.  On the exponential convergence of the h-p version for boundary element Galerkin methods on polygons , 1990 .

[10]  Yijun Liu,et al.  Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions , 1993 .

[11]  Martin Costabel,et al.  Boundary Integral Operators on Lipschitz Domains: Elementary Results , 1988 .

[12]  R. Kress.  Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering , 1985 .

[13]  S. Amini.  On the choice of the coupling parameter in boundary integral formulations of the exterior acoustic problem , 1990 .

[14]  Leszek Demkowicz,et al.  Toward a universal h-p adaptive finite element strategy , 1989 .

[15]  Christoph Schwab,et al.  Numerical Integration of Singular and Hypersingular Integrals in Boundary Element Methods , 1992 .

[16]  G. F. Miller,et al.  The application of integral equation methods to the numerical solution of some exterior boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.