论文信息 - Fast cluster techniques for BEM

Fast cluster techniques for BEM

In this paper, we will present a new approach for solving boundary integral equations with panel clustering. In contrast to all former versions of panel clustering, the computational and storage complexity of the algorithm scales linearly with respect to the number of degrees of freedom without any additional logarithmic factors. The idea is to develop alternative formulations of all classical boundary integral operators for the Laplace problem where the kernel function has a reduced singular behaviour. It turns out that the application of the panel-clustering method with variable approximation order preserves the asymptotic convergence rate of the discretisation and has significantly reduced complexity.

Stefan A. Sauter | Nico Krzebek

[1] V. Rokhlin. Rapid solution of integral equations of classical potential theory , 1985 .

[2] W. Hackbusch. Elliptic Differential Equations , 1992 .

[3] C. Schwab,et al. Quadrature for hp-Galerkin BEM in lR3 , 1997 .

[4] W. Hackbusch,et al. On the fast matrix multiplication in the boundary element method by panel clustering , 1989 .

[5] Stefan A. Sauter,et al. Efficient automatic quadrature in 3-d Galerkin BEM , 1998 .

[6] J. Nédélec,et al. Integral equations with non integrable kernels , 1982 .

[7] Wolfgang Hackbusch,et al. On the efficient use of the Galerkin-method to solve Fredholm integral equations , 1993 .

[8] Stefan A. Sauter,et al. Variable Order Panel Clustering , 2000, Computing.

[9] B. M. Fulk. MATH , 1992 .

[10] Ivan G. Graham,et al. Hybrid Galerkin boundary elements: theory and implementation , 2000, Numerische Mathematik.

[11] Wolfgang Hackbusch. Theory of Fredholm Integral Equations of the Second Kind , 1995 .

[12] Christian Lage,et al. Transformation of hypersingular integrals and black-box cubature , 2001, Math. Comput..

[13] J. Nédélec. Acoustic and electromagnetic equations , 2001 .

[14] C. Schwab,et al. Quadrature for $hp$-Galerkin BEM in ${\hbox{\sf l\kern-.13em R}}^3$ , 1997 .

[15] W. McLean. Strongly Elliptic Systems and Boundary Integral Equations , 2000 .