Compression Techniques for Boundary Integral Equations---Asymptotically Optimal Complexity Estimates

Authors:
Wolfgang Dahmen;Helmut Harbrecht;Reinhold Schneider
Affiliations:
-;-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2006

Citing 0
Cited 10

Efficient treatment of stationary free boundary problems

Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
Compact gradient tracking in shape optimization

Computational Optimization and Applications - Special issue: Numerical analysis of optimization in partial differential equations
Compact gradient tracking in shape optimization

Computational Optimization and Applications
On the numerical solution of Plateau's problem

Applied Numerical Mathematics
Wavelet BEM on molecular surfaces: parametrization and implementation

Computing
The black-box fast multipole method

Journal of Computational Physics
Fast wavelet BEM for 3d electromagnetic shaping

Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Tracking Neumann Data for Stationary Free Boundary Problems

SIAM Journal on Control and Optimization
Wavelet Galerkin Schemes for Multidimensional Anisotropic Integrodifferential Operators

SIAM Journal on Scientific Computing
Application of semiorthogonal spline wavelets and the Galerkin method to the numerical simulation of thin wire antennas

Computational Mathematics and Mathematical Physics

Quantified Score

Hi-index	0.01

Visualization

Abstract

Matrix compression techniques in the context of wavelet Galerkin schemes for boundary integral equations are developed and analyzed that exhibit optimal complexity in the following sense. The fully discrete scheme produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that is proven to stay proportional to the number of unknowns. Key issues are the second compression, which reduces the near field complexity significantly, and an additional a posteriori compression. The latter is based on a general result concerning an optimal work balance that applies, in particular, to the quadrature used to compute the compressed stiffness matrix with sufficient accuracy in linear time.