Biorthogonal wavelet approximation for the coupling of FEM-BEM

Harbrecht, Helmut; Paiva, Freddy; Pérez, Cristian; Schneider, Reinhold

doi:10.1007/s002110100283

Cited by 24 publications

(44 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The non-local boundary value problem (43) can be solved, e.g. along the lines of [37,38]. Finite elements are applied to discretize the Poisson equation on B.…”

Section: Coupling Of Fems and Bemsmentioning

confidence: 99%

See 1 more Smart Citation

Analytical and numerical methods in shape optimization

Harbrecht

2008

Math Methods in App Sciences

View full text Add to dashboard Cite

SUMMARYThis paper is intended to overview on analytical and numerical methods in shape optimization. We compute and analyse the shape Hessian in order to distinguish well-posed and ill-posed shape optimization problems. We introduce different discretization techniques of the shape and present existence and convergence results of approximate solutions in case of well posedness. Finally, we survey on the efficient numerical solution of the state equation, including finite and boundary element methods as well as fictitious domain methods.

show abstract

“…The non-local boundary value problem (43) can be solved, e.g. along the lines of [37,38]. Finite elements are applied to discretize the Poisson equation on B.…”

Section: Coupling Of Fems and Bemsmentioning

confidence: 99%

“…That way, applying wavelet matrix compression, the complexity is reduced (cf. [37]) and optimal preconditioners are available (cf. [38]).…”

Section: Coupling Of Fems and Bemsmentioning

confidence: 99%

Analytical and numerical methods in shape optimization

Harbrecht

2008

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…On the other hand, the system matrices are quasi-sparse and can be compressed without loss of accuracy such that the complexity for the solution of the boundary integral equations becomes linear, cf. References [11,13,27].…”

Section: The Wavelet Galerkin Schemementioning

confidence: 99%

Exterior electromagnetic shaping using wavelet BEM

Eppler¹,

Harbrecht²

2005

Math. Meth. Appl. Sci.

Self Cite

View full text Add to dashboard Cite

SUMMARYThe present paper is devoted to exterior electromagnetic shaping in two dimensions. We model the conductors by regular densities which leads to a ÿnite objective and allows a line-search. In order to compute the surface pressure we optimize an Augmented Lagrangian by a Newton method using a second-order approach for the Lagrange multiplier. Since the underlying state function satisÿes an exterior boundary value problem, we compute ÿrst and second order derivatives of its boundary data by boundary integral equations which are numerically solved by a fast wavelet Galerkin scheme. Numerical results prove that we succeeded in ÿnding a fast and robust algorithm for solving the considered class of problems.

show abstract

“…This is an important task for the coupling of FEM and BEM, cf. [24,25]. Additionally, in view of the discretization of operators of positive order globally continuous wavelets are available [2,5,16,23].…”

Section: Background and Motivationmentioning

confidence: 99%

Biorthogonal wavelet bases for the boundary element method

Harbrecht

Schneider

2004

Mathematische Nachrichten

View full text Add to dashboard Cite

Dedicated to the memory of Erhard MeisterAs shown by Dahmen, Harbrecht and Schneider [7,23,32], the fully discrete wavelet Galerkin scheme for boundary integral equations scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. The supposition is a wavelet basis with a sufficiently large number of vanishing moments. In this paper we present several constructions of appropriate wavelet bases on manifolds based on the biorthogonal spline wavelets of A. Cohen, I. Daubechies and J.-C. Feauveau [4]. By numerical experiments we demonstrate that it is worthwhile to spent effort on their construction to increase the performance of the wavelet Galerkin scheme considerably.

show abstract

Biorthogonal wavelet approximation for the coupling of FEM-BEM

Cited by 24 publications

References 26 publications

Analytical and numerical methods in shape optimization

Analytical and numerical methods in shape optimization

Exterior electromagnetic shaping using wavelet BEM

Biorthogonal wavelet bases for the boundary element method

Contact Info

Product

Resources

About