# Exploiting symmetry in boundary element methods

@article{Allgower1992ExploitingSI, title={Exploiting symmetry in boundary element methods}, author={Eugene L. Allgower and Klaus B{\"o}hmer and Kurt Georg and Rick Miranda}, journal={SIAM Journal on Numerical Analysis}, year={1992}, volume={29}, pages={534-552} }

Linear operator equations $\mathcal {L}f = g$ are considered in the context of boundary element methods, where the operator $\mathcal {L}$ is equivariant, i.e., commutes with the actions of a given finite symmetry group. By introducing a generalization of Reynolds projectors, a decomposition of the identity operator is constructed, which in turn allows the decomposition of the problem $\mathcal {L}f = g$ into a finite number of symmetric subproblems. The data function g does not need to possess…

## 50 Citations

Restriction matrices for numerically exploiting symmetry

- Mathematics, Computer ScienceAdv. Comput. Math.
- 2008

A technique for exploiting symmetry in the numerical treatment of boundary value problems (BVP) and eigenvalue problems which are invariant under a finite group $\mathcal{G}$ of congruences of ${\rm{I\!R}}^{m}$.

Numerical Exploitation of Equivariance 4;5

- Mathematics, Computer Science
- 1997

The present paper summarizes some of the recent work of the authors concerning systematic techniques for exploiting symmetry in the numerical treatment of systems of linear equations that arise from discretizing operator equations displaying symmetries.

A GENERALIZED FOURIER TRANSFORM FOR BOUNDARY ELEMENT METHODS WITH SYMMETRIES

- Mathematics, Computer Science
- 1998

A new symmetry exploiting algorithm, based on the Fourier transform on the symmetry group, is introduced which is capable of handling fixed points and can also be used to achieve further reductions when the right hand side of the proposed system has symmetries.

Numerical exploitation of symmetricstructures in BEM 1

- Mathematics, Computer Science
- 1997

The eecient solution of linear systems of equations and of eigenvalue problems with the Fourier transform method is discussed and some examples involving symmetric domains in the plane and in 3-space are concluded.

Numerical exploitation of symmetry in integral equations

- Computer Science, MathematicsAdv. Comput. Math.
- 1998

In this paper symmetry reduction is studied in connection with quadrature formulae and the Nyström method on the use of symmetry adapted bases and their automated generation.

Exploiting Symmetry in 3 D Boundary Element Methods

- Mathematics
- 1993

Many linear operator equations are defined on regions which are invariant under a group Γ of symmetry transformations. If in addition, the linear operator is equivariant with respect to Γ and if a…

Exploiting Symmetry in

- Mathematics
- 2004

: Classical integral operators usually display invariance with respect to orthogonal transformations. If the domain of an operator equation is symmetric with respect to some orthogonal…

Exploiting Symmetry in BEM 2

- Mathematics, Computer Science
- 1996

The present paper gives a new uniied presentation (giving several modiied deenitions of the Fourier transform) of adapted to the situation and special needs of BEM, and illustrates the reductions which take place when the rich symmetries of a three dimensional cube are exploited.

On group Fourier analysis and symmetry preserving discretizations of PDEs

- Mathematics, Computer Science
- 2006

Algorithms for computing matrix exponentials based on Fourier transforms on finite groups and novel applications of multivariate non-separable Chebyshev polynomials in the construction of spectral element bases on triangular and simplicial sub-domains are introduced.

Restrictions matrices for Platonic solids invariance and applications to space-time energetic BEM

- MathematicsJ. Comput. Appl. Math.
- 2019

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