Exploiting Symmetry in Boundary Element Methods

Exploiting Symmetry in 3D Boundary Element Methods

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 discretization is made which respects the equivariance, the original discretized problem can be decomposed into a collection of much smaller problems, and a significant reduction of computational cost...

A Generalized Fourier Transform for Boundary Element Methods with Symmetries∗

We study the solution of linear systems that typically arise in discretizations of boundary value problems on a domain with geometrical symmetries. If the discretization is done in an appropriate way, then such a system commutes with a group of permutation matrices. Recently, algorithms have been developed that exploit this special structure, however these methods are limited to the case that t...

Exploiting partial or complete geometrical symmetry in 3D symmetric Galerkin indirect BEM formulations

Critique for CS448B ARTDEFO: Accurate Real Time Deformable Objects

of Paper The paper presents an algorithm for physically accurate simulation of elastic deformable objects that are also fast enough for real-time animation. The algorithm uses Boundary Element Method (BEM) (vs. Finite Element Method). The algorithm applies to deformable objects that can be simulated by linear elastic models. It achieves interactive speeds by exploiting coherence in typical inte...

Numerical Exploitation of Equivariance4;5

Linear operators in equations describing physical problems on a symmetric domain often are also equivariant, which means that they commute with its symmetries, i.e., with the group of orthogonal transformations which leave the domain invariant. Under suitable dis-cretizations the resulting system matrices are also equivariant. Methods for exploiting this equivariance in the numerical solution o...