Progress in Boundary Element Methods (Vol. 1)

Boundary Concentrated Finite Element Methods

Principles of Boundary Element Methods

Boundary integral equations are a classical tool for the analysis of boundary value problems for partial differential equations. The term “ boundary element method” (BEM) denotes any method for the approximate numerical solution of these boundary integral equations. The approximate solution of the boundary value problem obtained by BEM has the distinguishing feature that it is an exact solution...

Boundary Element Methods for Eddy

Exploiting Symmetry in Boundary Element Methods

We consider linear operator equations Lf = g in the context of boundary element methods, where the operator L is equivariant i.e., commutes with the actions of a given finite symmetry group. By introducing a generalization of Reynolds projectors, we construct a decomposition of the identity operator, which in turn allows us to decompose the problem Lf = g into a finite number of symmetric subpr...

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...