Coupling of boundary element methods and finite element methods

EP Stephan - Encyclopedia of Computational Mechanics …, 2018 - Wiley Online Library
For the numerical treatment of elliptic boundary value problems, the coupling of boundary
element methods (BEM) and finite element methods (FEM) is widely used. Usually, the FEM …

A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

DP Hewett, S Langdon… - IMA Journal of …, 2015 - academic.oup.com
We propose and analyse a hybrid numerical–asymptotic boundary element method (BEM)
for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of …

The fast multipole method for the symmetric boundary integral formulation

G Of, O Steinbach, WL Wendland - IMA journal of numerical …, 2006 - academic.oup.com
A symmetric Galerkin boundary-element method is used for the solution of boundary-value
problems with mixed boundary conditions of Dirichlet and Neumann type. As a model …

Additive Schwarz method for the p-version of the boundary element method for the single layer potential operator on a plane screen

N Heuer - Numerische Mathematik, 2001 - Springer
We analyze an additive Schwarz preconditioner for the p-version of the boundary element
method for the single layer potential operator on a plane screen in the three-dimensional …

Multilevel decompositions and norms for negative order Sobolev spaces

T Führer - Mathematics of Computation, 2022 - ams.org
We consider multilevel decompositions of piecewise constants on simplicial meshes that are
stable in $ H^{-s} $ for $ s\in (0, 1) $. Proofs are given in the case of uniformly and locally …

Multilevel diagonal scaling preconditioners for boundary element equations on locally refined meshes

M Ainsworth, W McLean - Numerische Mathematik, 2003 - Springer
We study a multilevel preconditioner for the Galerkin boundary element matrix arising from a
symmetric positive-definite bilinear form. The associated energy norm is assumed to be …

An additive Schwarz method for the h‐p version of the boundary element method for hypersingular integral equations in ℜ3

N Heuer, EP Stephan - IMA journal of numerical analysis, 2001 - ieeexplore.ieee.org
We study a preconditioner for the h‐p version of the boundary element method for
hypersingular integral equations in three dimensions. The preconditioner is based on a …

An efficient preconditioner for the fast simulation of a 2D Stokes flow in porous media

B Quaife, P Coulier, E Darve - International Journal for …, 2018 - Wiley Online Library
We consider an efficient preconditioner for a boundary integral equation (BIE) formulation of
the two‐dimensional Stokes equations in porous media. While BIEs are well‐suited for …

Multiplicative Schwarz algorithms for the Galerkin boundary element method

M Maischak, EP Stephan, T Tran - SIAM journal on numerical analysis, 2000 - SIAM
We study the multiplicative Schwarz method for the h-and the p-version Galerkin boundary
element method for a hypersingular and a weakly singular integral equation of the first kind …

[图书][B] Schwarz methods and multilevel preconditioners for boundary element methods

EP Stephan, T Tran - 2021 - Springer
Several textbooks and monographs on preconditioners for FEM (finite element methods) are
available, but none exists for BEM (boundary element methods). For BEM, the topic is dealt …