# Boundary element methods for Helmholtz problems with weakly imposed boundary conditions

@article{Betcke2020BoundaryEM, title={Boundary element methods for Helmholtz problems with weakly imposed boundary conditions}, author={Timo Betcke and Erik Burman and Matthew W. Scroggs}, journal={ArXiv}, year={2020}, volume={abs/2004.13424} }

We consider boundary element methods where the Calderon projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed using techniques from augmented Lagrangian methods. Regardless of the boundary conditions, both the primal trace variable and the flux are approximated. We focus on the imposition of Dirichlet and mixed Dirichlet--Neumann conditions on the Helmholtz equation, and extend the analysis of the Laplace… Expand

#### References

SHOWING 1-10 OF 32 REFERENCES

Boundary Element Methods with Weakly Imposed Boundary Conditions

- Mathematics, Computer Science
- SIAM J. Sci. Comput.
- 2019

We consider boundary element methods where the Calder\'on projector is used for the system matrix and boundary conditions are weakly imposed using a particular variational boundary operator designed… Expand

Stabilized boundary element methods for exterior Helmholtz problems

- Mathematics, Computer Science
- Numerische Mathematik
- 2008

This paper describes and analyze some modified boundary element methods to solve the exterior Dirichlet boundary value problem for the Helmholtz equation and proposes regularization based on boundary integral operators which are already included in standard boundary element formulations. Expand

Mixed boundary integral methods for Helmholtz transmission problems

- 2007

In this paper we propose a hybrid between direct and indirect boundary integral methods to solve a transmission problem for the Helmholtz equation in Lipschitz and smooth domains. We present an… Expand

Boundary Integral Equations for Mixed Boundary Value Problems in R3

- Mathematics
- 1987

Both exterior and interior mixed Dirichlet-Neumann problems in R3 for the scalar Helmholtz equation are solved via boundary integral equations. The integral equations are equivalent to the original… Expand

Weak imposition of Signorini boundary conditions on the boundary element method

- Computer Science, Mathematics
- SIAM J. Numer. Anal.
- 2020

A complete numerical a priori error analysis is presented and some numerical examples to illustrate the theory are presented, focusing on Signorini contact conditions. Expand

Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements

- Mathematics
- 2007

Boundary Value Problems.- Function Spaces.- Variational Methods.- Variational Formulations of Boundary Value Problems.- Fundamental Solutions.- Boundary Integral Operators.- Boundary Integral… Expand

Symmetric boundary integral formulations for Helmhotz transmission problem

- Mathematics
- 2007

In this work we propose and analyze numerical methods for the approximation
of the solution of Helmholtz transmission problems in two or three dimensions. This
kind of problems arises in many… Expand

Stabilized FEM-BEM Coupling for Helmholtz Transmission Problems

- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 2006

asymptotic quasi-optimality of a combined finite element and boundary element Galerkin discretization for all frequencies is concluded. Expand

Coercivity of Combined Boundary Integral Equations in High-Frequency Scattering

- Mathematics
- 2015

We prove that the standard second-kind integral equation formulation of the exterior Dirichlet problem for the Helmholtz equation is coercive (i.e., sign-definite) for all smooth convex domains when… Expand

A Refined Galerkin Error and Stability Analysis for Highly Indefinite Variational Problems

- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 2007

The analysis is generalized to the Galerkin method and shows that the boundary element method does not suffer from the pollution effect, and the constant of quasioptimality is independent of $k$, which is an improvement over previously available results. Expand