Corpus ID: 216562402

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

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References

SHOWING 1-10 OF 32 REFERENCES
Boundary Element Methods with Weakly Imposed Boundary Conditions
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 designedExpand
Stabilized boundary element methods for exterior Helmholtz problems
TLDR
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
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 anExpand
Boundary Integral Equations for Mixed Boundary Value Problems in R3
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 originalExpand
Weak imposition of Signorini boundary conditions on the boundary element method
TLDR
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
Boundary Value Problems.- Function Spaces.- Variational Methods.- Variational Formulations of Boundary Value Problems.- Fundamental Solutions.- Boundary Integral Operators.- Boundary IntegralExpand
Symmetric boundary integral formulations for Helmhotz transmission problem
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 manyExpand
Stabilized FEM-BEM Coupling for Helmholtz Transmission Problems
TLDR
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
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 whenExpand
A Refined Galerkin Error and Stability Analysis for Highly Indefinite Variational Problems
TLDR
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
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