On the solution of time-harmonic scattering problems for Maxwell's equations
SIAM Journal on Mathematical Analysis
Domain decomposition methods via boundary integral equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Regularized Combined Field Integral Equations
Numerische Mathematik
Boundary element methods: an overview
Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
Numerical Mathematics (Texts in Applied Mathematics)
Numerical Mathematics (Texts in Applied Mathematics)
Computers & Mathematics with Applications
Stabilized FEM-BEM Coupling for Helmholtz Transmission Problems
SIAM Journal on Numerical Analysis
Detecting Interfaces in a Parabolic-Elliptic Problem from Surface Measurements
SIAM Journal on Numerical Analysis
Symmetric boundary integral formulations for Helmholtz transmission problems
Applied Numerical Mathematics
Journal of Computational Physics
Hi-index | 0.00 |
We present a novel boundary integral formulation of the Helmholtz transmission problem for bounded composite scatterers (that is, piecewise constant material parameters in "subdomains") that directly lends itself to operator preconditioning via Calderón projectors. The method relies on local traces on subdomains and weak enforcement of transmission conditions. The variational formulation is set in Cartesian products of standard Dirichlet and special Neumann trace spaces for which restriction and extension by zero are well defined. In particular, the Neumann trace spaces over each subdomain boundary are built as piecewise $\widetilde{H}^{-1/2}$ -distributions over each associated interface. Through the use of interior Calderón projectors, the problem is cast in variational Galerkin form with an operator matrix whose diagonal is composed of block boundary integral operators associated with the subdomains. We show existence and uniqueness of solutions based on an extension of Lions' projection lemma for non-closed subspaces. We also investigate asymptotic quasi-optimality of conforming boundary element Galerkin discretization. Numerical experiments in 2-D confirm the efficacy of the method and a performance matching that of another widely used boundary element discretization. They also demonstrate its amenability to different types of preconditioning.