The Poincaré-Steklov Operator in Hybrid Finite Element-Boundary Integral Equation Formulations
نویسنده
چکیده
The Poincaré-Steklov operator provides a direct relation between the tangential electric and magnetic field at the boundary of a simply connected domain, and a discrete equivalent of the operator can be constructed from the sparse finite element (FE) matrix of that domain by forming the Schur complement to eliminate the interior unknowns. Identifying the FE system matrix as a discretized version of the PoincaréSteklov operator allows us to describe and analyze FE and hybrid finite element-boundary integral equation (FE-BIE) formulations from an operator point of view. We show how this operator notation provides substantial theoretical insight into the analysis of spurious solutions in hybrid FE-BIE methods, and we apply the theory on a TM scattering example to predict the breakdown frequencies of different hybrid formulations.
منابع مشابه
Domain decomposition methods via boundary integral equations
Domain decomposition methods are designed to deal with coupled or transmission problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain decomposition methods are well suited for both parallelization and coupling of different discretization schemes. In general, the coupled problem is reduced to the Schur complem...
متن کاملBoundary element methods for potential problems with nonlinear boundary conditions
Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in twoand three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations...
متن کاملChallenges and Applications of Boundary Element Domain Decomposition Methods
Boundary integral equation methods are well suited to represent the Dirichlet to Neumann maps which are required in the formulation of domain decomposition methods. Based on the symmetric representation of the local Steklov– Poincaré operators by a symmetric Galerkin boundary element method, we describe a stabilized variational formulation for the local Dirichlet to Neumann map. By a strong cou...
متن کاملCoupled FE/BE Formulations for the Fluid–Structure Interaction
We present several coupled finite and boundary element formulations for the vibro-acoustic simulation of completely immersed bodies such as submarines. All formulations are based on the different use of standard boundary integral equations. In addition to the well known symmetric coupling we discuss two different approaches which are based on the weakly singular boundary integral equation only.
متن کاملA Posteriori Error Estimates for Boundary Element Methods
This paper deals with a general framework for a posteriori error estimates in boundary element methods which is specified for three examples, namely Symm's integral equation, an integral equation with a hypersingular operator, and a boundary integral equation for a transmission problem. Based on these estimates, an analog of Eriksson and Johnson's adaptive finite element method is proposed for ...
متن کامل