Numerische Mathematik Manuscript-nr. a Finite-element Capacitance Matrix Method for Exterior Helmholtz Problems
نویسنده
چکیده
We introduce an algorithm for the eecient numerical solution of exterior boundary value problems for the Helmholtz equation. The problem is reformulated as an equivalent one on a bounded domain using an exact non-local boundary condition on a circular artiicial boundary. An FFT-based fast Helmholtz solver is then derived for a nite-element discretization on an annular domain. The exterior problem for domains of general shape are treated using an imbedding or capacitance matrix method. The imbedding is achieved in such a way that the resulting capacitance matrix has a favorable spectral distribution leading to mesh independent convergence rates when Krylov subspace methods are used to solve the capacitance matrix equation.
منابع مشابه
Analysis of a coupled finite-infinite element method for exterior Helmholtz problems
Coupled finite-infinite element computations are very efficient for modeling large scale acoustics problems. Parallel algorithms, like sub-structuring and domain decomposition methods, have shown to be very efficient for solving huge linear systems arising from acoustics. In this paper, a coupled finite-infinite element method is described, formulated and analyzed for parallel computations purp...
متن کاملStabilized boundary element methods for exterior Helmholtz problems
In this paper we describe and analyze some modified boundary element methods to solve exterior boundary value problems for the Helmholtz equation with either Dirichlet or Neumann boundary conditions. The proposed approach avoids spurious modes even in the case of Lipschitz boundaries. Moreover, the regularisation is done based on boundary integral operators which are already available in standa...
متن کاملDiscrete Hodge operators
Many linear boundary value problems arising in computational physics can be formulated in the calculus of differential forms. Discrete differential forms provide a natural and canonical approach to their discretization. However, much freedom remains concerning the choice of discrete Hodge operators, that is, discrete analogues of constitutive laws. A generic discrete Hodge operator is introduce...
متن کاملStable numerical coupling of exterior and interior problems for the wave equation
The acoustic wave equation on the whole three-dimensional space is considered with initial data and inhomogeneity having support in a bounded domain, which need not be convex. We propose and study a numerical method that approximates the solution using computations only in the interior domain and on its boundary. The transmission conditions between the interior and exterior domain are imposed b...
متن کاملFast simplicial quadrature-based finite element operators using Bernstein polynomials
We derive low-complexity matrix-free finite element algorithms for simplicial Bernstein polynomials on simplices. Our techniques, based on a sparse representation of differentiation and special block structure in the matrices evaluating B-form polynomials at warped Gauss points, apply to variable coefficient problems as well as constant coefficient ones, thus extending our results in [14].
متن کامل