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Rapid Solution of the Wave Equation in Unbounded Domains
In this paper we propose and analyze a new, fast method for the numerical solution of time domain boundary integral formulations of the wave equation. Expand
A Refined Galerkin Error and Stability Analysis for Highly Indefinite Variational Problems
We generalize the analysis to the Galerkin method applied to an abstract highly indefinite variational problem. Expand
Multistep and Multistage Convolution Quadrature for the Wave Equation: Algorithms and Experiments
  • L. Banjai
  • Computer Science, Mathematics
  • SIAM J. Sci. Comput.
  • 1 August 2010
We describe how a time-discretized wave equation in a homogeneous medium can be solved by boundary integral methods. Expand
Runge–Kutta convolution quadrature for operators arising in wave propagation
An error analysis of Runge–Kutta convolution quadrature is presented for a class of non-sectorial operators whose Laplace transform satisfies, besides the standard assumptions of analyticity in a half-plane Re s > σ0 and a polynomial bound $${\operatorname{O}(|s|^{\mu_1})}$$ in convex sectors. Expand
Fast convolution quadrature for the wave equation in three dimensions
This work addresses the numerical solution of time-domain boundary integral equations arising from acoustic and electromagnetic scattering in three dimensions with Runge-Kutta convolution. Expand
Fast and Oblivious Algorithms for Dissipative and Two-dimensional Wave Equations
The use of time-domain boundary integral equations has proved very effective and efficient for three dimensional acoustic and electromagnetic wave equations. Expand
Wave Propagation Problems treated with Convolution Quadrature and BEM
In this review paper, a particular type of methods for treating time-domain boundary integral equations (TDBIE), the convolution quadrature, is described together with application areas and most recent improvements to the analysis and efficient implementation. Expand
Stable 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. Expand
Numerical solution of exterior Maxwell problems by Galerkin BEM and Runge–Kutta convolution quadrature
We discretize the time-domain electric field integral equation using Runge–Kutta convolution quadrature in time and a Galerkin method in space. Expand
Sparsity of Runge–Kutta convolution weights for the three-dimensional wave equation
Wave propagation problems in unbounded homogeneous domains can be formulated as time-domain integral equations. An effective way to discretize such equations in time are Runge–Kutta based convolutionExpand