2,846 research outputs found
Combining the Ultra-Weak Variational Formulation and the Multilevel Fast Multipole Method
International audienceBecause of its practical significance, many different methods have been developed for the solution of the time-harmonic Maxwell equations in an exterior domain at higher frequency. Often methods with complimentary strengths can be combined to obtain an even better method. In this paper we provide a numerical study of a method for coupling of the Ultra-Weak Variational Formulation (UWVF) of Maxwell's equations, a volume based method using plane wave basis functions, and an overlapping integral representation of the unknown field to obtain an exact artificial boundary condition on an auxiliary surface that can be very close to the scatterer. Combining the new algorithm with a multilevel fast multipole method we obtain an efficient volume based solver with an exact auxiliary boundary condition, but without the need for singular integrals
Discontinuous Galerkin Methods with Trefftz Approximation
We present a novel Discontinuous Galerkin Finite Element Method for wave
propagation problems. The method employs space-time Trefftz-type basis
functions that satisfy the underlying partial differential equations and the
respective interface boundary conditions exactly in an element-wise fashion.
The basis functions can be of arbitrary high order, and we demonstrate spectral
convergence in the \Lebesgue_2-norm. In this context, spectral convergence is
obtained with respect to the approximation error in the entire space-time
domain of interest, i.e. in space and time simultaneously. Formulating the
approximation in terms of a space-time Trefftz basis makes high order time
integration an inherent property of the method and clearly sets it apart from
methods, that employ a high order approximation in space only.Comment: 14 pages, 12 figures, preprint submitted at J Comput Phy
Boundary integral methods in high frequency scattering
In this article we review recent progress on the design, analysis and implementation of numerical-asymptotic boundary integral methods for the computation of frequency-domain acoustic scattering in a homogeneous unbounded medium by a bounded obstacle. The main aim of the methods is to allow computation of scattering at arbitrarily high frequency with finite computational resources
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