1,603 research outputs found
Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples
We present a new approach to three-dimensional electromagnetic scattering
problems via fast isogeometric boundary element methods. Starting with an
investigation of the theoretical setting around the electric field integral
equation within the isogeometric framework, we show existence, uniqueness, and
quasi-optimality of the isogeometric approach. For a fast and efficient
computation, we then introduce and analyze an interpolation-based fast
multipole method tailored to the isogeometric setting, which admits competitive
algorithmic and complexity properties. This is followed by a series of
numerical examples of industrial scope, together with a detailed presentation
and interpretation of the results
Boundary element methods for the wave equation based on hierarchical matrices and adaptive cross approximation
Time-domain Boundary Element Methods (BEM) have been successfully used in
acoustics, optics and elastodynamics to solve transient problems numerically. How ever, the storage requirements are immense, since the fully populated system matrices
have to be computed for a large number of time steps or frequencies. In this article,
we propose a new approximation scheme for the Convolution Quadrature Method
powered BEM, which we apply to scattering problems governed by the wave equa tion. We use H 2-matrix compression in the spatial domain and employ an adaptive
cross approximation algorithm in the frequency domain. In this way, the storage and
computational costs are reduced significantly, while the accuracy of the method is
preserved
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