Matrix valued adaptive cross approximation
| Autor: | L. Weggler, Sergej Rjasanow |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Scattering
General Mathematics Mathematical analysis General Engineering 020206 networking & telecommunications 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Matrix (mathematics) Convergence (routing) 0202 electrical engineering electronic engineering information engineering Fundamental solution Boundary value problem 0101 mathematics Boundary element method Mathematics Interpolation Block (data storage) |
| Zdroj: | Mathematical Methods in the Applied Sciences. 40:2522-2531 |
| ISSN: | 0170-4214 |
| Popis: | A new variant of the Adaptive Cross Approximation (ACA) for approximation of dense block matrices is presented. This algorithm can be applied to matrices arising from the Boundary Element Methods (BEM) for elliptic or Maxwell systems of partial differential equations. The usual interpolation property of the ACA is generalised for the matrix valued case. Some numerical examples demonstrate the efficiency of the new method. The main example will be the electromagnetic scattering problem, that is, the exterior boundary value problem for the Maxwell system. Here, we will show that the matrix valued ACA method works well for high order BEM, and the corresponding high rate of convergence is preserved. Another example shows the efficiency of the new method in comparison with the standard technique, whilst approximating the smoothed version of the matrix valued fundamental solution of the time harmonic Maxwell system. Copyright © 2016 John Wiley & Sons, Ltd. |
| Databáze: | OpenAIRE |
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