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High-order Runge-Kutta multiresolution time-domain methods for computational electromagnetics

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3 Author(s)
Qunsheng Cao ; Coll. of Inf. Sci. & Technol., Nanjing Univ. of Aeronaut. & Astronaut. ; Kanapady, R. ; Reitich, F.

In this paper we introduce a class of Runge-Kutta multiresolution time-domain (RK-MRTD) methods for problems of electromagnetic wave propagation that can attain an arbitrarily high order of convergence in both space and time. The methods capitalize on the high-order nature of spatial multiresolution approximations by incorporating time integrators with convergence properties that are commensurate with these. More precisely, the classical MRTD approach is adapted here to incorporate mth-order m-stage low-storage Runge-Kutta methods for the time integration. As we show, if compactly supported wavelets of order N are used (e.g., the Daubechies DN functions) and m=N, then the RK-MRTD methods deliver solutions that converge with this overall order; a variety of examples illustrate these properties. Moreover, we further show that the resulting algorithms are well suited to parallel implementations, as we present results that demonstrate their near-optimal scaling

Published in:

Microwave Theory and Techniques, IEEE Transactions on  (Volume:54 ,  Issue: 8 )

Date of Publication:

Aug. 2006

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