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Some Numerical Techniques for Maxwell’s Equations in Different Types of Geometries

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Topics in Computational Wave Propagation

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 31))

Summary

Almost all the difficulties that arise in finite difference time domain solutions of Maxwell's equations are due to material interfaces (to which we include objects such as antennas, wires, etc.) Different types of difficulties arise if the geometrical features are much larger than or much smaller than a typical wave length. In the former case, the main difficulty has to do with the spatial discretisation, which needs to combine good geometrical flexibility with a relatively high order of accuracy. After discussing some options for this situation, we focus on the tatter case. The main problem here is to find a time stepping method which combines a very low cost per time step with unconditional stability. The first such method was introduced in 1999 and is based on the ADI principle. We will here discuss that method and some subsequent developments in this area.

The work was supported by NSF grants DMS-0073048, DMS-9810751 (VIGRE), and also by a Faculty Fellowship from the University of Colorado at Boulder.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Colorado, 526 UCB, Boulder, CO, 80309, USA

    Bengt Fomberg

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  1. Bengt Fomberg
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Editors and Affiliations

  1. Department of Mathematics, University of Strathclyde, Richmond Street 26, Glasgow, G1 1XH, UK

    Mark Ainsworth  & Penny Davies  & 

  2. Department of Mathematics, Heriot-Watt University, Riccarton Campus, EH14 4AS, Edinburgh, UK

    Dugald Duncan  & Bryan Rynne  & 

  3. Department of Mathematics and Computer Sciences, Colorado School of Mines, 80401-1887, Golden, USA

    Paul Martin

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Fomberg, B. (2003). Some Numerical Techniques for Maxwell’s Equations in Different Types of Geometries. In: Ainsworth, M., Davies, P., Duncan, D., Rynne, B., Martin, P. (eds) Topics in Computational Wave Propagation. Lecture Notes in Computational Science and Engineering, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55483-4_7

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  • DOI: https://doi.org/10.1007/978-3-642-55483-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00744-9

  • Online ISBN: 978-3-642-55483-4

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