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An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics

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Abstract

In plasma simulations, where the speed of light divided by a characteristic length is at a much higher frequency than other relevant parameters in the underlying system, such as the plasma frequency, implicit methods begin to play an important role in generating efficient solutions in these multi-scale problems. Under conditions of scale separation, one can rescale Maxwell’s equations in such a way as to give a magneto static limit known as the Darwin approximation of electromagnetics. In this work, we present a new approach to solve Maxwell’s equations based on a Method of Lines Transpose (\(\hbox {MOL}^T\)) formulation, combined with a fast summation method with computational complexity \(O(N\log {N})\), where N is the number of grid points (particles). Under appropriate scaling, we show that the proposed schemes result in asymptotic preserving methods that can recover the Darwin limit of electrodynamics.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Yingda Cheng, Andrew J. Christlieb & Wei Guo

  2. Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI, 48824, USA

    Andrew J. Christlieb

  3. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, 49931, USA

    Benjamin Ong

Authors
  1. Yingda Cheng
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  2. Andrew J. Christlieb
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  3. Wei Guo
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  4. Benjamin Ong
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Corresponding author

Correspondence to Wei Guo.

Additional information

Y. Cheng: Research is supported by NSF Grant DMS-1318186.

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Cheng, Y., Christlieb, A.J., Guo, W. et al. An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics. J Sci Comput 71, 959–993 (2017). https://doi.org/10.1007/s10915-016-0328-0

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  • DOI: https://doi.org/10.1007/s10915-016-0328-0

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