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

Yingda Cheng, Andrew J. Christlieb, Wei Guo, Benjamin Ong

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 (MOL T) formulation, combined with a fast summation method with computational complexity O(Nlog 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.

Original languageEnglish
Pages (from-to)959-993
Number of pages35
JournalJournal of Scientific Computing
Volume71
Issue number3
DOIs
StatePublished - Jun 1 2017

Keywords

  • Asymptotic preserving method
  • Darwin approximation
  • Fast summation method
  • Implicit method
  • Maxwell’s equations
  • Method of Lines Transpose

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