TY - JOUR

T1 - An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics

AU - Cheng, Yingda

AU - Christlieb, Andrew J.

AU - Guo, Wei

AU - Ong, Benjamin

N1 - Funding Information:
Y. Cheng: Research is supported by NSF Grant DMS-1318186.
Publisher Copyright:
© 2016, Springer Science+Business Media New York.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

KW - Asymptotic preserving method

KW - Darwin approximation

KW - Fast summation method

KW - Implicit method

KW - Maxwell’s equations

KW - Method of Lines Transpose

UR - http://www.scopus.com/inward/record.url?scp=85001124003&partnerID=8YFLogxK

U2 - 10.1007/s10915-016-0328-0

DO - 10.1007/s10915-016-0328-0

M3 - Article

AN - SCOPUS:85001124003

VL - 71

SP - 959

EP - 993

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

IS - 3

ER -