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Title: Energy/dissipation-preserving Birkhoffian multi-symplectic methods for Maxwell's equations with dissipation terms

In this study, we propose two new energy/dissipation-preserving Birkhoffian multi-symplectic methods (Birkhoffian and Birkhoffian box) for Maxwell's equations with dissipation terms. After investigating the non-autonomous and autonomous Birkhoffian formalism for Maxwell's equations with dissipation terms, we first apply a novel generating functional theory to the non-autonomous Birkhoffian formalism to propose our Birkhoffian scheme, and then implement a central box method to the autonomous Birkhoffian formalism to derive the Birkhoffian box scheme. We have obtained four formal local conservation laws and three formal energy global conservation laws. We have also proved that both of our derived schemes preserve the discrete version of the global/local conservation laws. Furthermore, the stability, dissipation and dispersion relations are also investigated for the schemes. Theoretical analysis shows that the schemes are unconditionally stable, dissipation-preserving for Maxwell's equations in a perfectly matched layer (PML) medium and have second order accuracy in both time and space. Numerical experiments for problems with exact theoretical results are given to demonstrate that the Birkhoffian multi-symplectic schemes are much more accurate in preserving energy than both the exponential finite-difference time-domain (FDTD) method and traditional Hamiltonian scheme. Finally, we also solve the electromagnetic pulse (EMP) propagation problem and the numerical results show thatmore » the Birkhoffian scheme recovers the magnitude of the current source and reaction history very well even after long time propagation.« less
 [1] ;  [2]
  1. Renmin Univ. of China, Beijing (China). Dept. of Mathematics
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
Publication Date:
Report Number(s):
Journal ID: ISSN 0021-9991
Grant/Contract Number:
AC52-06NA25396; 10701081; 11071251
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 311; Journal ID: ISSN 0021-9991
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Renmin Univ. of China, Beijing (China)
Sponsoring Org:
USDOE Laboratory Directed Research and Development (LDRD) Program; National Natural Science Foundation of China (NNSFC)
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Structure-preserving method; Computational electromagnetics; Birkhoffian multi-symplectic method; Energy/dissipation-preserving method; Hamiltonian scheme; Maxwell's equations with dissipation terms
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1347461