Volume 1, Issue 1
Multiscale Numerical Algorithm for 3D Maxwell's Equations with Memory Effects in Composite Materials

Y. Zhang, L. Cao, W. Allegretto & Y. Lin

DOI:

Int. J. Numer. Anal. Mod. B, 1 (2010), pp. 41-57

Published online: 2010-01

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  • Abstract

This paper discusses the multiscale method for the time-dependent Maxwell's equations with memory effects in composite materials. The main difficulty is that one cannot use the usual multiscale asymptotic method (cf. [25, 4]) to solve this problem, due to the complication of the memory terms. The key steps addressed in this paper are to transfer the original integro-differential equations to the stationary Maxwell's equations by using the Laplace transform, to employ the multiscale asymptotic method to solve the stationary Maxwell's equations, and then to obtain the computational solution of the original problem by employing a quadrature formula for computing the inverse Laplace transform. Numerical simulations are then carried out to validate the multiscale numerical algorithm in the present paper.

  • Keywords

time-dependent Maxwell's equations memory effects multiscale asymptotic expansion Laplace transform composite materials

  • AMS Subject Headings

65F10 78M05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAMB-1-41, author = {}, title = {Multiscale Numerical Algorithm for 3D Maxwell's Equations with Memory Effects in Composite Materials}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2010}, volume = {1}, number = {1}, pages = {41--57}, abstract = {This paper discusses the multiscale method for the time-dependent Maxwell's equations with memory effects in composite materials. The main difficulty is that one cannot use the usual multiscale asymptotic method (cf. [25, 4]) to solve this problem, due to the complication of the memory terms. The key steps addressed in this paper are to transfer the original integro-differential equations to the stationary Maxwell's equations by using the Laplace transform, to employ the multiscale asymptotic method to solve the stationary Maxwell's equations, and then to obtain the computational solution of the original problem by employing a quadrature formula for computing the inverse Laplace transform. Numerical simulations are then carried out to validate the multiscale numerical algorithm in the present paper.}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/324.html} }
TY - JOUR T1 - Multiscale Numerical Algorithm for 3D Maxwell's Equations with Memory Effects in Composite Materials JO - International Journal of Numerical Analysis Modeling Series B VL - 1 SP - 41 EP - 57 PY - 2010 DA - 2010/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnamb/324.html KW - time-dependent Maxwell's equations KW - memory effects KW - multiscale asymptotic expansion KW - Laplace transform KW - composite materials AB - This paper discusses the multiscale method for the time-dependent Maxwell's equations with memory effects in composite materials. The main difficulty is that one cannot use the usual multiscale asymptotic method (cf. [25, 4]) to solve this problem, due to the complication of the memory terms. The key steps addressed in this paper are to transfer the original integro-differential equations to the stationary Maxwell's equations by using the Laplace transform, to employ the multiscale asymptotic method to solve the stationary Maxwell's equations, and then to obtain the computational solution of the original problem by employing a quadrature formula for computing the inverse Laplace transform. Numerical simulations are then carried out to validate the multiscale numerical algorithm in the present paper.
Y. Zhang, L. Cao, W. Allegretto & Y. Lin. (1970). Multiscale Numerical Algorithm for 3D Maxwell's Equations with Memory Effects in Composite Materials. International Journal of Numerical Analysis Modeling Series B. 1 (1). 41-57. doi:
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