TY - JOUR
T1 - Multiscale Numerical Algorithm for 3D Maxwell's Equations with Memory Effects in Composite Materials
AU - Y. Zhang, L. Cao, W. Allegretto & Y. Lin
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.