TY - JOUR
T1 - High-order accurate modeling of electromagnetic wave propagation across media - Grid conforming bodies
AU - Kashdan, Eugene
AU - Turkel, Eli
PY - 2006/11/1
Y1 - 2006/11/1
N2 - The Maxwell equations contain a dielectric permittivity ε that describes the particular media. For homogeneous materials at low temperatures this coefficient is constant within a material. However, it jumps at the interface between different media. This discontinuity can significantly reduce the order of accuracy of the numerical scheme. We solve the Maxwell equations, with an interface between two media, using a fourth-order accurate algorithm. We regularize the discontinuous dielectric permittivity by a continuous function either locally, near the interface, or globally, in the entire domain. We study the effect of this regularization on the order of accuracy for a one-dimensional time-dependent problem. We then implement this for the three-dimensional Maxwell equations in spherical coordinates with appropriate physical and artificial absorbing boundary conditions. We use Fourier filtering of the high frequency modes near the poles to increase the time-step.
AB - The Maxwell equations contain a dielectric permittivity ε that describes the particular media. For homogeneous materials at low temperatures this coefficient is constant within a material. However, it jumps at the interface between different media. This discontinuity can significantly reduce the order of accuracy of the numerical scheme. We solve the Maxwell equations, with an interface between two media, using a fourth-order accurate algorithm. We regularize the discontinuous dielectric permittivity by a continuous function either locally, near the interface, or globally, in the entire domain. We study the effect of this regularization on the order of accuracy for a one-dimensional time-dependent problem. We then implement this for the three-dimensional Maxwell equations in spherical coordinates with appropriate physical and artificial absorbing boundary conditions. We use Fourier filtering of the high frequency modes near the poles to increase the time-step.
KW - CEM
KW - Discontinuities
KW - Discontinuous coefficients
KW - FDTD
KW - High-order accuracy
KW - High-order methods
KW - Time-dependent Maxwell equations
UR - http://www.scopus.com/inward/record.url?scp=33748798020&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2006.03.009
DO - 10.1016/j.jcp.2006.03.009
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AN - SCOPUS:33748798020
SN - 0021-9991
VL - 218
SP - 816
EP - 835
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 2
ER -