TY - JOUR
T1 - A Numerical Method for 3D Time-Dependent Maxwell’s Equations in Axisymmetric Singular Domains with Arbitrary Data
AU - Assous, Franck
AU - Raichik, Irina
N1 - Publisher Copyright:
© 2023 The Author(s). Published by Vilnius Gediminas Technical University.
PY - 2023/9/4
Y1 - 2023/9/4
N2 - In this article, we propose to solve the three-dimensional time-dependent Maxwell equations in a singular axisymmetric domain with arbitrary data. Due to the axisymmetric assumption, the singular computational domain boils down to a subset of R2. However, the electromagnetic field and other vector quantities still belong to R3. Taking advantage that the domain is transformed into a two-dimensional one, by doing Fourier analysis in the third dimension, one arrives to a sequence of singular problems set in a 2D domain. The mathematical tools of such problems have been exposed in [4, 19]. Here, we derive a variational method from which we propose an original finite element numerical approach to solve the problem. Numerical experiments are also shown to illustrate that the method is able to capture the singular part of the solution. This approach can also be viewed as a generalization of the Singular Complement Method to three-dimensional problem.
AB - In this article, we propose to solve the three-dimensional time-dependent Maxwell equations in a singular axisymmetric domain with arbitrary data. Due to the axisymmetric assumption, the singular computational domain boils down to a subset of R2. However, the electromagnetic field and other vector quantities still belong to R3. Taking advantage that the domain is transformed into a two-dimensional one, by doing Fourier analysis in the third dimension, one arrives to a sequence of singular problems set in a 2D domain. The mathematical tools of such problems have been exposed in [4, 19]. Here, we derive a variational method from which we propose an original finite element numerical approach to solve the problem. Numerical experiments are also shown to illustrate that the method is able to capture the singular part of the solution. This approach can also be viewed as a generalization of the Singular Complement Method to three-dimensional problem.
KW - Fourier analysis
KW - axisymmet-ric geometry
KW - singularities
KW - time-dependent Maxwell equations
UR - http://www.scopus.com/inward/record.url?scp=85171997875&partnerID=8YFLogxK
U2 - 10.3846/mma.2023.17553
DO - 10.3846/mma.2023.17553
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AN - SCOPUS:85171997875
SN - 1392-6292
VL - 28
SP - 487
EP - 508
JO - Mathematical Modelling and Analysis
JF - Mathematical Modelling and Analysis
IS - 3
ER -