Energy estimates and numerical verification of the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell's system

被引：32
作者：
Beilina, Larisa [1 ,2 ]
机构：
[1] Chalmers Univ Technol, Dept Math Sci, S-42196 Gothenburg, Sweden
[2] Gothenburg Univ, S-42196 Gothenburg, Sweden
来源：
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2013年 / 11卷 / 04期
基金：
瑞典研究理事会;
关键词：
Maxwell's equation; Hybrid finite element/finite difference method; Energy estimates; Gauge condition; Stabilized finite element method; BOUNDARY; EQUATIONS;
D O I：
10.2478/s11533-013-0202-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We rigorously derive energy estimates for the second order vector wave equation with gauge condition for the electric field with non-constant electric permittivity function. This equation is used in the stabilized Domain Decomposition Finite Element/Finite Difference approach for time-dependent Maxwell's system. Our numerical experiments illustrate efficiency of the modified hybrid scheme in two and three space dimensions when the method is applied for generation of backscattering data in the reconstruction of the electric permittivity function.
引用
收藏
页码：702 / 733
页数：32
相关论文
共 27 条
  • [11] Explicit hybrid time domain solver for the Maxwell equations in 3D
    Edelvik F.
    Ledfelt G.
    [J]. Journal of Scientific Computing, 2000, 15 (01) : 61 - 78
  • [12] Finite elements and mass lumping for Maxwell's equations: the 2D case
    Elmkies, A
    Joly, P
    [J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (11): : 1287 - 1293
  • [13] ENGQUIST B, 1977, MATH COMPUT, V31, P629, DOI 10.1090/S0025-5718-1977-0436612-4
  • [14] Hughes T. J. R., 2012, FINITE ELEMENT METHO
  • [15] Jiang B.N., 1998, The Least-Squares Finite Element Method: Theory and Applications in Computational Fluid Dynamics and Electromagnetics, Scientific Computation
  • [16] The origin of spurious solutions in computational electromagnetics
    Jiang, BN
    Wu, J
    Povinelli, LA
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1996, 125 (01) : 104 - 123
  • [17] Jin J., 1993, FINITE ELEMENT METHO
  • [18] Joly P, 2003, LECT NOTES COMP SCI, V31, P201
  • [19] Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem
    Klibanov, Michael V.
    Fiddy, Michael A.
    Beilina, Larisa
    Pantong, Natee
    Schenk, John
    [J]. INVERSE PROBLEMS, 2010, 26 (04)
  • [20] Monk P., 2003, FINITE ELEMENT METHO
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