Volume 15, Issue 5
An Unpreconditioned Boundary-Integral for Iterative Solution of Scattering Problems with Non-Constant Leontovitch Impedance Boundary Conditions

D. Levadoux, F. Millot & S. Pernet

Commun. Comput. Phys., 15 (2014), pp. 1431-1460.

Published online: 2014-05

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  • Abstract

This paper concerns the electromagnetic scattering by arbitrary shaped three dimensional imperfectly conducting objects modeled with non-constant Leontovitch impedance boundary condition. It has two objectives. Firstly, the intrinsically wellconditioned integral equation (noted GCSIE) proposed in [30] is described focusing on its discretization. Secondly, we highlight the potential of this method by comparison with two other methods, the first being a two currents formulation in which the impedance condition is implicitly imposed and whose the convergence is quasioptimal for Lipschitz polyhedron, the second being a CFIE-like formulation [14]. In particular, we prove that the new approach is less costly in term of CPU time and gives a more accurate solution than that obtained from the CFIE formulation. Finally, as expected, It is demonstrated that no preconditioner is needed for this formulation.

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@Article{CiCP-15-1431, author = {}, title = {An Unpreconditioned Boundary-Integral for Iterative Solution of Scattering Problems with Non-Constant Leontovitch Impedance Boundary Conditions}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {5}, pages = {1431--1460}, abstract = {

This paper concerns the electromagnetic scattering by arbitrary shaped three dimensional imperfectly conducting objects modeled with non-constant Leontovitch impedance boundary condition. It has two objectives. Firstly, the intrinsically wellconditioned integral equation (noted GCSIE) proposed in [30] is described focusing on its discretization. Secondly, we highlight the potential of this method by comparison with two other methods, the first being a two currents formulation in which the impedance condition is implicitly imposed and whose the convergence is quasioptimal for Lipschitz polyhedron, the second being a CFIE-like formulation [14]. In particular, we prove that the new approach is less costly in term of CPU time and gives a more accurate solution than that obtained from the CFIE formulation. Finally, as expected, It is demonstrated that no preconditioner is needed for this formulation.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.250313.281013a}, url = {http://global-sci.org/intro/article_detail/cicp/7144.html} }
TY - JOUR T1 - An Unpreconditioned Boundary-Integral for Iterative Solution of Scattering Problems with Non-Constant Leontovitch Impedance Boundary Conditions JO - Communications in Computational Physics VL - 5 SP - 1431 EP - 1460 PY - 2014 DA - 2014/05 SN - 15 DO - http://dor.org/10.4208/cicp.250313.281013a UR - https://global-sci.org/intro/article_detail/cicp/7144.html KW - AB -

This paper concerns the electromagnetic scattering by arbitrary shaped three dimensional imperfectly conducting objects modeled with non-constant Leontovitch impedance boundary condition. It has two objectives. Firstly, the intrinsically wellconditioned integral equation (noted GCSIE) proposed in [30] is described focusing on its discretization. Secondly, we highlight the potential of this method by comparison with two other methods, the first being a two currents formulation in which the impedance condition is implicitly imposed and whose the convergence is quasioptimal for Lipschitz polyhedron, the second being a CFIE-like formulation [14]. In particular, we prove that the new approach is less costly in term of CPU time and gives a more accurate solution than that obtained from the CFIE formulation. Finally, as expected, It is demonstrated that no preconditioner is needed for this formulation.

D. Levadoux, F. Millot & S. Pernet. (2020). An Unpreconditioned Boundary-Integral for Iterative Solution of Scattering Problems with Non-Constant Leontovitch Impedance Boundary Conditions. Communications in Computational Physics. 15 (5). 1431-1460. doi:10.4208/cicp.250313.281013a
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