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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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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 well-conditioned 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 quasi-optimal 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 = {D. Levadoux, F. Millot and S. Pernet}, 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 well-conditioned 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 quasi-optimal 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 AU - D. Levadoux, F. Millot & S. Pernet JO - Communications in Computational Physics VL - 5 SP - 1431 EP - 1460 PY - 2014 DA - 2014/05 SN - 15 DO - http://doi.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 well-conditioned 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 quasi-optimal 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 and S. Pernet. (2014). 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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