Boundary-Integral Methods for Iterative Solution of Scattering Problems With Variable Impedance Surface Condition

Collino, Francis; Millot, Florence; Pernet, Sébastien

doi:10.2528/pier07103105

Cited by 34 publications

(20 citation statements)

References 20 publications

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“…We will also show that the solutions are accurate. Each result will be compared to the one obtained by using a Impedance Combined Field Equation (ICFIE) that we have proposed in [14]. We have proved that ICFIE is a relevant method to treat constant and variable impedance problems.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…What is less obvious is the computation of n × T. We have already treated this difficulty in [14] when we wanted to construct a Combined Field Integral Equation for the impedance problems. The technique is based on a discrete analogue of the Helmholtz decomposition and has been proposed by Christiansen and Nédélec in [12].…”

Section: Fourth Stepmentioning

confidence: 99%

“…In this case, the size becomes 2ntri. It is not a big system in the case of surface meshes and we have remarked [14] that the cost of the resolution of these kind of system by MUMPS is always negligible compared to the one of the resolution of the integral equation (dense system), even when we use a Fast Multipole Method.…”

Section: Second Stepmentioning

confidence: 99%

“…The last steps are: [14] proved that this step is negligible compared to the (dense) matrix-vector products even when FMM is used.…”

Section: Fourth Stepmentioning

confidence: 99%

“…only two matrix-vector products. Moreover [14] proposed an algorithm which only uses two fast multipole calculations to determine Ku + T v and Kv + T u.…”

Section: Fourth Stepmentioning

confidence: 99%

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A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition

Pernet¹

2010

ESAIM: M2AN

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Abstract. The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.Mathematics Subject Classification. 65R20, 15A12, 65N38, 65F10, 65Z05.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Fourth Stepmentioning

confidence: 99%

Section: Second Stepmentioning

confidence: 99%

“…The last steps are: [14] proved that this step is negligible compared to the (dense) matrix-vector products even when FMM is used.…”

Section: Fourth Stepmentioning

confidence: 99%

“…only two matrix-vector products. Moreover [14] proposed an algorithm which only uses two fast multipole calculations to determine Ku + T v and Kv + T u.…”

Section: Fourth Stepmentioning

confidence: 99%

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A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition

Pernet¹

2010

ESAIM: M2AN

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Parallelized multilevel fast multipole algorithm for scattering by objects with anisotropic impedance surfaces

Zhang

Jin

2014

Int J Numerical Modelling

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A parallelized multilevel fast multipole algorithm (MLFMA) is presented for simulating electromagnetic scattering from complex targets with anisotropic impedance surfaces. By employing both surface electric and magnetic currents as unknowns and weakly enforcing the anisotropic impedance boundary condition, a combined integral equation is formulated to generate a set of well-conditioned linear systems to be solved by MLFMA. To further improve the iterative convergence of the linear systems, a parallel sparse approximate inverse preconditioner is constructed from the near-field interaction of the system matrix. The MLFMA is parallelized to enable computation on a large number of processors for large-scale problems. Several numerical examples are presented to validate the algorithm and demonstrate its accuracy, scalability, and capability in handling large complex objects with anisotropic impedance surfaces. ÃG.r; r 0 / X.r 0 /d r 0113 construction would be more time consuming. An extensive analysis of the tradeoff between sparsity and effectiveness can be found in [23,24]. In our implementation, the sparsity pattern of the column of the SAI preconditioner associated with a given RWG is defined by retaining all the RWGs within its neighbouring cubes (including itself). If we define the indices of the nonzero columns of M asthe least-squares solution for problems (13) would involve only Q Z.W; J /. If we further denote the set of indices corresponding to the nonzero rows of Q Z.W; J / as I because the null rows do not affect the least-squares solution, the final least-squares problems can be expressed as min ke j .J / Q Z.I; J /m j .J /k 2 ; j D 1; 2; : : : ; N:Because, in MLFMA, the unknowns are grouped together by leaf cubes, it suffices to solve a single problem for each leaf cube, which is very convenient for the parallelization of MLFMA.

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An efficient approach for computing scattering by inhomogeneous objects with thin dielectric structures

Yang

Sun

Gao

et al. 2016

Int J Numerical Modelling

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This paper incorporates the compensated Mitzner boundary conditions (CMBC) into the hybrid finite elementboundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for fast and accurate computation of scattering by three-dimensional inhomogeneous objects with thin dielectric structures. In this CMBC-FE-BI-MLFMA, each thin dielectric layer is reduced to an interface with zero thickness; then CMBC is applied to establish the relation of electromagnetic fields across the interfaces. This approach can reduce the amount of computation and remain the advantages of versatility, accuracy, and efficiency of the conventional FE-BI-MLFMA algorithm. The formulation of this CMBC-FE-BI-MLFMA is presented in this paper. An efficient preconditioner based on the sparse approximate inverse is employed and further parallelized on memory-distributed platforms. Numerical results are presented to demonstrate the accuracy, efficiency, and capability of the parallel CMBC-FE-BI-MLFMA.

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Boundary-Integral Methods for Iterative Solution of Scattering Problems With Variable Impedance Surface Condition

Cited by 34 publications

References 20 publications

A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition

A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition

Parallelized multilevel fast multipole algorithm for scattering by objects with anisotropic impedance surfaces

An efficient approach for computing scattering by inhomogeneous objects with thin dielectric structures

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