Acceleration methods for the iterative solution of electromagnetic scattering problems

AbstractThis 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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Hybrid Accelerated Method via Volume-Surface Integral Equation for Efficient Calculation of Monostatic RCS

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.719-720.881 ◽

2015 ◽

Vol 719-720 ◽

pp. 881-885

Author(s):

Jia Qi Chen ◽

Yue Yuan Zhang

Keyword(s):

Electromagnetic Scattering ◽

Linear Equations ◽

Iterative Solution ◽

Low Rank ◽

Computational Time ◽

Surface Integral ◽

Scattering Problems ◽

Fast Analysis ◽

Efficient Calculation ◽

Successive Over Relaxation

A novel efficient hybrid accelerated method is proposed for the fast analysis of the monostatic electromagnetic scattering problems arising from volume-surface integral equations (VSIE) formulation. In the first step, by utilizing the low rank property, several largest eigenvalues and corresponding eigenvectors of the multiple right hand sides can be computed and saved efficiently by adaptive cross approximation (ACA) algorithm. The iterative solution of linear equations is required at these principle eigenvectors. Compared with solving linear equations at each angle repeatedly, the proposed method is able to greatly reduce the number of equations. In the second step, a disturbed symmetric successive over-relaxation (D-SSOR) preconditioner is constructed to speed up the convergence rate of iterative methods. Numerical results demonstrate that the present method can reduce the computational time significantly for monostatic VSIE calculation with high accuracy.

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Algebraic preconditioners for the Fast Multipole Method in electromagnetic scattering analysis from large structures: trends and problems

Electronic Journal of Boundary Elements ◽

10.14713/ejbe.v7i1.952 ◽

2009 ◽

Vol 7 (1) ◽

Cited By ~ 6

Author(s):

Bruno Carpentieri

Keyword(s):

Electromagnetic Scattering ◽

Fast Multipole Method ◽

Practical Interest ◽

Iterative Solution ◽

Fast Multipole ◽

Scattering Problems ◽

Preconditioning Techniques ◽

Large Structures ◽

Multipole Method ◽

Memory Complexity

<div>The Fast Multipole Method was introduced by Greengard and Rokhlin in a seminal paper appeared in 1987 for studying large systems of particle interactions with reduced algorithmic and memory complexity [60]. Developments of the original idea are successfully applied to the analysis of many scientific and engineering problems of practical interest. In scattering analysis, multipole techniques may enable to reduce the computational complexity of iterative solution procedures involving dense matrices arising from the discretization of integral operators from O(n2) to O(n log n) arithmetic operations. In this paper we discuss recent algorithmic developments of algebraic preconditioning techniques for the Fast Multipole Method for 2D and 3D scattering problems. We focus on design aspects, implementation details, numerical scalability, parallel performance on emerging computer systems, and give some minor emphasis to theoretical aspects as well. Thanks to the use of iterative techniques and efficient parallel preconditioners, fast integral solvers involving tens of million unknowns are nowadays feasible and can be integrated in the design processes. Keywords: algebraic preconditioners, Fast Multipole Method, Krylov solvers, electromagnetic scattering applications, Maxwell's equations.</div>

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