BiCG-FFT T-Matrix method for solving for the scattering solution from inhomogeneous bodies

Lin, Jaw-Guei; Chew, Weng Cho

doi:10.1109/22.508651

Cited by 21 publications

(11 citation statements)

References 16 publications

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“…The condition number of matrix S as defined in (7) increases rapidly with T [16]. This implies that the iterative solution of (6) via a Krylov technique is efficient only if some preconditioner is employed.…”

Section: Solution Of the Mie Systemmentioning

confidence: 99%

“…For DDM2, systems M i c i = a i can be solved independently for each subdomain. These techniques can be extended to 3D problems (see, e.g., [16,22,23]) to compute, e.g., the statistics of the RCS of the wake created by a hypersonic vehicle during its atmospheric reentry, or else by a satellite in the ionosphere. (11).…”

Section: Discussionmentioning

confidence: 99%

“…However, the cartesian mesh of V s entails that S is almost block-Toeplitz. As a consequence, its computation and storage are O(T ) and the cost of a matrix-vector product is O(T log N s ) [16]. In Section 3.1 we consider a Jacobi iterative solution of (6) …”

Section: Solution Of the Mie Systemmentioning

confidence: 99%

“…An additional difficulty arises for the FDTD when f (r) is frequency dependent, as is the case for the plasma originating from an atmospheric reentry, because a random realization of f (r) must be performed in the whole frequency range of interest and accurately approximated by a simple enough frequency model (e.g., Debye or Lorentz [10]). We have adopted here a Mie series approach in the frequency domain: the medium is discretized with small spheres [16], thus reducing considerably the number of unknowns compared with the BE-FEM. On account of the still very large size of the corresponding linear system and of the ill-conditioned character of its matrix [16], we propose a domain decomposition method (DDM) that reduces the numerical complexity.…”

Section: Introductionmentioning

confidence: 99%

“…We have adopted here a Mie series approach in the frequency domain: the medium is discretized with small spheres [16], thus reducing considerably the number of unknowns compared with the BE-FEM. On account of the still very large size of the corresponding linear system and of the ill-conditioned character of its matrix [16], we propose a domain decomposition method (DDM) that reduces the numerical complexity.…”

Section: Introductionmentioning

confidence: 99%

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Solution of the Electromagnetic Scattering Problem From an Electrically Large Random Dielectric Medium

Stupfel¹,

Picard²

2013

PIER B

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Abstract-The time-harmonic electromagnetic scattering problem from a random inhomogeneous dielectric medium (here a turbulent plasma wake created by the atmospheric reentry of a vehicle) is considered. The electronic density of the plasma, that gives rise to its dielectric permittivity, has a fluctuating part f (r), the variance and correlation function of which are known a priori. Because the electrical dimensions of the wake can be very large, the numerical solution of Maxwell's equations via a full-wave calculation performed with a boundary element and finite element method is prohibitive when statistical quantities such as the mean Radar Cross Section (RCS) and its variance are required, that necessitate a large number of random realizations. To remedy this difficulty, two approximations are considered and illustrated for a 2D scattering problem. First, a Mie series approach is adopted where the medium is discretized with small disks, thus reducing considerably the number of unknowns for a given random realization of f (r), and a domain decomposition method is proposed to further reduce the complexity of the numerical solution of the corresponding system. Second, the statistical mean and the variance of the RCS are derived in closed-form from the Born approximation and yield accurate results when, as expected, the statistical mean of the relative dielectric permittivity is close to unity and | f (r)| is small. Conversely, it is shown how these expressions can be used to validate the results obtained with the Mie series approximation. Numerical examples are presented that illustrate the potentialities of these techniques.

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Section: Solution Of the Mie Systemmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Solution Of the Mie Systemmentioning

confidence: 99%