A Hybrid Finite Element and Integral Equation Domain Decomposition Method for the Solution of the 3-D Scattering Problem

Stupfel, B.

doi:10.1006/jcph.2001.6814

Cited by 47 publications

(29 citation statements)

References 20 publications

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“…Furthermore, we count as two members of S, S mn and S nm , for the interface(s) between U m and U n . We shall omit our discussions on the treatment of the exterior boundary vU (or vU m ) since it can be addressed using well-documented approaches such as the absorbing boundary conditions (Stupfel 1994) and the BEMs (Stupfel 2001). Therefore, from here onwards, we shall drop the term v m ,n m × ((1/m r,m )V × u m ) vU m from the formulation.…”

Section: (A) Boundary-value Problem and Interior Penalty Formulationmentioning

confidence: 99%

Non-conformal domain decomposition methods for time-harmonic Maxwell equations

et al. 2012

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We review non-conformal domain decomposition methods (DDMs) and their applications in solving electrically large and multi-scale electromagnetic (EM) radiation and scattering problems. In particular, a finite-element DDM, together with a finite-element tearing and interconnecting (FETI)-like algorithm, incorporating Robin transmission conditions and an edge corner penalty term, are discussed in detail. We address in full the formulations, and subsequently, their applications to problems with significant amounts of repetitions. The non-conformal DDM approach has also been extended into surface integral equation methods. We elucidate a non-conformal integral equation domain decomposition method and a generalized combined field integral equation method for modelling EM wave scattering from non-penetrable and penetrable targets, respectively. Moreover, a plane wave scattering from a composite mockup fighter jet has been simulated using the newly developed multi-solver domain decomposition method.

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Section: (A) Boundary-value Problem and Interior Penalty Formulationmentioning

confidence: 99%

Non-conformal domain decomposition methods for time-harmonic Maxwell equations

et al. 2012

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“…However, the convergence of the Born series is not guaranteed and, if it converges, more than two terms may be needed in the series to achieve a reasonable accuracy [13,14]. For a given random realization of f (r), the cost of an "exact" numerical solution of this very large problem via a full-wave calculation performed in the frequency domain with a boundary element and finite element method (BE-FEM) is prohibitive even when efficient domain decomposition methods are employed (e.g., [5,6]). Note that an acceptable accuracy might still be achieved for a smaller cost if the integral equation is replaced by an approximate absorbing boundary condition (ABC-FEM: e.g., [7,8]).…”

Section: Introductionmentioning

confidence: 99%

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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“…Another domain of application is the use of this condition as an absorbing boundary condition to limit the computational domain of a finite elements method [25]. This condition plays also a major role in the domains decomposition method for Maxwell's equations [5,13,31]. Thus, it appears crucial to have efficient numerical methods well suited for such boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

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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A Hybrid Finite Element and Integral Equation Domain Decomposition Method for the Solution of the 3-D Scattering Problem

Cited by 47 publications

References 20 publications

Non-conformal domain decomposition methods for time-harmonic Maxwell equations

Non-conformal domain decomposition methods for time-harmonic Maxwell equations

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

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

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