A time-domain differential solver for electromagnetic scattering problems

Shankar, Vijaya; Hall, William J.; Mohammadian, A.H.

doi:10.1109/5.32061

Cited by 105 publications

(40 citation statements)

References 24 publications

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“…Bistatic RCS for a TE illumination is compared with results in Ref. [11] in Fig. 3(b), and again good agreement is seen.…”

Section: Numerical Results-2dmentioning

confidence: 55%

A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering

Deore

Chatterjee²

2010

PIER M

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Abstract-A cell-vertex based finite volume scheme is used to solve the time-dependent Maxwell's equations and predict electromagnetic scattering from perfectly conducting bodies. The scheme is based on the cell-vertex finite volume integration method, originally proposed by Ni [1], for solution of the two dimensional unsteady Euler equations of gas dynamics. The resulting solution is second-order accurate in space and time, and requires cell based fluctuations to be appropriately distributed to the state vector stored at cell vertices at each time step. Results are presented for two-dimensional canonical shapes and complex three dimensional geometries. Unlike in gas dynamics, no user defined numerical damping is required in this novel cell-vertex based finite volume integration scheme when applied to the time-domain Maxwell's equations.

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“…Bistatic RCS for a TE illumination is compared with results in Ref. [11] in Fig. 3(b), and again good agreement is seen.…”

Section: Numerical Results-2dmentioning

confidence: 55%

A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering

Deore

Chatterjee²

2010

PIER M

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“…Results are presented for TM and TE illumination for an electrical size corresponding to a/λ = 10, where a indicates the airfoil chord length. This problem was also solved by Shankar et al [1] for TM illumination. As in [1], a body-fitted grid is employed.…”

Section: Numerical Solutions -Airfoilmentioning

confidence: 86%

“…This problem was also solved by Shankar et al [1] for TM illumination. As in [1], a body-fitted grid is employed. The grid topology is identical to that used previously for the circular cylinder, is shown in the form of a schematic in Figure 6.…”

Section: Numerical Solutions -Airfoilmentioning

confidence: 86%

“…Higher-order, characteristic based numerical schemes are usually used to solve the time-domain Maxwell's equations written as a system of hyperbolic conservation laws in the Finite Volume Time-Domain (FVTD) method [1][2][3]. Electromagnetic scattering involving complex geometries, broad-band signals and diverse material properties can be dealt with advantageously using the FVTD method [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

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Efficient Implementation of Higher-Order Finite Volume Time-Domain Method for Electrically Large Scatterers

Chatterjee¹,

Myong²

2009

PIER B

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Abstract-The Finite Volume Time-Domain (FVTD) method finds limited application in the simulation of electromagnetic scattering from electrically large scatterers because of the fine discretization required in terms of points-per-wavelength. An efficient implementation of a higher-order FVTD method is proposed for electrically large, perfectly conducting scatterers. Higher-order and fine-grid accuracy are preserved, despite using only a first-order spatial accuracy and a coarse grid in substantial parts of the FVTD computational domain, by partially incorporating a time-domain Physical Optics (PO) approximation for the surface current. This can result in considerable savings in computational time while analyzing geometries containing electrically large, smooth sections using the FVTD method. The higher-order FVTD method in the present work is based on an Essentially Non-Oscillatory (ENO) reconstruction and results are presented for two-dimensional perfectly conducting scatterers subject to Transverse Magnetic (TM) or Transverse Electric (TE) illumination.

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“…We are interested here in FVTD methods, as have been developed in the past years, not necessarily on bodyfitted coordinates [20,21] but on unstructured finite element triangulations [5][6][7]18] or on totally destructured meshes [3]. More precisely, we consider a standard finite volume approximation, i.e.…”

mentioning

confidence: 99%

L²-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes

Piperno

2000

ESAIM: M2AN

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Abstract.We investigate sufficient and possibly necessary conditions for the L 2 stability of the upwind first order finite volume scheme for Maxwell equations, with metallic and absorbing boundary conditions. We yield a very general sufficient condition, valid for any finite volume partition in two and three space dimensions. We show this condition is necessary for a class of regular meshes in two space dimensions. However, numerical tests show it is not necessary in three space dimensions even on regular meshes. Stability limits for time and space schemes with higher orders of accuracy are numerically investigated. Résumé. Nous cherchonsàétablir des conditions suffisantes etéventuellement nécessaires de stabilitéL 2 pour le schéma en volumes finis décentré du premier ordre, appliqué auxéquations de Maxwell, avec des conditions aux limites absorbantes et métalliques. En deux et trois dimensions d'espace, nous proposons une condition suffisante de stabilité d'une grande généralité, puisqu'elle est valable pour toute forme de volumes finis. En deux dimensions, nous montrons que cette condition estégalement nécessaire pour une classe de maillages réguliers. En trois dimensions, des tests numériques montrent que cette condition n'est pas nécessaire, même pour des maillages réguliers. Nous recherchons les limites de stabilité observées numériquement pour des schémas plus précis en temps et en espace.

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A time-domain differential solver for electromagnetic scattering problems

Cited by 105 publications

References 24 publications

A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering

A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering

Efficient Implementation of Higher-Order Finite Volume Time-Domain Method for Electrically Large Scatterers

L²-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes

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A time-domain differential solver for electromagnetic scattering problems

Cited by 105 publications

References 24 publications

A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering

A Cell-Vertex Finite Volume Time Domain Method for Electromagnetic Scattering

Efficient Implementation of Higher-Order Finite Volume Time-Domain Method for Electrically Large Scatterers

L2-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes

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L²-stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes