Iterative Approaches to the Solution of Electromagnetic Boundary Value Problems

Mittra, R.; Chan, Chi Hou

doi:10.1080/02726348508908144

Cited by 31 publications

(9 citation statements)

References 15 publications

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“…The generation of this direction vector is considered in the next section. [20]. The comparison of the performances of the methods that result from these choices when applied to some canonical 3-D homogeneous problems is given in Section 4.…”

Section: Van Den Berg's Algorithmmentioning

confidence: 99%

“…Let KA denotes the adjoint of the kernel K; then the VBF which gives rise to the Conjugate Gradient method can be written as [14,20] The most desirable property of the CGM, either presented in its original form [15], or as a member of van den Berg's algorithm [14] lies in the orthogonal relationship between the basis functions at different steps. This relationship, which is expressed in inner product notation as is the key to the convergence guarantee when the CGM is applied to any problems, irrespective of the starting condition.…”

Section: Conjugatementioning

confidence: 99%

“…The third way of generating the VBF first arises from the study of Mittra and Chan [20] in connection with their SIT procedure.…”

Section: Generalized Neumann Series (Gns) Expansionmentioning

confidence: 99%

“…1 See Mittra and Chan [20] for a demonstration of this loss of orthogonality in connection with some microstrip line problems.…”

Section: Generalized Neumann Series (Gns) Expansionmentioning

confidence: 99%

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A unified family of FFT-based methods for dielectric scattering problems

Tran

McCowen

1994

Journal of Electromagnetic Waves and Applications

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A unified family of FFT-based methods for dielectric scattering problems Abstract-Investigation is conducted on the computational efficiency of van den Berg's integrated-squared-error algorithm with different variational basis functions (VBFs) when applied to dielectric problems. Members in this family include the Matrix interpretation of the Spectral Iteration Technique (MSIT) and the well-known Conjugate Gradient FFT (CGFFT)-each arises from choosing an appropriate form of the VBF. A third choice which is based on a generalized Neumann series (GNS) expansion of the inverse of the defining integral operator is shown to give much superior performance than either the MSIT or the CGFFT. Tests performed on a variety of object shapes and dielectric materials indicate that the GNS is the most efficient among all three FFT-based methods.

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Section: Van Den Berg's Algorithmmentioning

confidence: 99%

Section: Conjugatementioning

confidence: 99%

“…The third way of generating the VBF first arises from the study of Mittra and Chan [20] in connection with their SIT procedure.…”

Section: Generalized Neumann Series (Gns) Expansionmentioning

confidence: 99%

“…1 See Mittra and Chan [20] for a demonstration of this loss of orthogonality in connection with some microstrip line problems.…”

Section: Generalized Neumann Series (Gns) Expansionmentioning

confidence: 99%

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A unified family of FFT-based methods for dielectric scattering problems

Tran

McCowen

1994

Journal of Electromagnetic Waves and Applications

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“…However, numerical difficulties are also encountered in this scheme, as it suffers from machine round-off errors causing loss of orthogonality and linear independence [19], so the global error can decrease very slowly, resulting in a large number of iterations. Moreover, an erroneous behavior is observed in the current density even when using expansion functions for improving the rate of convergence [20].…”

Section: Introductionmentioning

confidence: 99%

Improved Spectral Iteration Technique for the Scattering by Thin Metal Plates

Costanzo¹,

Massa²

2008

PIER M

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Abstract-The problem of electromagnetic scattering by thin metal plates is formulated in terms of Electric Field Integral Equation and solved by an improved form of the Spectral Iteration Technique. The local solution at the edges of the plate is chosen as initial guess for the unknown surface current in order to guarantee and enhance the convergence of the iterative scheme. Numerical simulations on a square conducting plate are presented to validate the proposed approach.

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