scholarly journals Computation of Green’S Tensor Integrals for Three-Dimensional Electromagnetic Problems Using Fast Hankel Transforms

1984 ◽  
Vol 15 (3) ◽  
pp. 195-195
Author(s):  
W. L. Anderson
Keyword(s):  
Three Dimensional ◽  
Electromagnetic Problems ◽  
Hankel Transforms ◽  
Green's Tensor ◽  
Green’S Tensor

Computation of Green’s tensor integrals for three‐dimensional electromagnetic problems using fast Hankel transforms

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1754-1759 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Hankel Transform ◽  
Electromagnetic Modeling ◽  
Electromagnetic Problems ◽  
Hankel Transforms ◽  
Homogeneous Half Space ◽  
Green's Tensor ◽  
Green’S Tensor ◽  
The Many

A new method is presented that rapidly evaluates the many Green’s tensor integrals encountered in three‐dimensional electromagnetic modeling using an integral equation. Application of a fast Hankel transform (FHT) algorithm (Anderson, 1982) is the basis for the new solution, where efficient and accurate computation of Hankel transforms are obtained by related and lagged convolutions (linear digital filtering). The FHT algorithm is briefly reviewed and compared to earlier convolution algorithms written by the author. The homogeneous and layered half‐space cases for the Green’s tensor integrals are presented in a form so that the FHT can be easily applied in practice. Computer timing runs comparing the FHT to conventional direct convolution methods are discussed, where the FHT’s performance was about 6 times faster for a homogeneous half‐space, and about 108 times faster for a five‐layer half‐space. Subsequent interpolation after the FHT is called is required to compute specific values of the tensor integrals at selected transform arguments; however, due to the relatively small lagged convolution interval used (same as the digital filter’s), a simple and fast interpolation is sufficient (e.g., by cubic splines).

SEISMIC RECIPROCITY

Geophysics ◽  
1959 ◽  
Vol 24 (4) ◽  
pp. 681-691 ◽  
Author(s):  
Leon Knopoff ◽  
Anthony F. Gangi
Keyword(s):  
Scalar Product ◽  
Point Sources ◽  
Simple Experiment ◽  
Reciprocity Relations ◽  
Green's Tensor ◽  
Vector Case ◽  
Green’S Tensor

The reciprocity relationship describing the relations among the fields resulting from the interchange of point sources and receivers may be extended to the seismic case. Seismic reciprocity can be described either in terms of the scalar product of the vectors representing the excitation of the source and the field at the receiver, or in terms of a Green’s tensor describing these two quantities. Theoretical reciprocity relations give no information concerning reciprocity in the cases for which the scalar product vanishes. A simple experiment in the vector case demonstrates that reciprocity is not obtained when the scalar product of the two vectors vanishes.

scholarly journals A Modified Shuffled Frog Leaping Algorithm for the Topology Optimization of Electromagnet Devices

2020 ◽  
Vol 10 (18) ◽  
pp. 6186
Author(s):  
Wenjia Yang ◽  
Siu Lau Ho ◽  
Weinong Fu
Keyword(s):  
Topology Optimization ◽  
Local Search ◽  
Three Dimensional ◽  
Optimization Method ◽  
Memetic Algorithms ◽  
Local Optimum ◽  
Shuffled Frog Leaping Algorithm ◽  
Electromagnetic Problems ◽  
Electromagnetic Devices ◽  
Shuffled Frog Leaping

The memetic algorithms which employ population information spreading mechanism have shown great potentials in solving complex three-dimensional black-box problems. In this paper, a newly developed memetic meta-heuristic optimization method, known as shuffled frog leaping algorithm (SFLA), is modified and applied to topology optimization of electromagnetic problems. Compared to the conventional SFLA, the proposed algorithm has an extra local search step, which allows it to escape from the local optimum, and hence avoid the problem of premature convergence to continue its search for more accurate results. To validate the performance of the proposed method, it was applied to solving the topology optimization of an interior permanent magnet motor. Two other EAs, namely the conventional SFLA and local-search genetic algorithm, were applied to study the same problem and their performances were compared with that of the proposed algorithm. The results indicate that the proposed algorithm has the best trade-off between the results of objective values and optimization time, and hence is more efficient in topology optimization of electromagnetic devices.

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

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