The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform
Weng Cho Chew - One of the best experts on this subject based on the ideXlab platform.
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A Low Frequency Vector Fast Multipole Algorithm with Vector Addition Theorem
Communications in Computational Physics, 2020Co-Authors: Weng Cho ChewAbstract:In the low-frequency fast multipole algorithm (LF-FMA) [19, 20], scalar Addition Theorem has been used to factorize the scalar Green's function. Instead of this traditional factorization of the scalar Green's function by using scalar Addition Theorem, we adopt the vector Addition Theorem for the factorization of the dyadic Green's function to realize memory savings. We are to validate this factorization and use it to develop a low-frequency vector fast multipole algorithm (LF-VFMA) for lowfrequency problems. In the calculation of non-near neighbor interactions, the storage of translators in the method is larger than that in the LF-FMA with scalar Addition Theorem. Fortunately it is independent of the number of unknowns. Meanwhile, the storage of radiation and receiving patterns is linearly dependent on the number of unknowns. Therefore it is worthwhile for large scale problems to reduce the storage of this part. In thismethod, the storage of radiation and receiving patterns can be reduced by 25 percent compared with the LF-FMA. © 2010 Global-Science Press.link_to_subscribed_fulltex
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efficient ways to compute the vector Addition Theorem
Journal of Electromagnetic Waves and Applications, 1993Co-Authors: Weng Cho Chew, Y M WangAbstract:Two efficient ways of calculating the vector Addition Theorem are presented. One is obtained by relating the coefficients of the vector Addition Theorem to that of the scalar Addition Theorem for which an efficient recurrence relation exists. The second way is to derive recurrence relations directly for the coefficients of the vector Addition Theorem. These new ways of calculating the coefficients are of reduced computational complexity. Hence, when the number of coefficients required is large, the present methods are many times faster than the traditional method using Gaunt coefficients and Wigner 3j symbols.
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recurrence relations for three dimensional scalar Addition Theorem
Journal of Electromagnetic Waves and Applications, 1992Co-Authors: Weng Cho ChewAbstract:Recurrence relations for the elements of a translation matrix in the scalar Addition Theorem in three-dimensions using spherical harmonics are derived. These recurrence relations are more efficient to evaluate compared to the use of Gaunt coefficients evaluated with Wigner 3j symbols or with recurrence relations. The efficient evaluation of the Addition Theorem is important in a number of wave scattering calculations including fast recursive algorithms.
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recursive algorithm for wave scattering solutions using windowed Addition Theorem
Journal of Electromagnetic Waves and Applications, 1992Co-Authors: Weng Cho Chew, Y M Wang, L GurelAbstract:A review of a recursive algorithm with a more succinct derivation is first presented. This algorithm, which calculates the scattering solution from an inhomogeneous body, first divides the body into N subscatterers. The algorithm then uses an aggregate T matrix and translation formulas to solve for the solution of n+1 subscatterers from the solution for n subscatterers. This recursive algorithm has reduced computational complexity. Moreover, the memory requirement is proportional to the number of unknowns. This algorithm has been used successfully to solve for the volume scattering solution of two-dimensional scatterers for Ez -polarized waves. However, for Hz -polarized waves, a straightforward application of the recursive algorithm yields unsatisfactory solutions due to the violation of the restricted regime of the Addition Theorem. But by windowing the Addition Theorem, the restricted regime of validity is extended. Consequently, the recursive algorithm with the windowed Addition Theorem works well eve...
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a derivation of the vector Addition Theorem
Microwave and Optical Technology Letters, 1990Co-Authors: Weng Cho ChewAbstract:An alternative derivation of the vector Addition Theorem is presented using the completeness of vector wave functions and integration by parts. The advantage of this derivation is that it leads directly to the simplified results of Bruning and Lo and of Stein. Moreover, the dichotomous results of the Addition Theorem when a spherical Hankel function is involved can be derived by contour integration.
W. C. Chew - One of the best experts on this subject based on the ideXlab platform.
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The tensor Addition Theorem: From the viewpoint of group theory
2008 IEEE Antennas and Propagation Society International Symposium, 2008Co-Authors: B. He, W. C. ChewAbstract:In this paper, the tensor Addition Theorem is discussed. Some familiarity with the theory of Lie group is also presented.
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Diagonalization of the vector Addition Theorem
2007 IEEE Antennas and Propagation Society International Symposium, 2007Co-Authors: W. C. ChewAbstract:The development of fast algorithms for integral equation solvers opens up new realms for the applications of integral equation solvers [V. Rokhlin, 1990; C.C. Lu and W.C. Chew, 1994; J.M. Song and W.C. Chew, 1995; W.C. Chew et al., 2001]. One of these is their use in the arena of circuits, micro-circuits and nanotechnologies. Often time, the use of fast solvers in this arena calls for the combined use of fast algorithms where both wave physics and circuit physics are captured well by the solvers [L.J. Jiang and W.C. Chew, 2005].
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An efficient way to compute the vector Addition Theorem [EM scattering]
Proceedings of IEEE Antennas and Propagation Society International Symposium, 1993Co-Authors: Y M Wang, W. C. ChewAbstract:In this method, the coefficients of the vector Addition theory are obtained by relating them to that of the scalar Addition Theorem for which an efficient recurrence relation has been derived by Chew (1992). This new scheme of calculating the coefficients is of reduced computational complexity. Hence, when the number of coefficients required is large, the present methods are many times faster than the traditional method using Gaunt coefficients and Wigner 3j symbols.
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Scattering solution of three-dimensional array of patches using the recursive T-matrix algorithms
IEEE Microwave and Guided Wave Letters, 1992Co-Authors: L Gurel, W. C. ChewAbstract:The recursive T-matrix algorithms are used to solve for the vector electromagnet scattering problem of a three-dimensional array of patches. The formulation uses only the E/sub x/ and E/sub y/ components of the electromagnetic field wherein the three-dimensional scalar Addition Theorem can be used. The coefficients for the scalar Addition Theorem are calculated with an efficient recurrence relation. This results in reduced memory requirements and computation time. When the Addition Theorem is violated, a generalized recursive T-matrix algorithm is used to mitigate the problem caused by the violation of the Addition Theorem. The scattering solutions are validated by comparison with the method of moments, and the reduced computational complexity of the solution is demonstrated.
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Recursion relations for three-dimensional scalar Addition Theorem
Antennas and Propagation Society Symposium 1991 Digest, 1991Co-Authors: W. C. ChewAbstract:Efficient recursion relations for the elements of the translation matrix are derived. These recursion relations are a lot more efficient than the previous ones. It is noted that the efficient evaluation of the Addition Theorem is important in a number of scattering applications, especially in fast recursive algorithms.
J. J. Tsai - One of the best experts on this subject based on the ideXlab platform.
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Equivalence Between The Trefftz Method AndThe Method Of Fundamental Solutions ForGreen’s Function Of Concentric Spheres UsingThe Addition Theorem And Image Concept
Mesh Reduction Methods, 2009Co-Authors: J. T. Chen, H. C. Shieh, J. J. TsaiAbstract:Following the success of the mathematical equivalence between the Trefftz method and the method of fundamental solutions for the annular Green’s function, we extend to solve the Green’s function of 3-D problems in this paper. The Green’s function of the concentric sphere is first derived by using the image method which can be seen as a special case of method of fundamental solutions. Fixed-fixed boundary conditions are considered. Also, the Trefftz method is employed to derive the analytical solution by using the T-complete sets. By employing the Addition Theorem, both solutions are found to be mathematically equivalent when the number of Trefftz bases and the number of image points are both infinite. In the successive image process, the final two images freeze at the origin and infinity, where their singularity strengths can be analytically and numerically determined in a consistent manner. The agreement among the three results, including two analytical solutions by using the Trefftz method and the image method, and one numerical solution by using the conventional MFS is observed.
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equivalence between the trefftz method andthe method of fundamental solutions forgreen s function of concentric spheres usingthe Addition Theorem and image concept
WIT Transactions on Modelling and Simulation, 2009Co-Authors: J. T. Chen, H. C. Shieh, J. J. TsaiAbstract:Following the success of the mathematical equivalence between the Trefftz method and the method of fundamental solutions for the annular Green’s function, we extend to solve the Green’s function of 3-D problems in this paper. The Green’s function of the concentric sphere is first derived by using the image method which can be seen as a special case of method of fundamental solutions. Fixed-fixed boundary conditions are considered. Also, the Trefftz method is employed to derive the analytical solution by using the T-complete sets. By employing the Addition Theorem, both solutions are found to be mathematically equivalent when the number of Trefftz bases and the number of image points are both infinite. In the successive image process, the final two images freeze at the origin and infinity, where their singularity strengths can be analytically and numerically determined in a consistent manner. The agreement among the three results, including two analytical solutions by using the Trefftz method and the image method, and one numerical solution by using the conventional MFS is observed.
Homayoon Oraizi - One of the best experts on this subject based on the ideXlab platform.
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Electromagnetic Multiple PEC Object Scattering Using Equivalence Principle and Addition Theorem for Spherical Wave Harmonics
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Mohammad Alian, Homayoon OraiziAbstract:A novel domain decomposition procedure is presented to analyze the electromagnetic wave multiple scattering among separate PEC objects. The method is based on the equivalence principle algorithm (EPA) that transfers the primary unknowns on the objects to the unknowns on the equivalence surfaces. Each equivalence surface is considered to be a spherical surface encompassing a PEC object. Inside the equivalence spheres, the analysis is performed based on the Rao-Wilton-Glisson (RWG) basis functions where the electromagnetic interactions outside them are considered by means of the Addition Theorem for spherical wave harmonics (SWHs). The translation procedures are presented to translate the RWG basis functions to SWHs and vice versa. The reduction of unknowns in the presented method versus the conventional EPA (which uses translation operators among equivalence surfaces) shows its efficiency. Some numerical examples are presented to evaluate the efficacy of the proposed approach. The acceptable consistency among the results of the proposed method and the conventional EPA as well as the direct method of moments validates the proposed method.
Femke Olyslager - One of the best experts on this subject based on the ideXlab platform.
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a low frequency stable plane wave Addition Theorem
Journal of Computational Physics, 2009Co-Authors: Ignace Bogaert, Femke OlyslagerAbstract:The multilevel fast multipole algorithm (MLFMA) is a well known and very successful method for accelerating the matrix-vector products required for the iterative solution of Helmholtz problems. The MLFMA has an important drawback, namely its inability to handle scattering problems with a lot of subwavelength detail due to the low frequency (LF) breakdown of the MLFMA. There is a need to extend the MLFMA to LF, since alternative methods are less efficient (multipole methods) or hard to implement (spectral methods). In this paper a new Addition Theorem will be developed that does not suffer from an LF breakdown. Instead it suffers from a high-frequency (HF) breakdown. The new method relies on a novel set of distributions, the so-called pseudospherical harmonics, closely related to the spherical harmonics. These allow the discretization points and translation operators to be calculated in closed form. Hence the method presented in this paper allows the easy implementation of a method that is stable at LF. Furthermore, a combination of the traditional MLFMA and the new method allows for the construction of a broadband MLFMA.
