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Null Field
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Jeng-tzong Chen – One of the best experts on this subject based on the ideXlab platform.
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Scattering problems of the SH Wave by Using the Null–Field Boundary Integral Equation Method
Journal of Earthquake Engineering, 2017Co-Authors: Jeng-tzong Chen, Shing-kai Kao, Yin-hsiang Hsu, Yu FanAbstract:The scattering problem of seismic waves is an important issue for studying earthquake engineering. In this paper, the Null–Field boundary integral equation approach was used in conjunction with deg…
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Eigenanalysis for a confocal prolate spheroidal resonator using the Null–Field BIEM in conjunction with degenerate kernels
Acta Mechanica, 2014Co-Authors: Jeng-tzong Chen, Jia-wei Lee, Yi-chuan Kao, Shyue-yuh LeuAbstract:In this paper, we employ the Null–Field boundary integral equation method (BIEM) in conjunction with degenerate kernels to solve eigenproblems of the prolate spheroidal resonators. To detect the spurious eigenvalues and the corresponding occurring mechanisms which are common issues while utilizing the boundary element method or the BIEM, we use angular prolate spheroidal wave functions and triangular functions to expand boundary densities. In this way, the boundary integral of a prolate spheroidal surface is exactly determined, and eigenequations are analytically derived. It is revealed that the spurious eigenvalues depend on the integral, representations and the shape of the inner boundary. Furthermore, it is interesting to find that some roots of the confocal prolate spheroidal resonator are double roots no matter that they are true or spurious eigenvalues. Illustrative examples include confocal prolate spheroidal resonators of various boundary conditions. To validate these findings and accuracy of the present approach, the commercial finite-element software ABAQUS is also applied to perform acoustic analyses. Good agreement is obtained between the acoustic results obtained by the Null–Field BIEM and those provided by the commercial finite-element software ABAQUS.
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Null–Field BIEM for solving a scattering problem from a point source to a two-layer prolate spheroid
Acta Mechanica, 2013Co-Authors: Jia-wei Lee, Jeng-tzong Chen, Shyue-yuh Leu, Shing-kai KaoAbstract:In this paper, the acoustic scattering problem from a point source to a two-layer prolate spheroid is solved by using the Null–Field boundary integral equation method (BIEM) in conjunction with degenerate kernels. To fully utilize the spheroidal geometry, the fundamental solutions and the boundary densities are expanded by using the addition theorem and spheroidal harmonics in the prolate spheroidal coordinates, respectively. Based on this approach, the collocation point can be located on the real boundary, and all boundary integrals can be determined analytically. In real applications of a two-layer prolate spheroidal structure, it can be applied to simulate the kidney-stone biomechanical system. Here, we consider the confocal structure to simulate the kidney-stone system since its analytical solution can be analytically derived. The parameter study for providing some references in the clinical medical treatment is also considered. To check the validity of the Null–Field BIEM, a special case of the acoustic scattering problem of a point source by a rigid scatterer is also done by setting the density of the inner prolate spheroid to infinity. Results of the present method are compared with those obtained using the commercial finite element software ABAQUS.
Thomas Wriedt – One of the best experts on this subject based on the ideXlab platform.
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Light Scattering by Systems of Particles: Null–Field Method with Discrete Sources: Theory and Programs
, 2014Co-Authors: Adrian Doicu, Thomas Wriedt, Yuri EreminAbstract:Light Scattering by Systems of Particles comprehensively develops the theory of the Null–Field method, while covering almost all aspects and current applications. The Null–Field Method with Discrete Sources is an extension of the Null–Field Method (also called T-Matrix Method) to compute light scattering by arbitrarily shaped dielectric particles. It also incorporates FORTRAN programs and exemplary simulation results that demonstrate all aspects of the latest developments of the method. The FORTRAN source programs included on the enclosed CD exemplify the wide range of application of the T-matrix method. Worked examples of the application of the FORTRAN programs show readers how to adapt or modify the programs for his specific application.
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Review of the Null–Field method with discrete sources
Journal of Quantitative Spectroscopy & Radiative Transfer, 2007Co-Authors: Thomas WriedtAbstract:In this paper the state of the art of the Null–Field Method with Discrete Sources (NFM-DS) will be reviewed. The NFM-DS combines the advantages of the Null–Field method with the advantages of the method of discrete sources to overcome stability problems of the standard Null–Field methods encountered in computation of scattering by very elongated particles such as long finite fibres and very flat particles such as flat discs.
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Decomposition of objects for light scattering simulations with the Null–Field method with discrete sources
Conference on Electromagnetic and Light Scattering, 2007Co-Authors: Thomas Wriedt, Roman SchuhAbstract:The Null–Field method with discrete sources (NFM-DS) is used for the simulation of the light scattering by elongated particles. These particles can be decomposed into several identical parts with a small aspect ratio. The T-matrix computed for a single part is used to compose the T-matrix for the whole particle. For verification purposes the light scattering distributions computed with NFM-DS are compared with results from DDA (discrete dipole approximation).
Ying-te Lee – One of the best experts on this subject based on the ideXlab platform.
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Study on harbor resonance and focusing by using the Null–Field BIEM
Engineering Analysis With Boundary Elements, 2013Co-Authors: Jeng-tzong Chen, Jia-wei Lee, Ying-te LeeAbstract:Abstract In this paper, the resonance of a circular harbor is studied by using the semi-analytical approach. The method is based on the Null–Field boundary integral equation method in conjunction with degenerate kernels and the Fourier series. The problem is decomposed into two regions by employing the concept of taking free body. One is a circular harbor, and the other is a problem of half-open sea with a coastline subject to the impermeable (Neumann) boundary condition. It is interesting to find that the SH wave impinging on the hill can be formulated by the same mathematical model. After finding the analogy between the harbor resonance and hill scattering, focusing of the water wave inside the harbor as well as focusing in the hill scattering are also examined. Finally, two numerical examples, circular harbor problems of 60° and 180° opening entrance, are both used to verify the validity of the present formulation.
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Water wave interaction with surface-piercing porous cylinders using the Null–Field integral equations
Ocean Engineering, 2010Co-Authors: J. Chen, Yong-chin Lin, Ying-te LeeAbstract:Abstract Following the successful experiences of solving water wave scattering problems for multiple impermeable cylinders by the authors’ group, we extend the Null–Field integral formulation in conjunction with the addition theorem and the Fourier series to deal with the problems of surface-piercing porous cylinders in this paper. In the implementation, the Null–Field point can be exactly located on the real boundary free of calculating the Cauchy and Hadamard principal values, thanks to the introduction of degenerate kernels (or separable kernels) for fundamental solutions. This method is a semi-analytical approach, since errors attribute from the truncation of the Fourier series. Not only a systematic approach is proposed but also the effect on the near-trapped modes due to porous cylinders and disorder of layout is examined. Several advantages such as mesh-free generation, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence, over the conventional boundary element method (BEM) are achieved. It is found that the disorder has more influence to suppress the occurrence of near-trapped modes than the porosity. The free-surface elevation is consistent with the results of William and Li and those using the conventional BEM. Besides, the numerical results of the force on the surface of cylinders agree well with those of William and Li. Besides, the present method is a semi-analytical approach for problems containing circular and elliptical shapes at the same time.
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Revisit of Two Classical Elasticity Problems by using the Null–Field Boundary Integral Equations
Journal of Mechanics, 2010Co-Authors: J.-t. Chen, Ying-te Lee, K. H. ChouAbstract:In this paper, the two classical elasticity problems, Lame problem and stress concentration factor, are revisited by using the Null–Field boundary integral equation (BIE). The Null–Field boundary integral formulation is utilized in conjunction with degenerate kernels and Fourier series. To fully utilize the circular geometry, the fundamental solutions and the boundary densities are expanded by using degenerate kernels and Fourier series, respectively. In the two classical problems of elasticity, the Null–Field BIE is employed to derive the exact solutions. The Kelvin solution is first separated to degenerate kernel in this paper. After employing the Null–Field BIE, not only the stress but also the displacement Field are obtained at the same time. In a similar way, Lame problem is solved without any difficulty.