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Jeng-tzong Chen - One of the best experts on this subject based on the ideXlab platform.

  • Scattering problems of the SH Wave by Using the Null-Field Boundary Integral Equation Method
    Journal of Earthquake Engineering, 2017
    Co-Authors: Jeng-tzong Chen, Shing-kai Kao, Yin-hsiang Hsu, Yu Fan
    Abstract:

    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...

  • Eigenanalysis for a confocal prolate spheroidal resonator using the Null-Field BIEM in conjunction with degenerate kernels
    Acta Mechanica, 2014
    Co-Authors: Jeng-tzong Chen, Jia-wei Lee, Yi-chuan Kao, Shyue-yuh Leu
    Abstract:

    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.

  • Null-Field BIEM for solving a scattering problem from a point source to a two-layer prolate spheroid
    Acta Mechanica, 2013
    Co-Authors: Jia-wei Lee, Jeng-tzong Chen, Shyue-yuh Leu, Shing-kai Kao
    Abstract:

    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.

  • Study on harbor resonance and focusing by using the Null-Field BIEM
    Engineering Analysis With Boundary Elements, 2013
    Co-Authors: Jeng-tzong Chen, Jia-wei Lee, Ying-te Lee
    Abstract:

    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.

  • water wave problems using Null Field boundary integral equations ill posedness and remedies
    Applicable Analysis, 2012
    Co-Authors: Jeng-tzong Chen, Jia-wei Lee
    Abstract:

    In this article, we focus on the hydrodynamic scattering of water wave problems containing circular and/or elliptical cylinders. Regarding water wave problems, the phenomena of numerical instability due to fictitious frequencies may appear when the boundary element method (BEM) is used. We examine the occurring mechanism of fictitious frequency in the BEM through a water wave problem containing an elliptical cylinder. In order to study the fictitious frequency analytically, the Null-Field boundary integral equation method in conjunction with degenerate kernels is employed to derive the analytical solution. The modal participation factor for the numerical instability of zero divided by zero can be exactly determined in a continuous system even though the circulant matrix cannot be obtained in a discrete system for the elliptical case. It is interesting to find that irregular values depend on the geometry of boundaries as well as integral representations and happen to be zeros of the mth-order (even or odd)...

Thomas Wriedt - One of the best experts on this subject based on the ideXlab platform.

  • Light Scattering by Systems of Particles: Null-Field Method with Discrete Sources: Theory and Programs
    2014
    Co-Authors: Adrian Doicu, Thomas Wriedt, Yuri Eremin
    Abstract:

    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.

  • Review of the Null-Field method with discrete sources
    Journal of Quantitative Spectroscopy & Radiative Transfer, 2007
    Co-Authors: Thomas Wriedt
    Abstract:

    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.

  • Decomposition of objects for light scattering simulations with the Null-Field method with discrete sources
    Conference on Electromagnetic and Light Scattering, 2007
    Co-Authors: Thomas Wriedt, Roman Schuh
    Abstract:

    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).

  • Light scattering simulation by oblate disc spheres using the Null Field method with discrete sources located in the complex plane
    Journal of Modern Optics, 2006
    Co-Authors: Jens Hellmers, Thomas Wriedt, Adrian Doicu
    Abstract:

    The T-matrix method, which is also known as the Null Field method (NFM) or extended boundary condition method (EBCM), has established itself as a well known and highly regarded method for calculating light scattering by non-spherical particles. Its biggest advantage is the possibility to obtain all information about the scattering characteristics of the particle and to store it into one matrix. This enables one to do additional investigations with low efforts. Unfortunately the standard NFM fails to converge for particles with extremely non-spherical particle shapes, like long cylinders or coin-like flat cylinders. In this paper we investigate light scattering by finite particles in the form of an oblate disc sphere, which can be described as flat cylinders with a rounded edge. We use an advanced form of the T-matrix method—the Null Field method with discrete sources (NFM-DS). By presenting light scattering results we would like to demonstrate the potential this advanced NFM-DS offers. It allows one to ca...

  • Light Scattering by Cylindrical Fibers with High Aspect Ratio Using the Null‐Field Method with Discrete Sources
    Particle & Particle Systems Characterization, 2004
    Co-Authors: Sorin Pulbere, Thomas Wriedt
    Abstract:

    The problem of computing light scattering by cylindrical fibers with high aspect ratio in the framework of the Null-Field method with discrete sources is treated. Numerical experiments for investigating the scattering properties of two fiber geometries are performed using distributed spherical vector wave functions as discrete sources.

Ying-te Lee - One of the best experts on this subject based on the ideXlab platform.

  • Study on harbor resonance and focusing by using the Null-Field BIEM
    Engineering Analysis With Boundary Elements, 2013
    Co-Authors: Jeng-tzong Chen, Jia-wei Lee, Ying-te Lee
    Abstract:

    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.

  • Water wave interaction with surface-piercing porous cylinders using the Null-Field integral equations
    Ocean Engineering, 2010
    Co-Authors: J. Chen, Yong-chin Lin, Ying-te Lee
    Abstract:

    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.

  • Revisit of Two Classical Elasticity Problems by using the Null-Field Boundary Integral Equations
    Journal of Mechanics, 2010
    Co-Authors: J.-t. Chen, Ying-te Lee, K. H. Chou
    Abstract:

    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.

  • Torsional rigidity of an elliptic bar with multiple elliptic inclusions using a Null-Field integral approach
    Computational Mechanics, 2010
    Co-Authors: Jeng-tzong Chen, Ying-te Lee, Jia-wei Lee
    Abstract:

    Following the success of using the Null-Field integral approach to determine the torsional rigidity of a circular bar with circular inhomogeneities (Chen and Lee in Comput Mech 44(2):221–232, 2009), an extension work to an elliptic bar containing elliptic inhomogeneities is done in this paper. For fully utilizing the elliptic geometry, the fundamental solutions are expanded into the degenerate form by using the elliptic coordinates. The boundary densities are also expanded by using the Fourier series. It is found that a Jacobian term may exist in the degenerate kernel, boundary density or boundary contour integral and cancel out to each other. Null-Field points can be exactly collocated on the real boundary free of facing the principal values using the bump contour approach. After matching the boundary condition, a linear algebraic system is constructed to determine the unknown coefficients. An example of an elliptic bar with two inhomogeneities under the torsion is given to demonstrate the validity of the present approach after comparing with available results.

  • Revisit of Two Classical Elasticity Problems by using the Null-Field Boundary Integral Equations
    Journal of Mechanics, 2010
    Co-Authors: J.-t. Chen, Ying-te Lee, K. H. Chou
    Abstract:

    AbstractIn this paper, the two classical elasticity problems, Lamé 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, Lamé problem is solved without any difficulty.

Jia-wei Lee - One of the best experts on this subject based on the ideXlab platform.

  • Eigenanalysis for a confocal prolate spheroidal resonator using the Null-Field BIEM in conjunction with degenerate kernels
    Acta Mechanica, 2014
    Co-Authors: Jeng-tzong Chen, Jia-wei Lee, Yi-chuan Kao, Shyue-yuh Leu
    Abstract:

    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.

  • Null-Field BIEM for solving a scattering problem from a point source to a two-layer prolate spheroid
    Acta Mechanica, 2013
    Co-Authors: Jia-wei Lee, Jeng-tzong Chen, Shyue-yuh Leu, Shing-kai Kao
    Abstract:

    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.

  • Study on harbor resonance and focusing by using the Null-Field BIEM
    Engineering Analysis With Boundary Elements, 2013
    Co-Authors: Jeng-tzong Chen, Jia-wei Lee, Ying-te Lee
    Abstract:

    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.

  • water wave problems using Null Field boundary integral equations ill posedness and remedies
    Applicable Analysis, 2012
    Co-Authors: Jeng-tzong Chen, Jia-wei Lee
    Abstract:

    In this article, we focus on the hydrodynamic scattering of water wave problems containing circular and/or elliptical cylinders. Regarding water wave problems, the phenomena of numerical instability due to fictitious frequencies may appear when the boundary element method (BEM) is used. We examine the occurring mechanism of fictitious frequency in the BEM through a water wave problem containing an elliptical cylinder. In order to study the fictitious frequency analytically, the Null-Field boundary integral equation method in conjunction with degenerate kernels is employed to derive the analytical solution. The modal participation factor for the numerical instability of zero divided by zero can be exactly determined in a continuous system even though the circulant matrix cannot be obtained in a discrete system for the elliptical case. It is interesting to find that irregular values depend on the geometry of boundaries as well as integral representations and happen to be zeros of the mth-order (even or odd)...

  • on near trapped modes and fictitious frequencies for water wave problems containing an array of circular cylinders using a Null Field boundary integral equation
    European Journal of Mechanics B-fluids, 2012
    Co-Authors: Jeng-tzong Chen, I L Chen, Jia-wei Lee
    Abstract:

    Abstract To avoid using the addition theorem to translate the Bessel function, scattering of water waves by an array of circular cylinders is solved by using the Null-Field boundary integral equations, in conjunction with the adaptive observer system. Both the near-trapped modes (physics) and fictitious frequencies (mathematics) are observed. To alleviate the resonance problem of fictitious frequency for multiple cylinders, Combined Helmholtz Interior integral Equation Formulation (CHIEF) approach and Burton and Miller formulation are both considered. Regarding the Burton and Miller approach, hypersingular integrals can be easily calculated by using series summability without any difficulty owing to the introduction of degenerate kernels. The highly rank-deficient matrices for equal radius of cylinders are numerically examined and the rank is improved by adding valid CHIEF constraints. Besides, the selection of location and number for CHIEF points is addressed instead of trial and error. Parameter study of the incident angle on the resultant force is investigated. The effect of spacing and radius of cylinders on the near-trapped mode and fictitious frequency is also discussed. Several examples of water wave interaction by circular cylinders were demonstrated to see the validity of the present formulation.

Adrian Doicu - One of the best experts on this subject based on the ideXlab platform.

  • An overview of the Null-Field method. II: Convergence and numerical stability
    Physics Open, 2020
    Co-Authors: Adrian Doicu, Michael I. Mishchenko
    Abstract:

    Abstract In this paper we provide an analysis of the convergence and numerical stability of the Null-Field method with discrete sources. We show that (i) if the Null-Field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the Null-Field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the Null-Field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional Null-Field method with localized vector spherical wave functions which increases the stability of the numerical scheme.

  • Light Scattering by Systems of Particles: Null-Field Method with Discrete Sources: Theory and Programs
    2014
    Co-Authors: Adrian Doicu, Thomas Wriedt, Yuri Eremin
    Abstract:

    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.

  • Light scattering simulation by oblate disc spheres using the Null Field method with discrete sources located in the complex plane
    Journal of Modern Optics, 2006
    Co-Authors: Jens Hellmers, Thomas Wriedt, Adrian Doicu
    Abstract:

    The T-matrix method, which is also known as the Null Field method (NFM) or extended boundary condition method (EBCM), has established itself as a well known and highly regarded method for calculating light scattering by non-spherical particles. Its biggest advantage is the possibility to obtain all information about the scattering characteristics of the particle and to store it into one matrix. This enables one to do additional investigations with low efforts. Unfortunately the standard NFM fails to converge for particles with extremely non-spherical particle shapes, like long cylinders or coin-like flat cylinders. In this paper we investigate light scattering by finite particles in the form of an oblate disc sphere, which can be described as flat cylinders with a rounded edge. We use an advanced form of the T-matrix method—the Null Field method with discrete sources (NFM-DS). By presenting light scattering results we would like to demonstrate the potential this advanced NFM-DS offers. It allows one to ca...

  • Null-Field method to electromagnetic scattering from uniaxial anisotropic particles
    Optics Communications, 2003
    Co-Authors: Adrian Doicu
    Abstract:

    The electromagnetic scattering by a three-dimensional uniaxial anisotropic particle is studied. Electromagnetic Fields in a uniaxial medium are expressed in terms of a system of vector functions which are similar to the system of regular spherical vector wave functions. The scattering problem is solved by using the Null-Field method. Numerical simulations for uniaxial anisotropic ellipsoids are presented.

  • Null-Field method with circularly distributed spherical vector wave functions
    Optics Communications, 2002
    Co-Authors: Adrian Doicu
    Abstract:

    A novel formulation for improving the numerical stability of the Null-Field method for highly flattened particles is presented. The key step in this approach is to approximate the surface current densities by circularly distributed spherical vector wave functions. The circularly distributed spherical vector wave functions are obtained by integrating the spherical vector wave functions with a shifted origin over the azimuthal angle of the source point. The accuracy of the proposed method is investigated from a numerical point of view.