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

  • eigensolutions of the helmholtz equation for a multiply Connected Domain with circular boundaries using the multipole trefftz method
    Engineering Analysis With Boundary Elements, 2010
    Co-Authors: Jengtzong Chen
    Abstract:

    In this paper, 2D eigenproblems with the multiply Connected Domain are studied by using the multipole Trefftz method. We extend the conventional Trefftz method to the multipole Trefftz method by introducing the multipole expansion. The addition theorem is employed to expand the Trefftz bases to the same polar coordinates centered at one circle, where boundary conditions are specified. Owing to the introduction of the addition theorem, collocation techniques are not required to construct the linear algebraic system. Eigenvalues and eigenvectors can be found at the same time by employing the singular value decomposition (SVD). To deal with the eigenproblems, the present method is free of pollution of spurious eigenvalues. Both the eigenvalues and eigenmodes compare well with those obtained by analytical methods and the BEM as shown in illustrative examples.

  • regularized meshless method for solving acoustic eigenproblem with multiply Connected Domain
    Cmes-computer Modeling in Engineering & Sciences, 2006
    Co-Authors: K H Chen, Jengtzong Chen
    Abstract:

    In this paper, we employ the regularized meshless method (RMM) to search for eigenfrequency of two-dimension acoustics with multiply-Connected do- main. The solution is represented by using the double layer potentials. The source points can be located on the physical boundary not alike method of fundamental so- lutions (MFS) after using the proposed technique to reg- ularize the singularity and hypersingularity of the ker- nel functions. The troublesome singularity in the MFS methods is desingularized and the diagonal terms of in- fluence matrices are determined by employing the sub- tracting and adding-back technique. Spurious eigenval- ues are filtered out by using singular value decomposi- tion (SVD) updating term technique. The accuracy and stability of the RMM are verified through the numerical experiments of the Dirichlet and Neumann problems for Domainswithmultipleholes. Themethod isfoundtoper- form pretty well in comparison with analytical solutions and numerical resultsof boundaryelement method, finite element method and the point-matching method. keyword: Regularized meshless method, Hypersingu- larity, Eigenvalue, Eigenmode, Method of fundamental solutions,Acoustics.

  • regularized meshless method for multiply Connected Domain laplace problems
    Engineering Analysis With Boundary Elements, 2006
    Co-Authors: K H Chen, Jengtzong Chen, D L Young, M C Lu
    Abstract:

    Abstract In this paper, the regularized meshless method (RMM) is developed to solve two-dimensional Laplace problem with multiply-Connected Domain. The solution is represented by using the double-layer potential. The source points can be located on the physical boundary by using the proposed technique to regularize the singularity and hypersingularity of the kernel functions. The troublesome singularity in the traditional methods is avoided and the diagonal terms of influence matrices are easily determined. The accuracy and stability of the RMM are verified in numerical experiments of the Dirichlet, Neumann, and mixed-type problems under a Domain having multiple holes. The method is found to perform pretty well in comparison with the boundary element method.

  • boundary element analysis for the helmholtz eigenvalue problems with a multiply Connected Domain
    Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2001
    Co-Authors: Jengtzong Chen, S W Chyuan
    Abstract:

    For a Helmholtz eigenvalue problem with a multiply Connected Domain, the boundary integral equation approach as well as the boundary-element method is shown to yield spurious eigenvalues even if the complex-valued kernel is used. In such a case, it is found that spurious eigenvalues depend on the geometry of the inner boundary. Demonstrated as an analytical case, the spurious eigenvalue for a multiply Connected problem with its inner boundary as a circle is studied analytically. By using the degenerate kernels and circulants, an annular case can be studied analytically in a discrete system and can be treated as a special case. The proof for the general boundary instead of the circular boundary is also derived. The Burton-Miller method is employed to eliminate spurious eigenvalues in the multiply Connected case. Moreover, a modified method considering only the real-part formulation is provided. Five examples are shown to demonstrate that the spurious eigenvalues depend on the shape of the inner boundary. Good agreement between analytical prediction and numerical results are found.

Vladimir Mityushev - One of the best experts on this subject based on the ideXlab platform.

  • ℝ-linear and Riemann–Hilbert Problems for Multiply Connected Domains
    Advances in Applied Analysis, 2020
    Co-Authors: Vladimir Mityushev
    Abstract:

    The ℝ-linear problem with constant coefficients for arbitrary multiply Connected Domains has been solved. The method is based on reduction of the problem to a system of functional equations for a circular Domain and to integral equations for a general Domain. In previous works, theℝ-linear problem and its partial cases such as the Riemann –Hilbert problem and the Dirichlet problem were solved under geometrical restrictions to the Domains. In the present work, the solution is constructed for any circular multiply Connected Domain in the form of modified Poincar ´e series. Moreover, the modified alternating Schwarz method has been justified for an arbitrary multiply Connected Domain. This extends application of the alternating Schwarz method, since in the previous works geometrical restrictions were imposed on locations of the inclusions. The same concerns Grave’s method which was worked out before only for simple closed algebraic boundaries or for a collection of confocal boundaries.

  • l Formula for Multiply Connected Domains
    2020
    Co-Authors: Vladimir Mityushev
    Abstract:

    We derive a Schwarz-Christoe l formula for the conformal map- ping of an arbitrary n-Connected Domain D bounded by mutually disjoint circles jz akj = rk, k = 1; 2;:::;n, onto the exterior of mutually disjoint polygons. The derivation is based on the exact solution to a Riemann-Hilbert problem for D without any geometric restriction imposed upon the location of the non-overlapping disksjz akj rk.

  • Scalar Riemann–Hilbert Problem for Multiply Connected Domains
    Functional Equations in Mathematical Analysis, 2020
    Co-Authors: Vladimir Mityushev
    Abstract:

    We solve the scalar Riemann–Hilbert problem for circular multiply Connected Domains. The method is based on the reduction of the boundary value problem to a system of functional equations (without integral terms). In the previous works, the Riemann–Hilbert problem and its partial cases such as the Dirichlet problem were solved under geometrical restrictions to the Domains. In the present work, the solution is constructed for any circular multiply Connected Domain in the form of modified Poincare series.

  • mixed problem for laplace s equation in an arbitrary circular multiply Connected Domain
    2018
    Co-Authors: Vladimir Mityushev
    Abstract:

    Mixed boundary value problems for the two-dimensional Laplace’s equation in a Domain D are reduced to the Riemann-Hilbert problem Re \(\overline {\lambda (t)}\psi (t) = 0\), t ∈ ∂D, with a given Holder continuous function λ(t) on ∂D except at a finite number of points where a one-sided discontinuity is admitted. The celebrated Keldysh-Sedov formulae were used to solve such a problem for a simply Connected Domain. In this paper, a method of functional equations is developed to mixed problems for multiply Connected Domains. For definiteness, we discuss a problem having applications in composites with a discontinuous coefficient λ(t) on one of the boundary components. It is assumed that the Domain D is a canonical Domain, the lower half-plane with circular holes. A constructive iterative algorithm to obtain an approximate solution in analytical form is developed in the form of an expansion in the radius of the holes.

  • Schwarz-Christoffel Formula for Multiply Connected Domains
    Computational Methods and Function Theory, 2012
    Co-Authors: Vladimir Mityushev
    Abstract:

    We derive a Schwarz-Christoffel formula for the conformal mapping of an arbitrary n-Connected Domain D bounded by mutually disjoint circles ¦z − a k¦ = rk, k = 1,2,…,n, onto the exterior of mutually disjoint polygons. The derivation is based on the exact solution to a Riemann-Hilbert problem for D without any geometric restriction imposed upon the location of the non-overlapping disks ¦z − ak¦ ≤ rk.

Bai Yanping - One of the best experts on this subject based on the ideXlab platform.

  • A Method of Character Recognition Based on General Characteristic and Connected Regions
    2011 International Conference on Multimedia and Signal Processing, 2011
    Co-Authors: Meng Qing-yuan, H U Hongping, Bai Yanping
    Abstract:

    In this paper, by analyzing the number of concave Domain and cycles and the characteristic of Connected Domain of the characters, we present a method of character recognition based on above mentioned features. At first, the characters are divided into two classes according to cycles: the character with cycles and the character without cycles. Then, we detect if the character has sunk parts in its four directions (up, down, left, right).According to the results, the character can be recognized or divided into six classes. At last, we recognize the character using the characteristic of Connected Domain, and obtain the final recognition results. The experiment shows that the algorithm has a good performance in English characters recognition.

Bingzhong Wang - One of the best experts on this subject based on the ideXlab platform.

  • new autofocus and reconstruction method based on a Connected Domain
    Optics Letters, 2018
    Co-Authors: Haiyan Ou, Yong Wu, Bingzhong Wang
    Abstract:

    In this Letter, we propose a new method for auto-focusing and reconstruction without defocus noise in optical scanning holography. By using a Connected Domain (CD) to calculate the area of different Domains, which are labeled by a Connected component, the focus distance can be found via the smallest area of each CD. Meanwhile, the sectional images without defocus noise can also be reconstructed based on the labeled Domains. The effectiveness of this method has been verified with a simulation and experiments.

Vagia Vlachou - One of the best experts on this subject based on the ideXlab platform.