The method of fundamental solutions for Helmholtz eigenvalue problems in simply and multiply connected domains

2006 ◽  
Vol 30 (3) ◽  
pp. 150-159 ◽  
Author(s):  
S. Yu. Reutskiy
Keyword(s):  
Eigenvalue Problems ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Multiply Connected Domains ◽  
Multiply Connected

scholarly journals Method of Fundamental Solutions for Plate Vibrations in Multiply Connected Domains

2006 ◽  
Vol 22 (3) ◽  
pp. 235-245 ◽  
Author(s):  
C. C. Tsai ◽  
D. L. Young ◽  
C. M. Fan
Keyword(s):  
Potential Method ◽  
Fundamental Solutions ◽  
Method Of Fundamental Solutions ◽  
Multiply Connected Domains ◽  
Continuous Version ◽  
Multiply Connected ◽  
Plate Vibrations ◽  
Annular Plates ◽  
Complex Valued ◽  
Spurious Eigenvalues

AbstractThis paper develops the method of fundamental solutions (MFS) to solve eigenfrequencies of plate vibrations of multiply connected domains. The complex-valued MFS combined with the mix potential method are utilized in order to avoid the spurious eigenvalues. The benchmarked problems of annular plates with clamped, simply supported and free boundary conditions are studied analytically as well as numerically. Wherein the results demonstrate that all true eigenvalues are contained and no spurious eigenvalues are included. In the analytical studies, the continuous version of the MFS is utilized to obtain the eigenequation by applying the degenerate kernels and Fourier series. The proposed numerical method is free from singularities, meshes, and numerical integrations and thus can be easily utilized to solve plate vibrations free from spurious eigenvalues in multiply connected domains.

scholarly journals Theoretical scheme on numerical conformal mapping of unbounded multiply connected domain by fundamental solutions method

2000 ◽  
Vol 24 (2) ◽  
pp. 129-137 ◽  
Author(s):  
Tetsuo Inoue ◽  
Hideo Kuhara ◽  
Kaname Amano ◽  
Dai Okano
Keyword(s):  
Dirichlet Problem ◽  
Conformal Mapping ◽  
Fundamental Solutions ◽  
Multiply Connected Domains ◽  
Multiply Connected Domain ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Theoretical Scheme ◽  
Weighted Polynomials ◽  
Numerical Conformal Mappings

A potentially theoretical scheme in the fundamental solutions method, different from the conventional one, is proposed for numerical conformal mappings of unbounded multiply connected domains. The scheme is introduced from an algorithm on numerical Dirichlet problem, based on the asymptotic theorem on extremal weighted polynomials. The scheme introduced in this paper has the characteristic called “invariant and dual.”

scholarly journals Experiment on numerical conformal mapping of unbounded multiply connected domain in fundamental solutions method

2001 ◽  
Vol 26 (1) ◽  
pp. 55-63
Author(s):  
Tetsuo Inoue ◽  
Hideo Kuhara ◽  
Kaname Amano ◽  
Dai Okano
Keyword(s):  
Conformal Mapping ◽  
Fundamental Solutions ◽  
High Accuracy ◽  
Conformal Mappings ◽  
Multiply Connected Domains ◽  
Multiply Connected Domain ◽  
Numerical Conformal Mapping ◽  
Multiply Connected ◽  
Weighted Polynomials ◽  
Numerical Conformal Mappings

We are concerned with the experiment on numerical conformal mappings. A potentially theoretical scheme in the fundamental solutions method, different from the conventional one, has been recently proposed for numerical conformal mappings of unbounded multiply connected domains. The scheme is based on the asymptotic theorem on extremal weighted polynomials. The scheme has the characteristic called “invariant and dual.” Applying the scheme for typical examples, we will show that the numerical results of high accuracy may be obtained.

Conformal and Quasiconformal Mappings of Close Multiply-Connected Domains

2002 ◽  
Vol 9 (2) ◽  
pp. 367-382
Author(s):  
Z. Samsonia ◽  
L. Zivzivadze
Keyword(s):  
Integral Equations ◽  
Quasiconformal Mappings ◽  
Multiply Connected Domains ◽  
Multiply Connected

Abstract Doubly-connected and triply-connected domains close to each other in a certain sense are considered. Some questions connected with conformal and quasiconformal mappings of such domains are studied using integral equations.

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