Jeng-Tzong Chen

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A nonsingular integral formulation for the Helmholtz eigenproblem is developed in this paper. This novel method contains only imaginary-part kernels instead of complex-part kernels in the complexvalued BEM. Based on the imaginary-part formulation without singular source, no singular or hypersingular integrals are present. Although this formulation avoids(More)
A problem of a nonconfocal suspended strip in an elliptical waveguide is analyzed by using a semianalytical approach, which is the so-called null-field boundary integral-equation method (BIEM). The null-field BIEM is proposed by introducing the idea of null field, degenerate kernels, and eigenfunction expansion to improve the conventional dual(More)
Boundary integral equations and boundary element methods were employed analytically, semi-analytically and numerically to study the occurrence of fictitious frequency for the exterior Helmholtz equations subject to the mixedtype boundary conditions. A semi-infinite rod and a circular radiator of problems were addressed. Degenerate kernel of the fundamental(More)
Boundary value problems on the eccentric annulus are quite complex and cannot directly be solved analytically using cartesian or polar coordinates. Many mathematical techniques have been used to solve such a problem by using conformal mapping and bipolar coordinate. In the literature, Carrier and Pearson [Partial differential equation-theory and technique.(More)
Series expansions of fundamental solutions are essential to algorithms and analysis of the null field method (NFM) and to analysis of the method of fundamental solutions (MFS). For linear elastostatics, new Fourier series expansions of FS are derived, directly from integration. The new expansions of the FS are simpler than those in Chen et al. (J Mech(More)
In this paper, a semi-analytical approach is proposed to solve natural frequencies and natural modes for circular plates with multiple circular holes by using the indirect formulation in conjunction with degenerate kernels and Fourier series. All the kernels in the indirect formulation are expanded into degenerate form. By uniformly collocating points on(More)
Consider the over-determined system Fx = b where $${{\bf F}\in\mathcal{R}^{m \times n}, m \geq n}$$ and rank (F) = r ≤ n, the effective condition number is defined by $${{\rm Cond_{-}eff }= \frac {\|{\bf b}\|}{\sigma_r\|{\bf x}\|}}$$ , where the singular values of F are given as σ max = σ 1 ≥ σ 2 ≥ . . . ≥ σ r > 0 and σ r+1 = . . . = σ n = 0. For the(More)