An indirect BIE free of degenerate scales

<p style='text-indent:20px;'>Thanks to the fundamental solution, both BIEs and BEM are effective approaches for solving boundary value problems. But it may result in rank deficiency of the influence matrix in some situations such as fictitious frequency, spurious eigenvalue and degenerate scale. First, the nonequivalence between direct and indirect method is analytically studied by using the degenerate kernel and examined by using the linear algebraic system. The influence of contaminated boundary density on the field response is also discussed. It's well known that the CHIEF method and the Burton and Miller approach can solve the unique solution for exterior acoustics for any wave number. In this paper, we extend a similar idea to avoid the degenerate scale for the interior two-dimensional Laplace problem. One is the external source similar to the null-field BIE in the CHIEF method. The other is the Burton and Miller approach. Two analytical examples, circle and ellipse, were analytically studied. Numerical tests for general cases were also done. It is found that both two approaches can yield an unique solution for any size.</p>

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Degenerate scale for the Laplace problem in the half-plane; Approximate logarithmic capacity for two distant boundaries

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2013.02.009 ◽

2013 ◽

Vol 37 (5) ◽

pp. 836-841 ◽

Cited By ~ 15

Author(s):

A. Corfdir ◽

G. Bonnet

Keyword(s):

Half Plane ◽

Logarithmic Capacity ◽

Degenerate Scale ◽

Laplace Problem

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On the linkage between influence matrices in the BIEM and BEM to explain the mechanism of degenerate scale for a circular domain

Journal of Mechanics ◽

10.1093/jom/ufab003 ◽

2021 ◽

Vol 37 ◽

pp. 339-345

Author(s):

Jeng-Tzong Chen ◽

Jia-Wei Lee ◽

Yi-Ling Huang ◽

Cheng-Hsiang Shao ◽

Cheng-Hsuan Lu

Keyword(s):

Discrete System ◽

Continuous System ◽

Circulant Matrix ◽

Circular Domain ◽

Boundary Integral ◽

Finite Dimensional Space ◽

System Boundary ◽

Influence Matrix ◽

Degenerate Scale ◽

Eigenvalue And Eigenvector

ABSTRACT In this paper, we proposed two ways to understand the rank deficiency in the continuous system (boundary integral equation method, BIEM) and discrete system (boundary element method, BEM) for a circular case. The infinite-dimensional degree of freedom for the continuous system can be reduced to finite-dimensional space using the generalized Fourier coordinates. The property of the second-order tensor for the influence matrix under different observers is also examined. On the other hand, the discrete system in the BEM can be analytically studied, thanks to the spectral property of circulant matrix. We adopt the circulant matrix of odd dimension, (2N + 1) by (2N + 1), instead of the previous even one of 2N by 2N to connect the continuous system by using the Fourier bases. Finally, the linkage of influence matrix in the continuous system (BIE) and discrete system (BEM) is constructed. The equivalence of the influence matrix derived by using the generalized coordinates and the circulant matrix are proved by using the eigen systems (eigenvalue and eigenvector). The mechanism of degenerate scale for a circular domain can be analytically explained in the discrete system.

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Degenerate-scale problem of the boundary integral equation method/boundary element method for the bending plate analysis

Engineering Computations ◽

10.1108/ec-06-2016-0187 ◽

2017 ◽

Vol 34 (5) ◽

pp. 1527-1550 ◽

Cited By ~ 1

Author(s):

Jeng-Tzong Chen ◽

Shyh-Rong Kuo ◽

Yu-Lung Chang ◽

Shing-Kai Kao

Keyword(s):

Integral Equation ◽

Boundary Element Method ◽

Boundary Element ◽

Arbitrary Shape ◽

Boundary Integral ◽

Degenerate Kernel ◽

Content Type ◽

Degenerate Scale ◽

Circular Case ◽

Plate Analysis

Purpose The purpose of this paper is to detect the degenerate scale of a 2D bending plate analytically and numerically. Design/methodology/approach To avoid the time-consuming scheme, the influence matrix of the boundary element method (BEM) is reformulated to an eigenproblem of the 4 by 4 matrix by using the scaling transform instead of the direct-searching scheme to find degenerate scales. Analytical degenerate scales are derived from the boundary integral equation (BIE) by using the degenerate kernel only for the circular case. Numerical results of the direct-searching scheme and the eigen system for the arbitrary shape are also considered. Findings Results using three methods, namely, analytical derivation, the direct-searching scheme and the 4 by 4 eigen system, are also given for the circular case and arbitrary shapes. Finally, addition of a constant for the kernel function makes original eigenvalues (2 real roots and 2 complex roots) of the 4 by 4 matrix to be all real. This indicates that a degenerate scale depends on the kernel function. Originality/value The analytical derivation for the degenerate scale of a 2D bending plate in the BIE is first studied by using the degenerate kernel. Through the reformed eigenproblem of a 4 by 4 matrix, the numerical solution for the plate of an arbitrary shape can be used in the plate analysis using the BEM.

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Analytical derivation and numerical experiment of degenerate scale by using the degenerate kernel of the bipolar coordinates

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2017.08.006 ◽

2017 ◽

Vol 85 ◽

pp. 70-86 ◽

Cited By ~ 4

Author(s):

Jeng-Tzong Chen ◽

Shing-Kai Kao ◽

Jia-Wei Lee

Keyword(s):

Numerical Experiment ◽

Degenerate Kernel ◽

Bipolar Coordinates ◽

Analytical Derivation ◽

Degenerate Scale

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The unique solution on two dimensional Laplace problem with the maximum principle

Applied Mathematical Sciences ◽

10.12988/ams.2014.46411 ◽

2014 ◽

Vol 8 ◽

pp. 4641-4644

Author(s):

P. Haarsa ◽

S. Pothat

Keyword(s):

Maximum Principle ◽

Unique Solution ◽

Two Dimensional ◽

The Maximum Principle ◽

Laplace Problem

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Influence matrix and schema theory: Two views on the human relational system

PsycEXTRA Dataset ◽

10.1037/e548922014-001 ◽

2014 ◽

Author(s):

Lindsay M. Anmuth ◽

Gregg R. Henriques ◽

Christopher B. Hill ◽

Krystal M. Studivant

Keyword(s):

Schema Theory ◽

Relational System ◽

Influence Matrix

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Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

Astronomy and Astrophysics ◽

10.1051/0004-6361/202038023 ◽

2020 ◽

Vol 640 ◽

pp. A53

Author(s):

L. Löhnert ◽

S. Krätschmer ◽

A. G. Peeters

Keyword(s):

Growth Rate ◽

Numerical Simulations ◽

Accretion Disks ◽

Gravitational Instability ◽

Turbulent Viscosity ◽

Radial Distance ◽

Maximum Growth ◽

Wave Number ◽

Radiative Cooling ◽

Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

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Short Channel Poly-Si TFT with Single Grain Boundary by Excimer Laser Annealing on Al-masked a-Si Layer

MRS Proceedings ◽

10.1557/proc-715-a7.8 ◽

2002 ◽

Vol 715 ◽

Author(s):

Sang-Hoon Jung ◽

Jae-Hoon Lee ◽

Min-Koo Han

Keyword(s):

Grain Boundary ◽

Laser Annealing ◽

Thin Film Transistor ◽

High Mobility ◽

Silicon Layer ◽

Silicon Thin Film ◽

Short Channel ◽

Excimer Laser Annealing ◽

Boundary Density ◽

Single Grain

AbstractA short channel polycrystalline silicon thin film transistor (poly-Si TFT), which has single grain boundary in the center of channel, is reported. The reported poly-Si TFT employs lateral grain growth method through aluminum patterns, which acts as a selective beam mask and a lateral heat sink during the laser irradiation, on an amorphous silicon layer. The electrical characteristics of the proposed poly-Si TFT have been considerably improved due to grain boundary density lowered. The reported short channel poly-Si TFT with single grain boundary exhibits high mobility as 222 cm2/Vsec and large on/off current ratio exceeding 1 × 108.

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