Tangential derivative of singular boundary integrals with respect to the position of collocation points

Heat conduction in anisotropic materials has important applications in science and engineering. In this paper the virtual boundary element method (VBEM) is applied to solve these problems. Due to the fact of a virtual boundary outside the real boundary, the VBEM does not need to treat the singular boundary integrals, and thus, is more accurate and convenient than the traditional one. Numerical examples are presented, to demonstrate the efficiency and accuracy of this method.

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Precorrected-FFT Accelerated Singular Boundary Method for High-Frequency Acoustic Radiation and Scattering

Mathematics ◽

10.3390/math10020238 ◽

2022 ◽

Vol 10 (2) ◽

pp. 238

Author(s):

Weiwei Li ◽

Fajie Wang

Keyword(s):

High Frequency ◽

Acoustic Radiation ◽

Low Frequency ◽

Singular Boundary ◽

Cpu Time ◽

Interpolation Matrix ◽

Collocation Points ◽

Boundary Method ◽

Frequency Regime ◽

Singular Boundary Method

This paper presents a precorrected-FFT (pFFT) accelerated singular boundary method (SBM) for acoustic radiation and scattering in the high-frequency regime. The SBM is a boundary-type collocation method, which is truly free of mesh and integration and easy to program. However, due to the expensive CPU time and memory requirement in solving a fully-populated interpolation matrix equation, this method is usually limited to low-frequency acoustic problems. A new pFFT scheme is introduced to overcome this drawback. Since the models with lots of collocation points can be calculated by the new pFFT accelerated SBM (pFFT-SBM), high-frequency acoustic problems can be simulated. The results of numerical examples show that the new pFFT-SBM possesses an obvious advantage for high-frequency acoustic problems.

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Application of exponential transformation coupled with adaptive subdivision technique for nearly singular boundary integrals in elasticity problems

Boundary Elements and Other Mesh Reduction Methods XXXVI ◽

10.2495/bem360321 ◽

2013 ◽

Author(s):

Guizhong Xie ◽

Jianming Zhang

Keyword(s):

Singular Boundary ◽

Boundary Integrals ◽

Exponential Transformation ◽

Adaptive Subdivision ◽

Elasticity Problems

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Numerical Investigation on Convergence Rate of Singular Boundary Method

Mathematical Problems in Engineering ◽

10.1155/2016/3564632 ◽

2016 ◽

Vol 2016 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

Junpu Li ◽

Wen Chen ◽

Zhuojia Fu

Keyword(s):

Short Communication ◽

Convergence Rates ◽

Fundamental Solutions ◽

Benchmark Problems ◽

Singular Boundary ◽

Intensity Factors ◽

Collocation Points ◽

Boundary Method ◽

Collocation Scheme ◽

Singular Boundary Method

The singular boundary method (SBM) is a recent boundary-type collocation scheme with the merits of being free of mesh and integration, mathematically simple, and easy-to-program. Its essential technique is to introduce the concept of the source intensity factors to eliminate the singularities of fundamental solutions upon the coincidence of source and collocation points in a strong-form formulation. In recent years, several numerical and semianalytical techniques have been proposed to determine source intensity factors. With the help of these latest techniques, this short communication makes an extensive investigation on numerical efficiency and convergence rates of the SBM to an extensive variety of benchmark problems in comparison with the BEM. We find that in most cases the SBM and BEM have similar convergence rates, while the SBM has slightly better accuracy than the direct BEM. And the condition number of SBM is lower than BEM. Without mesh and numerical integration, the SBM is computationally more efficient than the BEM.

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