Comparison of complex methods for numerical solutions of boundary problems of the Laplace equation

S.M. Aleynikov; A.V. Stromov

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Comparison of complex methods for numerical solutions of boundary problems of the Laplace equation

机译：拉普拉斯方程边界问题数值解的复杂方法的比较

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摘要

The complex polynomial method (CPM) and the complex variable boundary element method (CVBEM) are used when solving boundary problems for the Laplace equation in flat domains of complex shape. These methods have been compared according to numerical efficiency using the example of some problems of mathematical physics (heat transfer, filtration, torsion of prismatic rods). Numerical results have been correlated with the known analytical and approximate solutions. Recommendations are given for practical application of the CPM and the CVBEM for engineering calculations.

机译：在求解形状复杂的平面域中的Laplace方程的边界问题时，将使用复杂多项式方法（CPM）和复杂变量边界元方法（CVBEM）。这些方法已通过使用一些数学物理问题（传热，过滤，棱柱杆的扭转）来根据数值效率进行了比较。数值结果已经与已知的解析解和近似解相关。对于CPM和CVBEM在工程计算中的实际应用，提出了一些建议。

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来源
《Engineering analysis with boundary elements》 |2004年第6期|p.615-622|共8页
作者
S.M. Aleynikov; A.V. Stromov;
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作者单位

Department of Mathematics, Voronezh State University of Architecture and Civil Engineering, 20-Letiya Oktyabrya Str, 84, Voronezh 394006, Russia;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类工程数学;
关键词
complex variable boundary element method; complex polynomial method;

机译：复变边界元法;复多项式法;

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1. Method of boundary integral equations as applied to the numerical solution of the three-dimensional Dirichlet problem for the laplace equation in a piecewise homogeneous medium [J] . Zakharov E. V., Kalinin A. V. Computational mathematics and mathematical physics . 2009,第7期

机译：分段均质介质中拉普拉斯方程三维Dirichlet问题数值解的边界积分方程法
2. In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given. [J] . M. M. Khader, M. Adel Nonlinear engineering: Modeling and application . 2016,第3期

机译：在本文中，我们采用分数阶复杂变换方法将非线性分数阶Klein-Gordon方程（FKGE）转换为常微分方程。我们使用变分迭代方法（VIM）来解决所得的ODE。分数导数以Caputo形式表示。提出了一些数值例子来验证所提出的技术。最后，与使用四阶Runge-Kutta的数值解进行了比较。
3. Numerical methods for determining the inhomogeneity boundary in a boundary value problem for Laplace's equation in a piecewise homogeneous medium [J] . Gavrilov S.V., Denisov A.M. Computational mathematics and mathematical physics . 2011,第8期

机译：确定分段均质介质中拉普拉斯方程边值问题中不均匀边界的数值方法
4. Wavelet Boundary Element Method for Numerical Solution of Laplace Equation [C] . Yuhuan Cui, Jingguo Qu, Yamian Peng, International conference on green communications and networks;GCN 2011 . 2011

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5. On the numerical solution of Laplace's equation with nonlinear boundary conditions for corrosion of steel in concrete. [D] . Ji, Ge. 2006

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6. A Numerical Method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries [O] . Liang Ge, Fotis Sotiropoulos -1

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7. Alternative Formulations of The Laplace Transform Boundary Element (LTBE) Numerical Method for the Solution of Diffusion-Type Equations [O] . G. J. Moridis 1992

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8. Alternative formulations of the Laplace transform boundary element (LTBE) numerical method for the solution of diffusion-type equations [R] . Moridis, G 1992

机译：用于求解扩散型方程的拉普拉斯变换边界元（LTBE）数值方法的替代公式

Comparison of complex methods for numerical solutions of boundary problems of the Laplace equation

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