HIGHER NUMERICAL EFFICIENCY AND ACCURACY THROUGH MESHLESS EVALUATION OF DOMAIN INTEGRALS

通过域积分的无网格评估提高数值效率和准确性

• 批准号: 13650080
• 负责人: TANAKA Masataka
• 金额: $ 2.24万
• 依托单位: SHINSHU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650080/
• 关键词: Computational Mechanics; Boundary Element Method; Integral Equation; Domain Integral; Dual Reciprocity Method; Meshless Evaluation; Fundamental Solution; Heat Conduction

The main advantage of the boundary element methods is that in most linear problems accurate numerical analysis can be performed through mesh division of the boundary only. However, even for the linear problems of inhomogeneous materials where the property changes as a function of coordinates or of the inhomogeneous initial conditions, domain integrals inevitably arise in the boundary integral equation to be solved. In these cases, we have to evaluate the domain integrals using the cell or element division of the domain. This would lead to reducing attraction of the boundary element method. In other cases an "approximate" fundamental solution is employed for the formulation, we have to discretize the domain and include the nodal quantities in the domain as the final system of equations. Therefore, it has been one of the main subjects of the BEM how to effectively evaluate such domain integrals.In boundary element research so far, there are several methods available in the literature : The boundary-domain element or Green element method, multi-reciprocity or dual reciprocity method, the analog equation method, and so on. Among them, the dual reciprocity method seems to be very attractive to evaluate approximately the domain integrals by using rather simple functions.This paper is concerned with numerical investigations of the dual reciprocity method for some typical problems frequently encountered in practice. First, we had been collecting a wide range of approximate functions which can be used for the dual reciprocity method. Then, we had applied some selected functions to the problem solving and checked the numerical properties of solution procedure based on the dual reciprocity principle. Through these investigations we can develop very good computer codes for accurate, efficient analysis of the problems. A series of the academic papers on the topics have been submitted to international journals, and most of them have been already published.

边界元法的主要优点是，在大多数线性问题中，仅通过边界的网格划分就可以进行精确的数值分析。然而，即使对于非均匀材料的线性问题，其中属性作为坐标或非均匀初始条件的函数而变化，在待解的边界积分方程中也不可避免地出现区域积分。在这些情况下，我们必须使用区域的单元或元素划分来计算区域积分。这将导致减少吸引力的边界元法。在其他情况下，一个“近似”的基本解决方案是用于制定，我们必须离散域，并包括在域中的节点量作为最终的方程组。因此，如何有效地计算这类区域积分一直是边界元法的主要课题之一。在边界元研究中，目前文献中有几种方法：边界域单元或绿色单元法、多重互易或双重互易法、模拟方程法等，其中，对偶倒易法是一种很有吸引力的方法，它可以用简单的函数近似计算区域积分，本文对一些典型的区域积分问题进行了数值研究。首先，我们已经收集了广泛的近似函数，可用于双互易方法。在此基础上，我们选取了一些函数进行求解，并根据对偶互易原理对求解过程的数值性质进行了检验。通过这些调查，我们可以开发出非常好的计算机代码，用于准确，有效地分析问题。在国际期刊上发表了一系列关于这一课题的学术论文，其中大部分已经发表。

项目成果

Masataka Tanaka: "An inverse problem of coupled thermoelasticity in reconstructing heat fluxes and thermal stresses"Proc.11^<th> Annual ASCE Conf. 173-176 (2003)

Masataka Tanaka：“重建热通量和热应力中耦合热弹性的反问题”Proc.11^<th>年度 ASCE Con​​f。

田中 正隆: "傾斜機能材料中の非定常熱伝導問題に対する時間ステップBEMへのDRMの適用(3次元問題の検討)"境界要素法論文集. 19. 21-26 (2002)

Masataka Tanaka：“DRM 在功能梯度材料非稳态热传导问题中的应用（三维问题研究）” 边界元方法论文 19. 21-26 (2002)。

M.Tanaka, T.Matsumoto, Y.Suda: "A dual reciprocity BEM applied to the thermoelastic problem of temperature-dependent materials"Trans. JSME, Ser.A. Vol.68A. 1285-1291 (2002)

M.Tanaka、T.Matsumoto、Y.Suda：“应用于温度相关材料的热弹性问题的双互易边界元法”Trans。

M.Tanaka, T.Matsumoto, Y.Suda: "A dual receiprocity BEM applied to the steady-state heat conduction problem in temperature-dependent materials"Trans. JSME, Ser.A. Vol.68A. 717-722 (2002)

M.Tanaka、T.Matsumoto、Y.Suda：“应用于温度相关材料的稳态热传导问题的双互易边界元法”Trans。

Krishna M. Singh: "Dual reciprocity boundary element analysis of transient advection-diffusion"Int.J.Numerical Methods for Heat & Fluid Flow. 13. 663-646 (2003)

Krishna M. Singh：“瞬态平流扩散的双互易边界元分析”Int.J.热数值方法