位势平面问题的新的规则化边界积分方程  

Novel Regularized Boundary Integral Equations for Potential Plane Problems

作　　者：张耀明[1] 吕和祥[2] 王利民[1] 

机构地区：[1]山东理工大学数学学院应用数学所,山东淄博255049 [2]大连理工大学力学系,大连116024

出　　处：《应用数学和力学》2006年第9期1017-1022,共6页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10571110);山东省自然科学基金资助项目(2003ZX12)

摘　　要：广泛实践集中在直接变量边界积分方程的规则化研究,其本质是利用简单解消除边界积分的奇异性.然而,至今关于平面位势问题的第一类边界积分方程的规则化研究尚未涉足.致力于间接变量边界积分方程的规则化方法研究,基于一种新的思想和观点,确立平面位势问题的间接变量规则边界积分方程,它不包含CPV强奇异积分和HFP超奇异积分.数值算例表明现在的方法可取得很好的精度和效率,特别是边界量的计算.The universal practices have been centralizing on the research of regularization to the DBIE. The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation was mainly devoted to the research on the regularization of the singular boundary integral equations with indirect unknowns. A novel view and idea was presented herein, in which the regularized boundary integral equations with indirect unknowns excluding the CPV and HFP integrals were established for the plane potential problems. With some numerical results, it is shown that the better accuracy and higher efficiency, especially on the boundary, can be achieved by the present system.

关 键 词：位势平面问题 边界积分方(BIEs) 间接变量BIEs 规则化BIEs 

分 类 号：O342[理学—固体力学]