三维非定常扩散方程的虚边界元法  

VIRTUAL BOUNDARY ELEMENT METHOD FOR 3-D UNSTEADY DIFFUSION EQUATION

作　　者：何媛媛[1] 祝家麟[2] 

机构地区：[1]武汉理工大学华夏学院信息工程系,武汉430223 [2]重庆大学数理学院,重庆400044

出　　处：《数值计算与计算机应用》2010年第2期99-107,共9页Journal on Numerical Methods and Computer Applications

摘　　要：根据位势问题虚边界元法的基本思想,结合扩散方程与时间有关的基本解,提出了针对单层热势的三维非定常扩散方程虚边界元-配点法的一个具体实施方案.该方法既保留了边界元法的优点,也避免了传统边界元法中时间和空间上的奇异积分计算,采用较少的边界单元即可达到较高的精度.算例表明此方法的有效性和可行性,不过虚实边界比例选取范围比虚边界元方法应用于椭圆型问题时狭窄很多,对此本文进行了探讨,但还应继续从理论上加以论证.Based on the virtual boundary element method （VBEM） for potential theory and time- dependent fundamental solution of diffusion equations, an implementation of VBEM- colla- tion method for 3-D unsteady diffusion equation is proposed. VBEM not only retains the advantages of boundary element method, but also avoids singular integration or nearly sin- gular integration. High accuracy and efficiency have been observed just with a small number of boundary elements in the method. Several test problems have been examined, and the results are in excellent agreement with available analytical solutions. In addition, the choos- ing range of distance between the real boundary and the virtual boundary is investigated, which is narrower than VBEM applied in elliptic problems.

关 键 词：虚边界元 配点法 单层热势 非定常扩散方程 

分 类 号：O241.8[理学—计算数学]