快速多极边界元法在阴极保护求解电位分布应用.pdfVIP

快速多极边界元法在阴极保护求解电位分布中的应用 1,2 1,2 1,2 1,2 张东东 ，杜翠薇 ，程学群 ，李晓刚 （1.北京科技大学腐蚀与防护中心，北京 100083；2. 腐蚀与防护教育部重点实验室，北京 100083） 摘要：边界元法是伴随着有限元法发展起来的一种数值算法，它已被广泛应用于电位分布的数值模拟计算中。但 传统边界元法形成的系数矩阵为非对称满阵，当求解问题的规模增大时，求解效率下降得很快，存储量和计算量 已经成为制约边界元法发展的瓶颈。快速多极边界元是伴随快速多极算法发展起来、利用快速多极算法加速求解 的边界元新型求解方法。快速多级边界元法为解决大规模阴极保护工程数值计算问题提供了可行的思路。本文通 过二维算例证明此算法可以应用在阴极保护领域。 关键词：阴极保护；边界元；快速多极算法 Fast Multipole Boundary Element Methods for Cathodic Protection Potential Distribution Problems ZHANG Dongdong1,2, DU Cuiwei1,2, CHEN Xuequn1,2, LI Xiaogang1,2 (1.Corrosion and Protection Center, University of Science and Technology Beijing, Beijing 100083, China ；2. Key Laboratory for Corrosion and Protection (MOE), Beijing 100083, China) Abstract: Boundary element method (BEM) is a numerical scheme along with the development of finite element method(FEM). It has been widely used in the numerical simulation of potential distribution problems. Conventional boundary element method is not efficient for large-scale problems because of the dense and asymmetric matrix. The fast multipole method (FMM) is a very effective way to accelerate the numerical solutions of the methods based on Green ’s functions or fundamental solutions. Combined with FMM, BEM can now solve large-scale problems of cathodic protection system with several million unknowns on the desk computer. In this paper, a scheme of two-dimensional potential distribution is presented. The result shows that, the method can be used in cathodic p