A ROBUST AND ACCURATE SOLVER OF LAPLACE＇S EQUATION WITH GENERAL BOUNDARY CONDITIONS ON GENERAL DOMAINS IN THE PLANE  

作　　者：Rikard Ojala 

机构地区：[1]Numerical Analysis, Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden

出　　处：《Journal of Computational Mathematics》2012年第4期433-448,共16页计算数学（英文）

摘　　要：A robust and general solver for Laplace＇s equation on the interior of a simply connected domain in the plane is described and tested. The solver handles general piecewise smooth domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an integral equation formulation of the problem. Difficulties due to changes in boundary conditions and corners, cusps, or other examples of non-smoothness of the boundary are handled using a recent technique called recursive compressed inverse preconditioning. The result is a rapid and very accurate solver which is general in scope, its performance is demonstrated via some challenging numerical tests.A robust and general solver for Laplace＇s equation on the interior of a simply connected domain in the plane is described and tested. The solver handles general piecewise smooth domains and Dirichlet, Neumann, and Robin boundary conditions. It is based on an integral equation formulation of the problem. Difficulties due to changes in boundary conditions and corners, cusps, or other examples of non-smoothness of the boundary are handled using a recent technique called recursive compressed inverse preconditioning. The result is a rapid and very accurate solver which is general in scope, its performance is demonstrated via some challenging numerical tests.

关 键 词：Laplace＇s equation Integral equations Mixed boundary conditions Robinboundary conditions. 

分 类 号：O175.2[理学—数学] O175.25[理学—基础数学]