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

• 来源期刊: 计算数学（英文版）
• 关键词: Laplace's equation Integral equations Mixed boundary conditions Robin boundary conditions
• 年，卷（期）: 2012,（4）
• 页码范围: 433-448
• 页数: 16页
• 语种: 英文
• DOI: 10.4208/jcm.1201-m3644

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.