On the convergence of the panel method for potential problems with non-smooth domains

The linear convergence rate of the panel method is often observed in problems with smooth boundaries. When corners are present in the problem domain, the convergence rate slows down greatly. A study on the convergence rate of the panel method for potential problems with non-smooth domains was conducted and is reported in this paper. It has been found that for Dirichlet boundary value problems, the relative errors in the normal flux produced by the panel method at corners persist regardless of mesh refinement level. This is the main factor that deteriorates the overall convergence rate of the panel method for Dirichlet type of problems with non-smooth domains. Methods to improve convergence and accuracy at corners are proposed and are demonstrated in the paper.