A Nonoverlapping Domain Decomposition Method for Symm's Equation for Conformal Mapping

Symm’s equation is a first-kind integral equation for computing conformal maps of simply connected regions. The package CONFPACK solves Symm’s equation by an indirect boundary element method using an accurate corner representation. This solution technique is extended here to include nonoverlapping domain decomposition. Degrees of freedom are introduced on one or more interfaces and different unknowns are used, leading to a system of second-kind equations. The corresponding linear system can be expressed in Schur complement form. The accurate treatment of corners is preserved in the new formulation. The results of serial and parallel MATLAB implementations of the new algorithm show significant speedups as the number of unknowns grows.