A nonoverlapping domain decomposition method for Symm's equation for conformal mapping

Symm's equation is a first-kind integral equation for computing conformal m aps of simply connected regions. The package CONFPACK solves Symm's equatio n by an indirect boundary element method using an accurate corner represent ation. This solution technique is extended here to include nonoverlapping d omain decomposition. Degrees of freedom are introduced on one or more inter faces and different unknowns are used, leading to a system of second-kind e quations. The corresponding linear system can be expressed in Schur complem ent form. The accurate treatment of corners is preserved in the new formula tion. The results of serial and parallel MATLAB implementations of the new algorithm show significant speedups as the number of unknowns grows.