A Preconditioner Determined by a Subdomain Covering the Interface

Abstract

A method for construction of a preconditioner for the capacitance matrix on the interface is described. The preconditioner is determined by a subdomain covering the interface, and the condition number of the preconditioned matrix is dependent on the width of the covering subdomain and independent of the discrete mesh size and discontinuity of the coefficients of the differential operator. Some applications of our theory are presented at last.