A Trace-Based Interface Reduction Method for Highly Conducting Interfaces

Abstract

We develop a reduced interface formulation for elliptic interface problems with highly conducting interfaces. The interface condition consists of continuity of the primal variable together with a jump in the normal flux proportional to the surface Laplacian of the interface trace. Instead of using the solution jump as the interface unknown, we employ the common interface trace and derive a trace-based Schur complement formulation. For prescribed interface trace data, independent extension problems are solved in the two subdomains, leading to a reduced interface equation involving the Dirichlet-to-Neumann jump operator and a surface stiffness operator. Finite-dimensional trace approximations produce compact reduced systems posed only on the interface. Numerical experiments for circular, smooth noncircular, and heart-shaped interfaces illustrate the effectiveness of the method and the role of interface-mode enrichment.