Space Reduction for Linear Systems with Local Symmetry

A space reduction method for structural operator equations is proposed in this paper. It turns out that many interface problems derived by applying the idea of domain decomposition can be categorized into this framework. A seemingly simple algebraic technique is proposed to reduce the complexity of operator equations. The connection between this technique and the integral equation method is revealed. Under mild conditions, we prove that the reduced operator equation by space reduction is well-posed, and its solution is the same as that of the original one. As two applications, we apply the proposed method to solve a planar triangular lattice problem and an exterior problem of modified Helmholtz equation with FEM discretization. The numerical evidence validates the effectiveness.