New Interface Conditions for Non-overlapping Domain Decomposition Iterative Procedures

A Seidel-type interface condition is considered for non-overlapping domain decomposition iterative methods. With a suitable pseudo-energy defined on interfaces, the convergence speed of the iterative scheme is shown to be as twice fast as that of the Jacobi scheme. Our analysis is entirely independent of the governing model problems of a specific type of partial differential equations, but depends only on the scheme of updating interface data. By this, our analysis covers Seidel-type schemes for a general class of problems, such as elliptic, Helmholtz, Maxwell, and elasticity problems, etc. In order to avoid the sequential nature of Seidel schemes and to implement them on parallel computers, red-black Gauss-Seidel schemes are also considered with equivalent efficiency to Seidel schemes.