A numerical method for problems in infinite strips with irregularities extending to infinity

Abstract

The Dirichlet-to-Neumann (DtN) Finite Element Method is a combined analytic-numerical method for boundary value problems in infinite domains. The use of this method is usually based on the assumption that, in the infinite domain D exterior to the finite computational domain, the governing differential equations are sufficiently simple. In particular, in D it is generally assumed that the equations are linear, homogeneous, and have constant coefficients. In this article, an extension of the DtN method is proposed, which can be applied to elliptic problems with ªirregularitiesº in the exterior domain D, such as (a) inhomogeneities, (b) variable coefficients, and (c) nonlinearities. This method is based on iterative ªregularizationº of the problem in D, and on the efficient treatment of infinite-domain integrals. Semi-infinite strip problems are used for illustrating the method. Convergence of the iterative process is analyzed both theoretically and numerically. Nonuniformity difficulties and a way to overcome them are discussed.

High-Order Two-Way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering

“…In Section 8.3 we briefly discuss alternative approaches to the nonlinear iterations. We note that iterative approaches have been used previously in numerical simulations of problems over infinite domains, although in completely different settings; see, e.g., [12,13,22].…”