A NUMERICAL-METHOD FOR PROBLEMS IN INFINITE STRIPS WITH IRREGULARITIES EXTENDING TO INFINITY

The Dirichlet-to-Neumann (DtN) Finite Element Method is a combined ana lytic-numerical method for boundary value problems in infinite domains . The use of this method is usually based on the assumption that, in t he infinite domain D exterior to the finite computational domain, the governing differential equations are sufficiently simple. In particula r, in D it is generally assumed that the equations are linear, homogen eous, and have constant coefficients. In this article, an extension of the DtN method is proposed, which can be applied to elliptic problems with (a)irregularities(o) in the exterior domain D, such as (a) inhom ogeneities, (b) variable coefficients, and (c) nonlinearities. This me thod is based on iterative (a)regularization(o) of the problem in D, a nd on the efficient treatment of infinite-domain integrals. Semi-infin ite strip problems are used for illustrating the method. Convergence o f the iterative process is analyzed both theoretically and numerically . Nonuniformity difficulties and a way to overcome them are discussed. (C) 1998 John Wiley & Sons, Inc.