A multidomain integrated-radial-basis-function collocation method for elliptic problems

Abstract

This article is concerned with the use of integrated radial-basis-function networks (IRBFNs) and non-overlapping domain decompositions (DDs) for numerically solving one- and two-dimensional elliptic problems. A substructuring technique is adopted, where subproblems are discretized by means of one-dimensional IRBFNs. A distinguishing feature of the present DD technique is that the continuity of the RBF solution across the interfaces is enforced with one order higher than with conventional DD techniques. Several test problems governed by second- and fourth-order differential equations are considered to investigate the accuracy of the proposed technique.