collocation method for elliptic problems N. Mai-Duy ∗ and T. Tran-Cong

Abstract This paper is concerned with the use of integrated radial-basis-function networks (IRBFNs) and non-overlapping domain decompositions (DDs) for numer-ically solving one- and two-dimensional elliptic problems. A substructuring tech-nique is adopted, where subproblems are discretized by means of one-dimensional IRBFNs. A distinguishing feature of the present DD technique is that the continu-ity 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. KEY WORDS: non-overlapping domain decomposition; radial basis function; collo-cation technique; high-order differential equations