A multidomain integrated RBF collocation method for elliptic differential equations

Abstract

[Abstract]: This paper describes a non-overlapping multidomain radial-basis-function (RBF) technique that improves smoothness of the approximate solution across subdomain interfaces. In general, the procedure is similar to the Schur complement approach where the interface solutions are obtained before the subdomain solutions. In particular, subdomain problems are solved using the integrated RBF collocation technique. On each subdomain, highest-order derivatives in the given differential equation (DE) are approximated using RBF networks, and lower-order derivatives and the variable itself are then obtained through integration. The present integrated RBF technique introduces integration constants which provide an effective means to collocate the DE on the interfaces. Continuity enforcements employed in the Schur complement system and the satisfaction of the DE on the subdomain interfaces in the subdomain discrete system leads to a solution that is continuous across the interfaces with one order higher than with conventional domain decomposition techniques.