Iterative schemes for the solution of systems of equations arising from the DRM in multidomains

The aim of this work is to carry out a systematic experimental study of the use of iterative techniques in the context of solving the linear system of equations arising from the solution of the diffusion–convection equation with variable velocity field through the use of the dual reciprocity method in multidomains (DRMMD). We analyse the efficiency and accuracy of the computed solutions obtained from the DRM-MD integral equation numerical approach applying various iterative algorithms. For every iterative method tested, we consider a set of different preconditioners, depending on the features of the input matrix to be solved with the chosen method. To check the accuracy of the solutions obtained through the selected iterative methods, they are contrasted against the solutions obtained applying some direct methods such as singular value decomposition, Golub’s method and Cholesky decomposition. The numerical results are also compared with a benchmark analytical solution. Furthermore, we present a comparative analysis of the linear systems of algebraic equations obtained from DRM-MD considering two approximating functions: the conical function r plus a constant, i.e. (1 + r), and the augmented thin plate spline, both of them radial basis functions.