The local boundary knots method for solution of Stokes and the biharmonic equation

Abstract

The paper focuses on the derivation of a local variant of the boundary knot method (BKM) for the cases of Stokes flow and the biharmonic equation. Compared to the global variant, the local one leads to a sparse result matrix of the system of equations and thus makes the solution of especially large-scale problems more efficient. It is also important to keep the conditionality of the interpolation matrix within reasonable bounds. For the localization, a combination of BKM and finite collocation method was used. The results of the local variant were compared on several examples and the dependence of the solution on the density of the point network and the dimensions of the stencil used was also tested in the paper.