A subdomain collocation method based on Voronoi domain partition and reproducing kernel approximation

A subdomain collocation method based on Voronoi diagrams and reproducing kernel approximation is presented. The unkonwn field variables are approximated via reproducing kernel approximation. The body integration arising from the numerical evaluation of Galerkin weak form is converted into much cheaper contour integration along the boundary of each Voronoi cell. The Voronoi cells also provide an natural structure to perform h-adaptivity. Some 2D numerical examples are presented.