A Novel Approach to the Weighted Laplacian Formulation Applied to 2D Delaunay Triangulations

In this work, a novel smoothing method based on weighted Laplacian formulation is applied to resolve the heat conduction equation by finite-volume discretizations with Voronoi diagram. When a minimum number of vertices is obtained, the mesh is smoothed by means of a new approach to the weighted Laplacian formulation. The combination of techniques allows to solve the resulting linear system by the Conjugate Gradient Method. The new approach to the weighted Laplacian formulation within the set of techniques is compared to other 4 approaches to the weighted Laplacian formulation. Comparative analysis of the results shows that the proposed approach allows to maintain the approximation and presents smaller number of vertices than any of the other 4 approaches. Thus, the computational cost of the resolution is lower when using the proposed approach than when applying any of the other approaches and it is also lower than using only Delaunay refinements.