The presented article offers a 3D mesh generation routine as well as its further application to the 3D electrodiffusional problem.
The proposed mesh generator provides a confident way to creature a quite uniform mesh built with elements having mostly desired volume. Mesh elements have been adjusted to assumed sizes by making use of both the Metropolis algorithm and the Delaunay criterion. Mesh quality depicted in histograms occurs to be fairly satisfactory. Moreover, goodness of obtained meshes together with robustness of their applications to the Finite Element Method have been also tested by solving the 3D Laplace problem and the 3D diffusion equation on them. Comparison between these numerical solutions and analytical results shows very good agreement.
To find solutions to a nonlinear problem defined by a system of coupled equations describing electrodiffusion the FEM approach and the Newton's method have been jointly applied. Analysis of obtained results confirms usefulness of the presented solver to deal with nonlinear differential problems.