Mesh Simplification Method Based on Monte-Carlo Algorithm

In order to grasp the operation law of aluminum electrolytic cell, it is necessary to conduct coupling simulation of thermodynamic field and hydrodynamics field, and obtain a grid with dielectric constant parameters through a series of processing results. In electromagnetic computation, the calculation platform is unable to calculate if the mesh is too dense and the tetrahedral elements are not uniform, hence the mesh must be simplified. This work proposes a Monte Carlo stochastic algorithm-based method for mesh simplification as a solution to the problem that the number of mesh is high relative to the computing platform and their distribution across scales is uneven. The octree was used to evaluate the mesh density in the region, the deletion probability of vertices was calculated, and the reserved points were utilized to renew a set of mesh using the Delaunay triangulation method. The most essential aspect of the Monte-Carlo algorithm is determining the deletion probability of each point to ensure that the freshly created mesh is sparse and uniform. Example of hemisphere will then be provided to demonstrate the mesh simplification effect of this strategy. Compared to previous mesh simplification methods in terms of time cost, memory cost, and calculation results, the outcomes are comparable, and the time and space costs are drastically decreased. Compared to previous simplification methods for tetrahedral mesh, this method is straightforward and user-friendly, with a time complexity of O(N) (where N is the number of vertices) and a space complexity of O(N).