Efficient and Robust Parallel Mesh Motion Solver Using Radial Basis Functions

Abstract

This paper presents a parallel mesh deformation solver using radial basis function (RBF) interpolation. The solver computes the displacement of each internal point independently without using the topological relations, and is further accelerated by an incremental approach based on the data reduction algorithm. The incremental approach makes full use of the matrix and solution of the previous step during the greedy selection procedure, and gives a better initial solution of the current RBF system of equations. To enhance the robustness and efficiency of the solver in parallel, for nonpredefined boundary movement, each CPU process computes the same interpolation function; for predefined movement, an additional process can be used to calculate the interpolation function one step earlier and broadcast it to other processes. Four typical mesh motion cases are simulated to demonstrate the deforming capability and parallel performance of the proposed method. Finally, several parametric setting rules of the deformation approach are presented for better usage.