Research On Fast Stress Analysis Algorithm For Large Scale Mesh Editing Based On Domain Decomposition

With the rapid development of prototyping technologies such as 3D printing,it has become an important research direction in the field of computer graphics to provide ordinary users with quick and easy 3D interactive editing tools.Existing physical simulation research using finite element method is not enough to combine user editing operation and stress analysis,and there is room for optimization of computing of large-scale grid.Therefore,this paper presents a new algorithm design by the combination of local subspace and multi-grid method based on domain decomposition,which provides users with a quick preview and gradual feedback of stress distribution after editing operation in the background of millions of degrees of freedom grid.In this paper,the domain of the editing layer and the calculation layer are constructed by the domain decomposition technique,so as to complete the block-division and compression of the stiffness matrix.After editing the shape of a domain,only the corresponding local data structures in the solver are updated,thus avoiding the high costs of re-factorization in the direct solver.The solver algorithm in this paper uses the boundary mode to construct a local subspace for the dimensionality reduction of the static balance system,providing a quick preview of stress analysis.Then,according to the algebraic multigrid method,this paper constructs a three-level multi-grid solver by removing the middle nodes in the edges and lump the unknowns using Schur complement method.This paper updates and solves grid editing and stress analysis in parallel on the basis of domain decomposition.The results of experiments show that the proposed solver algorithm outperforms the commercial solver Intel MKL with the grid of millions of DOFs.Speedups of 50%-70%can be achieved for large-scale meshes with reasonable pre-computation costs.