Parallel Finite Element Analysis Of Electric Field In Aluminum Reduction Cell Based On Domain Decomposition Method

Finite element analysis for physical fileds of large-scale complicated structure, such as aluminum reductions cell, makes higher demand on memory capacity and calculation speed of computer, resulting in failure or inefficiency of traditional serial computation for such large-scale problems constantly. The combination of finite element method and parallel computation is an inevitable treand. In this paper, the parallel finite element analysis of electric field in aluminum reduction cell is studied based on domain decomposition method.Firstly, the finite element discrete format of electric field in aluminum reduction cell is derived from the basic equations of electromagnetic field, by Galerkin weighted residual method. The computational formula of elemental coefficient matrix is transformed from global coordinate system to locally elemental coordinate system based on the iosparametric element method, and then calculated by the14-points Gauss integral method.Secondly, the parallelization of Jacobi preconditioned conjugate gradient (PCG) algorithm is studied based on domain decomposition method, and two parallel finite element algorithms, SBS-PCG and EBE-PCQ are derived. The distributed compressed storage of coefficient matrix is discussed with the basic idea of EBE (element-by-element) method as a reference, and processing of boundary conditions, including current load and fixed potential constraint, is parallelized. Both the hardware platform and the software environment of distributed memeory parallel computing are constructed and configured. Parallel program of finite element analysis based on domain decomposition method is developed using C language and MPI standard library, thereupon parallel system of finite element analysis is designed and implemented.Finally, the implemented parallel finite element analysis system is applied to numeric simulation of electric field distribution in aluminum reduction cell. Both calculation precision and parallel performance of the developed program are concluded, and computational efficiency of domain decomposition method and EBE method is quantitatively compared. A coordinate-based division method is used for task partition, considering structural characteristics of the aluminum reduction cell. Experiment results show that parallel finite element method based on domain decomposition is of very high acceleration performance and can greatly shorten the calculation time, which indicates the effectiveness of its use in parallel simulation of physical fields in large-scale complicated structures, such as aluminum reduction cell. And comparison reveals that domain decomposition method possesses better parallel effect and higher computational efficiency than EBE method.