Parallel Realization of Element by Element Analysis of Eddy Current Field Based on Graphic Processing Unit
Keywords:
Eddy current filed, element by element method, graphic processing unit, parallel computingAbstract
The element by element parallel finite element method (EbE-PFEM) applied to engineering eddy current problem is presented in this paper. Unlike classical finite element method (FEM), only element matrix is needed to store for EbE method. Thereby more storage memory saved. Element by element conjugated gradient (EbE-CG) method is used to solve the equations which are discretized from elements level. Considering the ill-conditioned character of system equations, highly parallel Jacobi preconditioned (JP) method is used to accelerate the convergence. Besides, the process of dealing with boundary condition based on EbE theory is introduced. To validate the method, a 2D eddy current problem in complex frequency domain is used. The numerical analysis is carried out on the graphic processing units (GPU) with a compute unified device architecture (CUDA) parallel programming model to accelerate the convergence. And the results demonstrate that the JP method and GPU platform are effective in solving eddy current field with improved convergence.
Downloads
References
T. J. R. Hughus, I. Levit, and J. Winget, “An element-by-element solution algorithm for problems of structural and solid mechanics,” Computer Methods in Applied Mechanics and Engineering, vol. 36, pp. 241-254, 1983.
A. F. P. Camargos and V. C. Silva, “Performance analysis of multi-GPU implementations of Krylovsubspace methods applied to FEA of electromagnetic phenomena,” IEEE Transactions on Magnetics, vol. 51, no. 3, March 2015.
T. Okimura, T. Sasayama, and N. Takahashi, “Parallelization of finite element analysis of nonlinear magnetic fields using GPU,” IEEE Transactions on Magnetics, vol. 49, no. 5, May 2013.
O. Bottauscio, M. Chiampi, J. Hand, et al., “A GPU computational code for eddy-current problems in voxel-based anatomy,” IEEE Transactions on Magnetics, vol. 51, no. 3, March 2015.
D. M. Fernández, M. M. Dehnavi, and W. J. Gross, “Alternate parallel processing approach for FEM,” IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 399-402, 2012.
I. Kiss, S. Gyimóthy, Z. Badics, et al., “Parallel realization of the element-by-element FEM technique by CUDA,” IEEE Transactions on Magnetics, vol. 48, no. 2, pp. 507-510, 2012.
D. Y. Wu, R. Y. Tang, and D. X. Xie, “Element by element finite element method applied to eddy current problem,” CEFC’2014, France, May 25-28, 2014.
D. Y. Wu, X. K. Yan, R. Y. Tang, D. X. Xie, and Z. W. Chen, “GPU acceleration of EBE method for 3- D linear steady eddy current field,” ICEMS’2015, Thailand, October 25-28, 2015.
D. X. Xie, “Finite element method applied to the calculation of skin effect of current-carrying conductor in an open slot,” HIET Journal, vol. 4, no. 1, pp. 6-23, 1981. (In Chinese).