A Study On Asynchronous Parallel Iterative Algorithms For Solving Electromagnetic Problems

Solving electromagnetic fields with numerical methods is widely used now, and it is very importrant to solve the linear equations in numerical methods. With the electromagnetic fields becoming more and more complex and the increasing scale of linear equations, the serial algorithms can not do work well.In view of this, it proposes an asynchronous parallel iterative algorithm based on the Gauss-Seidel iteration. In this thesis, large-scale linear equations are partitioned into many different linear equations which are calculated in different processors. The processor sends the results to the other processors and receives their latest data after completing the calculation, and then it continues calculating the new linear equation with the data received. The numerical experiments show that this algorithm has higher processing speed. We apply it into the solution of two dimensional electromagnetic fields, which indicates that this new algorithm is practical.The convergence of some linear equations is poor. For this, it proposes an asynchronous parallel algorithm based on the Range Subspace Projection Method. In this algorithm, large-scale linear equations are partitioned into many different projection equations by columns which are calculated in different processors. After completing the calculation, the processor sends the results to the other processors and receives their latest data and then it go on calculating the new projection equation with the data received. The numerical experiments show that the proposed algorithm has good convergence and high processing speed. We apply it into the solution of electromagnetic scattering, which indicates the new algorithm is practical.