Preliminary Acceleration on Speeding up ICCG Method for High Frequency Electromagnetic Field Simulation
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Iterative methods such as the Krylov subspace method suffer from poor convergence in solving complex symmetric linear equations obtained in high frequency electromagnetic field analysis using the edge element finite element method. The convergence becomes worse and it takes much time as the analysis becomes larger and more complex. Hence, there is a great demand for faster iterative methods. To improve convergence, preconditioning for iterative methods such as Incomplete Cholesky (IC) decomposition preconditioning are often applied. In addition, parallelization methods such as the block ICCG and Algebraic block multi-color (ABMC) ordering method are also used for acceleration. While these methods are applicable to various types of matrices, they may lead to excessive dropping of non-zero elements or reordering of non-zero element positions, resulting in extremely poor convergence. Therefore, in this study, we propose a parallelization method that focuses on the distribution of non-zero elements in the matrix. While conventional parallelization method is applied to the entire matrix, we categorized the matrices of electromagnetic field analysis problems into several regions and proposed a parallelization method suitable for each of them. This method prevents extreme reordering of non-zero elements and dropping of non-zero elements, and improves the convergence and the parallelization efficiency. We performed some numerical experiments for matrices obtained from high frequency electromagnetic field problems. The proposed method succeeded in reducing both of the number of iterations and computation time compared to the block ICCG method in all cases, by up to 59%. In future work, we investigate the results of reordering methods.