This paper describes the parallel simulation technique of the Discrete Element Method on multi-core processors. Recently the multi-core processors like CPUs or GPUs attract the attention to accelerate the computer simulations in various fields. In those simulations, effective usage of memory space is important. In the present study, the link-list was applied and optimized to utilize the memory space effectively on multi-core processors. In the past studies, the performances of the GPUs were reported to be dozens of times faster than those of the CPUs, while these comparisons were unfair. In this study, the simulation codes were developed and optimized for multi-core CPUs and GPU with almost the same algorithm. The latest CPUs and GPU were used to compare their performances fairly. The simulation results show that difference of these performances is not eminent.
Iterative methods for linear equations with coefficients of complex symmetric matrices appearing in finite element analysis of the high-frequency electromagnetic field have poor convergence. Besides, as the target of analysis becomes more extensive and more complicated, the convergence further deteriorates. Multiple-precision arithmetic operations such as pseudo-quadruple precision using two double precision and arbitrary precision arithmetic operation arbitrarily specifying accuracy are useful for improvement of convergence. In this research, we apply a multiple-precision arithmetic operation to an iterative method for a complex symmetric matrix, with a matrix representing the whole-body cavity resonator model of TEAM workshop problem 29 and succeed in improving convergence and calculation time.
The high frequency electromagnetic field simulation with the E formulation and the edge finite element method leads complex symmetric systems of linear equations. For solving such systems, the iterative method such as COCG method has been widely used, however, it suffers from slow convergence rate and high computational time. To improve the convergence rate, we have been studied to utilize the double-double arithmetic of complex numbers in an iterative process. This study focuses on parallelization and performance optimization of mixed-precision iterative methods for complex symmetric systems. Some numerical examples with OpenMP are demonstrated.