Some Efficient Parallel Algorithms For Solutions Of Multi-group Badiation Diffusion Problem And Die Filling Problem

The solution of multi-group radiation diffusion problem is of great importance in the numerical simulation of inertial con?nement fusion. As the multiple spatialtemporal scales, strongly nonlinear and multi-physics strongly coupling characteristics, there are still many challenges to conduct effcient parallel algorithms and implementations for the solution of large-scale discrete systems. Die ?lling problem is a class of particulate ?ows with broad application background, while Trubal is one of the widely used codes in two- and three-dimensional die ?lling processes.Due to the need of larger number of particles and higher effciency of simulation,it is an urgent and signi?cant work to parallelize Trubal. In this study, we focus on the effcient parallel solvers for the aforementioned two problems, while the acquired main results are as follows.The performances of the most widely used preconditioners(ILU(k) and AMG)and their symmetric and unsymmetric combinations(Bcoand?Bco) are ?rstly investigated, and the drawbacks on their feasibilities are also provided for the solution of discrete problems originating from a class of multi-group radiation diffusion problems. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature.Moreover, we present an adaptive combined AMG preconditioner Bαcoinvolving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bαco-GMRES holds the best robustness and effciency, and validate the applicability of Bαcoin large-scale realistic radiation hydrodynamic simulations.At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.The attribute of patch-correlation is ?rstly proposed for cells of two dimensional monolayer piecewise structured grid without any suspensions based on the patch hierarchy of JASMIN, and all the cells are classi?ed via their attributes,yielding to a new permutation Cifor patch Qi, and the convertion is also given between Ciand the lexicographical order Di. We secondly construct a parallel ILU(0)struct using Ciand Di, and the struct-based ILU(0) decomposition and substitution algorithm. Compared with the well-known Euclid library, our proposed parallel ILU(0) is of higher effciency. At last, we provide the parallel Bαco-GMRES solver by dint of the default Boomer AMG in HYPRE library. Numerical results demonstrate the proposed parallel Bαco-GMRES solver is more robust and more effcient than Boomer AMG-GMRES.The variational formulation and many fundamental properties of the corresponding bilinear form are proposed for the preserving-symmetry ?nite volume element scheme of a class of multi-material axially symmetric two-dimensional three-temperature problem, and two nonoverlapping domain decomposition(DD)preconditioners with a simple coarse space are constructed. It is worth mentioning that the second preconditioned CG and GMRES methods possess better convergence, robustness and universality. We acquire the nearly optimal estimation O((1 + logd h)3) on the condition numbers of these two preconditioned systems through a detailed theoretical analysis under certain assumptions, and develop the parallel program modules for DD preconditioned CG and GMRES solvers. Numerical results validate the aforementioned theoretical estimation, and state the good algorithmic and parallel scalability of the parallel solvers clearly.Parallelization of a discrete element method code titled Trubal is carried out based on the Symmetric Multi-Processor and CPU-GPU heterogeneous architectures where both two- and three-dimensional cases are assessed. We ?rstly investigate the globally static single-precision storage structure, and devise a locally dynamic storage based modularized simulator Trubal-new, which has better applicability and parallelism. Secondly, we resolve the con?ict of memory access using the sparse matrix technology, and develop an Open MP-based parallel simulator Trubal-omp. Furthermore, we compose a CUDA-based parallel simulator Trubalgpu using the heterogeneous storage system and other GPU technologies. Numerical results show that Trubal-omp and Trubal-gpu both possess better speedups.