Study On Multi-scale And Massively Parallel Discontinuous Galerkin Time Domain Methods

With the rapid development of social science technology,the design of various electromagnetic devices is becoming more complex and sophisticated.The design of these industrial products requires more precise and efficient electromagnetic algorithms to simulate,thereby shortening the development cycle and saving resources.Based on the discontinuous Galerkin time domain(DGTD)method,which has been widely reported in recent years,this dissertation studies the multi-scale technologies and the parallel strategies of the DGTD method.In addition,parallel DGTD methods based on the domestic processors have been researched.Main contributions of this dissertation are summarized as follows:1.Based on the DGTD method with higher-order vector hierarchical basis functions,the explicit time integration schemes and implicit time integration schemes and stability are discussed in detail.The problem of excessive bandwidth and long memory access time of DGTD matrix in the Crank-Nicholson(CN)scheme is solved,the Reverse Cuthill Mc Kee(RCM)diagonal preconditions are introduced into the solution of the CN-DGTD equation,which reduces the bandwidth of the CN-DGTD sparse matrix and improves the decomposition speed.2.Aiming at the multi-scale problem of the DGTD method,the implicit-explicit mix(IMEX)method and the local time stepping(LTS)technique were studied respectively.Firstly,aiming at the problem that the IMEX method occupies more memory,the IMEX method is improved,and the improved algorithm can automatically divide the optimized explicit region and the implicit region by introducing a global element time-steps gradient criterion,which reduces the peak memory of the IMEX-DGTD method and improves its solution speed.Aiming at the problem of poor accuracy of the conventional Multi-class LTS(MLTS)method,this dissertation proposed an alternative boundary LTS(ABLTS)method to improve the accuracy of MLTS while maintaining the speed of MLTS by applying the second-order Taylor expansion of the time term to the junction layer during multilayer division,combined with the alternating propulsion characteristics of the leapfrog scheme.Finally,combined with the idea of multi-time stepping(MTS)in fluid dynamics,the improved IMEX method and MLTS technology are effectively combined through the global element time-steps second order gradient criterion,which further improves the ability of the DGTD method to solve multi-scale problems.3.The heterogeneous parallelism technique of the DGTD method is studied.The corresponding DGTD heterogeneous methods are studied for the common GPU heterogeneous processors,domestic heterogeneous processors DCU and Sunway manycores processors.Firstly,the similarities and differences between GPU and DCU are summarized,and a DCU-DGTD method based on domestic DCU is proposed with reference to the conventional GPU-DGTD method,and the HIP streaming technology is combined to successfully improve the computing efficiency and achieve similar performance to the highperformance GPU on the DCU.The SW-DGTD method for Sunway many-cores processor is studied,through the fine-grained optimization of the algorithm,an efficient DMA communication strategy of SW-DGTD method is proposed,and an RMA-DB method using slave cores warps communication is further proposed for the new Sunway processor,which effectively expand the computing power of the DGTD method on the domestic Sunway processor.4.Aiming at the efficiency problem of massive parallelism of the DGTD method,the massively parallel DGTD method is studied.Firstly,the isomorphic parallel DGTD method based on Open MP is studied,then the graph matching strategy is introduced into the communication of multi-layer k-way topology of the DGTD method,and an MRT communication strategy based on the principle of minimal round-trip is proposed,which optimizes the sequence of DGTD point-to-point communication,plans the point-to-point communication without coupling to be executed within the same cycle,compresses the communication cycle of the multi-layer k-way topology to the shortest,thereby reducing the waiting time during blocking and non-blocking communications,improving the scalability of the algorithm and realizing efficient DGTD massively parallel computing.In addition,the parallel method of multi-scale technology of DGTD method is studied,and the parallel strategy for IMEX method is proposed,the MRT communication strategy is applied to the parallel computing of MLTS technology,which effectively improves the computing power of the two multi-scale methods.In addition,combined with the heterogeneous parallel computing technology of DGTD,the SW-DGTD method is successfully applied to the domestic supercomputer Sunway Taihu-Light and the new generation E-class supercomputer for quickly solving practical problems,which proves the effectiveness and engineering value of the proposed method.In summary,this dissertation discusses the DGTD method for multi-scale and massively parallelism problem based on domestic processors.The proposed methods improve the efficiency for the DGTD method to solve large-scale and multi-scale problems.