Research On Parallel Algorithm Of Numerical Simulation In Geophysics For Tianhe Supercomputing System

At present,the independence of hardware and software has become the inevitable trend of domestic development.Tianhe supercomputing system is independently developed by the National University of Defense Technology.The development of software for Tianhe supercomputing system architecture is of positive significance to the development of high-performance computing and software independence in our country.Magnetotelluric and geodynamics are two important fields in geophysics.Magnetotelluric plays a very important role in mineral exploration,oil and gas exploration,and deep underground structure research.The study of geodynamics is of great importance for the formation and evolution of the earth’s structure,the search for resources and energy,and the prevention and mitigation of natural disasters.As the scale of computation increases,the accuracy demand increases,and the timeliness requirement increases,the study of scalable parallel algorithms and parallel algorithms for the architecture has become an important topic in high-performance computing research and geophysical research.In this paper,the Tianhe supercomputing system is used as the platform to develop the 3D parallel forward modeling software of magnetotelluric for isotropic media and anisotropic media and conduct research on parallel algorithms for geodynamic numerical simulation according to the architecture.The main work and achievements of this paper are as follows:(1)For the isotropic three-dimensional magnetotelluric forward modeling problem,we propose a vector finite element parallel algorithm based on unstructured grids,design a distributed storage method based on a local matrix,and develop a three-level parallel computing algorithm.The first two levels are process-level parallelism for frequency and linear system solution,followed by fine-grained thread-level parallelism.We developed the magnetotelluric isotropic forward modeling software.The algorithm is validated by model simulation.The test results show that the parallel algorithm has good performance.On the Tianhe Qunxing supercomputing system,the speedup of 2520 cores compared to100 cores in the strong scalability test is 1609,and the parallel efficiency is 60%.On Tianhe new-generation supercomputing system,the speedup of 10752 cores compared to256 cores in the strong scalability test is 6040,and the parallel efficiency is 56%.(2)For anisotropic 3D magnetotelluric forward modeling,we propose a vector finite element parallel algorithm based on unstructured grids,design a distributed storage method based on local grids,and develop parallelism with various granularities.Processlevel parallelism for subdomains,frequencies,and solving linear systems were developed by MPI,and thread-level parallelism for merge sort,element analysis,matrix assembly,and imposed boundary conditions were developed by Open MP.We developed the magnetotelluric anisotropic forward modeling software.The algorithm is validated by model simulation,and the influence of conductivity anisotropy on apparent resistivity and phase is studied.Scalability tests were performed on the Tianhe-2 supercomputer,and three parallel direct method solvers,SUPERLU,MUMPS,and PASTIX were compared.The test results show that the algorithm has good parallel performance.The speedup of 7560 cores compared to 192 cores in the strong scalability test with SUPERLU,MUMPS and PASTIX are 6188.00,4664.53,and 4570.99,respectively,and the parallel efficiency are81.85%,61.70%,60.46%.MUMPS and PASTIX solve faster than SUPERLU.(3)In order to solve the problem of poor computing performance of geodynamics numerical simulation software on Phytium multi-core processor,we propose a storage format for model boundary separation,design node multicolor algorithm and block multicolor algorithm,develop fine-grained parallelism of Gauss-Seidel smoother,and design a fused symmetric Gauss-Seidel smoother,which reduces the computational complexity.We design multithreaded parallel algorithms for other kernel functions such as multigrid restriction,multigrid prolong,sparse matrix multiplication vector,and so on.The grids of different sizes are tested on the FT2000 plus processor and the performance analysis is carried out.The test results show that the performance of the optimized Gauss-Seidel is improved by 4.3-6.99 times,and the linear system performance of the optimized Uzawa is improved by 3.6-5.6 times.(4)In order to solve the heterogeneous acceleration problem of geodynamics numerical simulation software on Matrix accelerator,we propose heterogeneous parallel algorithms for Gauss-Seidel based on node multicolor and for sparse matrix multiplication vector,and design a data block method according to the storage characteristics of the Matrix accelerator,effectively utilizes the on-chip storage,improves the memory access speed,designs a double-buffer strategy for overlapping computing and communication,and implements a mixed-precision algorithm to improve performance while ensuring accuracy.The grids of different sizes are tested on the Matrix accelerator M-DSP and the performance analysis is carried out.The test results showed that Sp MV and Gauss-Seidel achieved a peak performance of 5.46Gflops/s and 6.20Gflops/s,and the bandwidth utilization are up to 72% and 81%,the computational performance of mixed-precision Sp MV and Gauss-Seidel are improved by 1.6 and 1.45 times,respectively.