Research On Acceleration Of Direct Current Forward Modelling And Magnetotelluric Inversion Based On GPU

Electrical prospecting as an important branch of geophysics plays an important role in scientific research and actual production.With the growth of production needs and the development of computing technology,it is necessary to develop high-precision,high complexity and rapid numerical simulation.In addition to developing new algo-rithms,parallel computing as an important means for accelerating numerical calculation is widely used in simulation research in various subjects.The traditional parallel com-puting,also namely CPU parallel,assigns the computing task to different CPU core,and uses the MPI and OpenMP as a way of communication,together to complete the calculation task.The burgeoning heterogeneous parallel computing,also namely GPU parallel,is gain popularity by researchers in recent years.GPU has large Input/Output bandwidth than CPU on the hardware,and it divides the computing resources into differ-ent levels.GPU has the characteristics of cost-effective,powerful computing resources and simple programming mode,and it's suitable to the problem which has high con-currency.This paper focuses on the application of GPU to the numerical simulation of electrical exploration,including three-dimensional direct current forward modelling and two-dimensional magnetotelluric inversion.In three-dimensional direct current forward modelling,the governing equations are transformed into the corresponding variational problem and solved by finite element method.After the process of regional discretization,element analysis,matrix assembly and boundary condition addition,finally the variational problem is equivalent to solving large scale sparse linear equations.Solving the equations is the most time-consuming step in forward modelling,and many researchers have studied how to accelerate solv-ing equations based on GPU,including parallel preconditioning matrices on the GPU,efficient storage matrices,accelerating the matrix and vector product,using different levels of memory to release read and write delays and so on.Over years of research and optimization,NVIDIA corporation has provided cuBALS,cuSPARSE and other functional libraries which have been made the corresponding optimization,and these libraries include almost all of the above research.At present,there are few researches on multi-GPU clusters because of the problem of how to parallel preconditioning matrix and efficient communication between multi-GPU clusters.In this paper,the SSORAI preconditioning by directly approximating the SSOR preconditioning matrix has been obtained based on the traditional SSOR precondition-ing,and the two-time triangular matrix backtracking solution with inherent serialization is substituted by matrix and vector product with high parallelism on GPU.What' s more,GPU using the latest GPU cluster communication means can communicate across the nodes directly combined with the CUDA-Aware MPI,which improves the efficiency of GPU communication.Furthermore,the procedure is optimized with RCM bandwidth reduction algorithm to reduce the original matrix's bandwidth,which makes the GPU computing and communications overlap each other,to achieve the purpose of improving the communication efficiency.Our researches have successfully solved these problems through the above methods,and the ideal speedup and scalability on the GPU cluster has bee obtained.In the magnetotelluric inversion,the parallel computing has been used in MT for-ward modelling to indirect acceleration inversion.However using GPU to implement the MT inversion has not been reported until now.In this part,the GPU is applied to the two-dimensional magnetotelluric inversion.Through analyzing the inversion pro-cess,the inversion can be attributed to four parts:forward modelling,Jacobian matrix solution,matrix vector operation and dense linear equations solution.We distribute MT frequency points to GPU SM and use this way to implement coarse-grained MPI par-allelism.On each SM,SM generates many threads to work together to complete the calculation of various parts,and use this way to simulate fine-grained OpenMP paral-lelism.The coarse-grained and fine-grained methods are used to transplant the program to the GPU.The 2D MT inversion based on GPU achieved a good speedup,and the fac-tors influencing the acceleration ratio have been discussed.In this paper,the forward modelling and inversion are based on GPU and GPU clusters used in electric method lay the foundation for further application of GPU in electrical prospecting.