Application Of Algebraic Multiple Grid Method In MTSS

With the increasing complexity of microwave device design,traditional design methods can not meet the design needs.Using electromagnetic simulation software for simulation design instead of the preliminary experiment can reduce design costs and improve design efficiency.In electromagnetic simulation software MTSS,sparse linear equations need to be solved during the electromagnetic simulation of complex models,and the solution time will account for about 80% of the total simulation time.Therefore,accelerating the solving efficiency of sparse linear equations can greatly improve the design efficiency of electromagnetic simulation software.In this paper,for sparse linear equations generated by MTSS,the storage and operation of the sparse matrix are first implemented.Then,based on the above algorithms,the AMG-CG algorithm is implemented to solve sparse linear equations quickly.Compared with the original Jacobi conjugate gradient(JPCG)algorithm of MTSS,the speed of solving large sparse linear equations is about 5 times faster,and the convergence is very good.But memory consumption is also twice as high as that of JPCG.For the storage operation of a sparse matrix,four compression storage methods including the ternary method,cross-linked list method,row compression(CSR)method,and column compression method are studied.Because The Times of matrix by matrix and matrix by the vector in MTSS are very frequent,the CSR method is chosen as the storage method.Then,all kinds of operations based on CSR storage are implemented: sparse matrix storage,matrix transpose,matrix addition and subtraction,matrix by matrix,matrix by a vector,matrix trigonometric decomposition,etc.,laying a foundation for the rapid solution of sparse linear equations.Jacobi iteration,Gauss-Seidel iteration,SOR iteration,conjugate gradient(CG)algorithm,and algebraic multiple grid(AMG)algorithm are studied for solving sparse linear equations.The difficulties in the AMG algorithm are solved: when to stop coarsening,how to minimize the number of strong influence points,how to quickly generate coarse mesh matrix,and how to implement different multiple mesh schemes.By combining AMG and CG,the conjugate gradient method(AMG-CG)with algebraic multigrid as preprocessor is realized,which solves the problem of poor convergence in solving ill-conditioned equations.Then the AMG-CG algorithm is compiled with C++,and the function and flow of the program are explained by a class diagram and flow chart.The usability of the AMGCG algorithm program in MTSS is verified by calculating an example of the electron gun.The key points of the AMG-CG algorithm are verified: multi-grid cycle mode,K cycle parameter t value,smooth iteration times,and the effect of the coarsest layer grid solution algorithm on solving efficiency.Compared with the solving speed and convergence of the AMG-CG algorithm,CG algorithm,JPCG algorithm,and Gauss-Seidel iteration,the solving speed of the AMG-CG algorithm is more than 5 times that of other algorithms when solving large sparse linear equations,which is verifies the superiority of AMG-CG algorithm.Then,the peak memory of the AMG-CG algorithm is compared with that of the JPCG algorithm,and it is verified that the AMG-CG algorithm sacrifices memory to improve the solving speed.