Research On Subspace Methods For Sequences Of Linear Systems

In response to the needs of the development of science and technology,the rapid and efficient solution of large-scale continuous linear equations has become an important topic in scientific computing.For example,the solution of large-scale continuous linear systems is involved in the fields of quantum chromodynamics,radiation hydrodynamics,finite element analysis to simulate the fatigue and fracture process of electronic components,multi-dimensional elliptic partial differential equation calculation,and electromagnetic scattering calculation.At present,gcro-dr algorithm is a mature and stable subspace method to solve such problems.Thesis deeply studies a cyclic Krylov subspace method for solving such equations,optimizes and improves the algorithm from two aspects: the construction of subspace basis and the design of restart parameters,and puts forward three kinds of algorithms.Firstly,for the purpose of reducing the computational cost,a simpler variant of GCRODR is firstly proposed,which takes less computational cost within one cycle than GCRODR.Secondly,an adaptive strategy for setting restart parameters is introduced in order to overcome the non-stability problem and out-of-memory problem of the proposed simpler GGRO-DR method,as well as to improve its convergence.At the same time,in both circumstances that many restart numbers are required by such method for solving large linear systems given in sequence,and neighbouring coefficient matrices share relevant spectral information,a better restart parameter is determined by reinforcement learning based on the learning samples provided by the adaptive strategy for setting restart parameters.Finally,the effectiveness of the proposed three types of algorithms is proved by numerical experiments from the point of view of solving a single linear system and solving a series of linear systems.