Domain Decomposition Parallel Computing And Its Application In Large-scale Structure Analysis

The kernel calculation of large-scale structure finite element analysis often comes down to the solution of sparse symmetric linear equations.With the demand for the development of domestic large aerospace vehicles,engineering structural design is becoming more complex and large-scale,which makes the order of linear equations increase rapidly.Solving these problems has gradually become a bottleneck of engineering numerical calculation.At the same time,with the development of computer technology and the advent of parallel computers,Domain decomposition Method emerge as the times require.Through subdomain division,the problem in original calculation domain is splitting into the parallel solution of coupled problems on distributed-memory machines,which makes the numerical solution of large-scale engineering structure possible.Research on parallel computing technology of structural finite element problems has obvious engineering value and far-reaching theoretical significance for improving the design efficiency and shortening the development period of aircraft structure.However,there are two obstacles in the way of numerical solution of large-scale structure finite element problems.One obstacle is the iterative solution for sparse symmetric linear equations.The increase of the order of equations often leads to the poor properties of coefficient matrix,and the convergence speed of iterative method itself will be very slow.The other is that due to the long solution time and large memory consumption of large-scale structural finite element problems,especially the increasing popularity of parallel computers,it is difficult for traditional serial methods to meet the needs of modern science and engineering analysis for high-performance computing.In the present thesis,based on the conjugate gradient method,it aims to study the preconditioned iterative solution method for sparse symmetric linear equations,and to discuss the fast construction method of incomplete decomposition preconditioner in sparse storage format,so as to improve the iterative efficiency for solving linear equations.Meanwhile,within the MPI cluster parallel computing environment,the finite element tearing and interconnecting method possessing "model level" parallelism and the Preconditioning Conjugate Projected Gradient iterative method for solving the frame equations are studied to improve the parallel computing efficiency of structural finite element problems.Based on conjugate gradient method,the deduction process of preconditioning acceleration mechanism in iterative process is researched to improve the efficiency of iterative solution for sparse symmetric linear equations.Through discussing the existing preconditioning techniques,the filled incomplete factorization preconditioner is researched with a combination strategy: one is the correction of diagonal elements,and the other is the filtering of non-diagonal fill-in according to the level of matrix symbolic factorization.Making use of Open MP technology,the multithread parallel scheme of Cholesky decomposition is proposed for sparse symmetric matrix in CSR storage format.At the same time,in order to further reduce the amount of calculation in the process of matrix level calculation and incomplete decomposition,the Sch?nauer algorithm for reducing matrix profile is introduced and improved,that is,a feasible recurrence formula of vertex cardinality is given basing on the proposed concepts of vertex cardinality and vertex weight.In this way,the sorting of each layer’s vertices in Sch?nauer algorithm is simpler and easier to operate.At last,through the plate bending model,this paper discusses and analyzes the iterative solution process under the preconditioner,and gives suggestions on the selection of the better parameters in the preconditioning.Based on the parallel solution of large-scale structure finite element elastic problems,the finite element tearing and interconnecting method is researched,which is one kind of domain decomposition algorithm and based on Lagrange multiplier.Then,combined with the condensation technique for stiffness matrix,the condensation finite element tearing and interconnecting algorithm is proposed in present research,and its correctness is verified by the plate bending model of two subdomains.The proposed algorithm can effectively reduce the storage space and calculation time in the process of calculating the boundary flexibility matrix of floating subdomains,and the Schur complement matrix generated in the process of condensation is naturally suitable for acting as the Dirichlet preconditioner of each subdomain boundary flexibility matrix.For the solution of frame equations system,the re-orthogonalization Preconditioning Conjugate Projected Gradient(PCPG)iterative method is researched on its deduction procedure and iterative process,and the formulas of iterative initial value and rigid-body mode amplitude are derived in detail.In order to improve the numerical calculation efficiency for domain decomposition with non-matched meshes,the Radial Basis Function(RBF)which performs high numerical accuracy and adaptability is adopted as the data transfer method in present thesis.The local coordinate system is introduced into the non-matched interface,so that the transfer matrix on the partition boundaries with the same interface form(line or surface)but arbitrary cutting directions has a unified format,which avoids the problem of coordinate selection caused by the singularity of interpolation matrix in RBF.Then,taking the plate bending model of4-subdomains with coarse,fine and non-matched mesh sizes as an example,the effectiveness of the algorithm is verified by comparing with the numerical results of ABAQUS.Finally,based on the finite element subroutine library developed by the research group,the parallel computing program for elastic solution of structure finite element is developed using the popular mixed programing mode of Open MP and MPI and Fortran programing language,and the program test is completed on the small cluster parallel development platform built by the existing PC Cluster.In addition,through the parallel solution of the simplified wing plate bending model and the large-scale wing structure,the main factors that affect the calculation efficiency and accuracy of the parallel algorithm are discussed,and numerical result indicates the effectiveness of the algorithm in solving the elastic problems of structure finite element in parallel.