Parallel Analysis And Software Implementation Of Transient Response Based On Multi-level Substructure Algorithm

In view of the increasingly complex engineering structure,the increasing scale of numerical analysis,and the increasingly diversified types of analysis of complex engineering finite element analysis problems,the previous single computing node single threaded finite element analysis has been unable to meet the needs of practical engineering applications.Therefore,the research of large-scale parallel finite element analysis algorithm and software has become a key problem to solve the bottleneck of numerical calculation.The multi-level substructure algorithm decomposes the whole structure into multi-layer substructures.Different substructures can be computed independently.The information transmission between the upper and lower levels can be reduced by condensing the internal degrees of freedom to the exit degrees of freedom.The substructure rotation,mirror image and translation can avoid the repeated calculation of substructures with the same structure.The characteristics of these multi-level substructure methods are exactly in line with the optimal parallel strategy in parallel computing,which divides and conquers,reduces the traffic of each computing node and reduces the computational load.Therefore,based on the above ideas,aiming at the distributed system in the supercomputing environment,this paper constructs a hybrid parallel finite element computing framework of MPI and OpenMP for distributed parallel computation of multi-level and multi-level substructures and shared memory of sub-structure finite element process.The implementation of the parallel computing strategy is based on the SiPESC open structure finite element analysis system and utilizes the abundant finite element analysis functions of the SiPESC platform.The direct method parallel solver is used to ensure the parallel accuracy of the multi-level sub-structure algorithm.Through the deployment of over-computing environment,the solution of finite element model with tens of millions of degrees of freedom and the call of 100-core computing resources are realized,and the accuracy of the solution is consistent with that of commercial software.Based on the hybrid parallel finite element computation framework of multi-level substructures,for the transient response analysis of finite element,the system motion changes with time need to be obtained by recursive iteration of the initial state of the system.On the basis of discretization of time,the equivalent static equilibrium equation at each time point is satisfied,and the system state at the next time point is obtained by solving the equation.Because the solving steps of the equivalent static equilibrium equation are the same as those of the multi-level substructure static problem,and the multi-time-step equivalent static equilibrium equation does not need to be recalculated,thus avoiding the most time-consuming calculation process in the multi-level substructure,the parallel frame of the multi-level substructure is more efficient than the static problem.Based on the above advantages,this paper develops a multi-level and multi-level sub-structure transient parallel software framework based on the multi-level and multi-level sub-structure parallel framework.The framework takes advantage of the parallel characteristics of multi-level and multi-level substructure framework,and carries out coarse-grained parallelism on the equivalent stiffness matrix and the equivalent external force load,etc.The effectiveness of the framework is proved by numerical examples.In addition,aiming at some technical difficulties in parallel software development,this paper proposes corresponding solutions.In order to solve the problem of load balancing in parallel finite element computation,the node and element of finite element model are mapped to vertex of graph by introducing hypergraph structure,and the topological relationship is mapped to edge.The corresponding relationship between degree of freedom and mesh and the constraints of finite element model are accurately described,and a more balanced substructure model of degree of freedom is obtained.Aiming at the problems of memory leak and low parallel efficiency when assembling general stiffness matrix,it is found that on the one hand,too many memory fragments are generated when applying for binary tree at the same time,so that memory can not be recovered.On the other hand,in order to use ordinary binary tree to process substructure matrix,it is easy to insert data unilaterally to form worst-case binary tree.In this paper,memory pool and interval binary tree are used to solve this problem.Interval binary tree is developed based on ordinary binary tree.By changing the key value pairing stored by binary tree nodes into interval key value pairing,the height of binary tree is reduced,the memory fragments are reduced and memory leaks are avoided.On the basis of the interval binary tree,a two-stage distributed parallel assembly outline for multiple and multi-level substructures is further developed.The two-step assembly is carried out on the bottom substructure and the top substructure,respectively,in order to achieve the purpose of parallel assembly stiffness matrix and further improve the parallel efficiency.