Research On Parallel Direct Algorithm Of FEM Based On Multi-frontal Method

Due to the advantages in dealing with inhomogeneous media and complex structures,the finite element method(FEM)has always been one of the most powerful tools in electromagnetic computation.With the progress of science technology and growth of demand in engineering,complex structure,multi-media and large electrical size are becoming main features of current electromagnetic targets,and this leading to rapid computational time and memory growth in solving sparse matrix equations generated by FEM.Limited by the computational resources,traditional FEM is difficult to effectively solve those electromagnetic problems,related researchers often make use of domain decomposition methods(DDMs)combined with iterative solver to break through this bottleneck,however,above approach may experience convergence issues and lose efficiency at multiple excitation runs,so stable and reliable direct solvers are still the preferred solvers for FEM.Thus,there is an irreconcilable contradiction between the rapid-growing computational memory demand and the limited computing resources.Therefore,the more effective electromagnetic algorithm and sparse solver rather than advanced computers are the key to solve this problem.The multifrontal method is one of mainstream algorithms for sparse solver.It can avoid storing entire matrix in memory and make use of technique of dense solver,which makes the multifrontal method more efficient,stable,flexible and reliable in solving sparse matrix equations.Under this scenario.Based on the higher-order finite element method(HOFEM),a parallel in-core direct method for solving sparse matrix equations is proposed in this thesis.By dividing the global system matrix equation into several local matrix equations,the memory demand for the computation is significantly reduced.At the same time,to overcome the unbalance problem that commonly used sparse solvers have,the multi-frontal method and the dense matrix direct solving technique are combined into in-core method.However,because of performing two times decomposition,in-core method takes twice as long to complete simulation as commonly used sparse solvers.To improve the in-core method,later a parallel out-of-core direct method is studied in this thesis.The LU factors are stored on the hard disk and can be read from hard disk in the backward process,so two times decomposition can be avoided,and the solution speed of proposed method is similar to that of the conventional sparse solver.The advantage and practicability of proposed method are fully illustrated in the case of the influence of mobile phone antenna on human radiation and the radiation characteristics of wing antenna.All in all,this research makes it possible to use FEM to complete accurate simulation of larger electromagnetic problems with the same computing resources.