The Research Of Fast Computation Methods Based On KPOD Reduced-order Model With Isogeometric Analysis

In order to achieve high-performance computing with both accuracy and efficiency,a new fast calculation method called KPOD method is proposed.The proposed method introduces the Reduced-Order Model(ROM)based on the Proper Orthogonal Decomposition(POD)into the dynamic problem for efficiency improvement and combines with the Krylov subspace method to achieve extrapolation.Meanwhile,Isogeometric Analysis(IGA)is introduced for exact expression of computational domain,which could improve the precision of calculation.Moreover,IGA could realize the combination of CAD model and CAE model,avoiding the time-consuming meshing process.Especially in the ROM of the variable size problem,IGA can maintain the same degree of freedom,and the pre-processing is omitted.The main research contents of this thesis are as follows:First,the theories of IGA are elaborated,including spline construction,mapping relationship form parameter space to physical space,mesh refinement method,and model splice method.Besides,IGA is applied to the spatial discretization of linear elasticity problems.Eventually,compared with FEM,the effectiveness,reliability,and advantages in accuracy of the IGA are proved by numerical instance.Second,in order to overcome the difficult of applying POD-based ROM on extrapolation problem,Krylov subspace method and POD are combined to achieve an extrapolation algorithm KPOD,which realize the reduced-order computation of dynamic problem.Meanwhile,the proposed KPOD not only realize effective extrapolation,but also improve the accuracy of interpolation.Besides,through computational cases,the accuracy and efficiency of the proposed KPOD are proved.More specifically,the efficiency is increased by more than 20 times with 100,000 Degrees of Freedom(DOF)while the error is around 1%.Moreover,some important parameters and settings that affect the efficiency and accuracy of the proposed method are discussed.And the effect of ROM will rise,as the scale of the problem increases.Third,a KPOD-based ROM of nonlinear problems is established.First,the tangent matrix iterative method is introduced to solve the nonlinear equations.For the steadystate nonlinear heat transfer problem,the feasibility and accuracy of the tangent matrix iterative method are verified,compared with the results of commercial software.In transient nonlinear heat transfer problem,the KPOD extrapolation algorithm is introduced to construct a ROM.And the nonlinear equations are solved in the reducedorder subspace,which reduces the amount of calculation to a certain extent and decreases time cost of the matrix assemble by speeding up convergence.In addition,the main limitation of the ROM applied to nonlinear problems is analyzed,that is,the matrix needs to be reassembled for each iteration.But the ROM cannot improve the efficiency of matrix assembly.Therefore,the effect of ROM is reduced in large-scale problems,where matrix assembly occupies a large part of the calculation.Finally,numerical examples are used to verify the accuracy and efficiency of the KPOD extrapolation algorithm in nonlinear problems.