The combined approximations (CA) method is an effective reanalysis approach providing high quality results. The CA method is suitable for a wide range of structural optimization problems including linear reanalysis, nonlinear reanalysis and eigenvalue reanalysis. However, with increasing complexity and scale of engineering problems, the efficiency of the CA method might not be guaranteed. A major bottleneck of the CA is how to obtain reduced basis vectors efficiently. Therefore, a modified CA method, based on approximation of the inverse matrix, is suggested. Based on the symmetric successive over-relaxation (SSOR) and compressed sparse row (CSR), the efficiency of CA method is shown to be much improved and corresponding storage space markedly reduced. In order to further improve the efficiency, the suggested strategy is implemented on a graphic processing unit (GPU) platform. To verify the performance of the suggested method, several case studies are undertaken. Compared with the popular serial CA method, the results demonstrate that the suggested GPU-based CA method is an order of magnitude faster for the same level of accuracy.

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