基于本征正交分解加速的二维位势问题边界元法分析

基于本征正交分解(POD)的思想,采用奇异值分解法(SVD),将物理问题的求解空间分解为几何子空间和设计子空间,通过线性组合几何与设计子空间获得随机变量响应结果.与传统加速算法不同,采用径向基函数(RBF)近似设计子空间响应,实现了系统信息的压缩表达,有效降低了计算成本.采用边界元法(BEM)求解二维位势问题,并结合S...

Boundary Element Method Analysis of Two-dimensional Potential Problem Based on Proper Orthogonal Decomposition Acceleration

Based on the idea of Proper Orthogonal Decomposition(POD), Singular Value Decomposition(SVD) is used to decompose the solution space of physical problems into geometric subspace and design subspace, and random variable response results are obtained by linearly combining geometry and design subspace. Different from the traditional acceleration algorithm, the radial basis function(RBF) is adopted to approximate the design of the subspace response, the compressed expression of system information is realized, and the cost of calculation is reduced effectively. The boundary element method(BEM) is used for numerical analysis of two-dimensional potential problems, and the combination of SVD and RBF methods accelerates the rapid response analysis of BEM-based potential problems. Finally, a circular structure example is used to test the correctness and effectiveness of the algorithm developed.