A modified PODI-RBF method to improve the accuracy of local solutions for real-time finite element simulations of indenter contact problems

In this paper, a novel method is proposed to improve the accuracy of local solutions of the PODI-RBF method for real-time finite element (FE) simulations of indenter contact problems. In the offline stage, proper orthogonal decomposition (POD) basis vectors and coefficients are extracted from solution snapshots collected from full-order FE simulations of indenter contact problems with training contact locations and indentation depths. In the online stage, RBF interpolation is used to estimate POD basis vectors and coefficients for a new contact loading. Although the POD with interpolation (PODI) method using RBFs is very useful for obtaining FE solutions of indenter contact problems in real time, local solutions near a new contact location are less accurate when a new contact location is not close to the training contact locations. To improve the accuracy of local solutions near a new contact location, the first POD basis vector is replaced by the shifted first POD basis vector for the closest training contact location to the new contact location. Numerical results show that the modified PODI-RBF method is efficient and effective to achieve real-time FE simulations of indenter contact problems while improving the accuracy of local solutions near contact locations.