A fast meshless method based on proper orthogonal decomposition for the transient heat conduction problems

In order to improve computational efficiency of meshless methods based on Galerkin weak form, a fast and efficient method based on the proper orthogonal decomposition (POD) technique for transient heat conduction problems is proposed in the paper. At the first stage of the proposed method numerical simulation results or experiment data are collected as snapshots, then singular value decomposition (SVD) is applied to obtain the optimal POD basis, subsequently POD in conjunction with meshless method is used to generate the reduced model. The efficient and accuracy of the provided algorithm are examined by three examples, and the numerical examples illustrate that the meshless methods coupled with POD technique not only keeps computational accuracy, but also brings significant computational time saving for solving transient heat conduction problems.