Abstract: In this talk, we mainly introduce model reduction methods for stochastic partial differential equations to improve the efficiency of numerical simulation. we propose a novel variable-separation (NVS) method. We firstly introduce the NVS method for generic multivariate functions, which can be used to get the separated representation of model’s input. The idea of the novel VS is extended to obtain the solution in tensor product structure for stochastic partial differential equations (SPDEs). In order to effectively simulate stochastic saddle point problems, we consider the VS method to solve the stochastic saddle point (SSP) problems. Then, we present the NVS method for nonlinear PDEs with random inputs. Finally, nonlinear model reduction methods are considered for the transport-dominated problems.
Tencent Meeting Number : 702-6472-0755