Probabilistic collocation method for strongly nonlinear problems: 2. Transform by displacement

The probabilistic collocation method (PCM) is widely used for uncertainty quantification and sensitivity analysis. In paper 1 of this series, we demonstrated that the PCM may provide inaccurate results when the relation between the random input parameter and the model response is strongly nonlinear, and presented a location-based transformed PCM (xTPCM) to address this issue, relying on the transform between response and location. However, the xTPCM is only applicable for one-dimensional problems, and two or three-dimensional problems in homogeneous media. In this paper, we propose a displacement-based transformed PCM (dTPCM), which is valid in two or three-dimensional problems in heterogeneous media. In the PCM, we first select collocation points and run model/simulator to obtain response, and then approximate the response by polynomial construction. Whereas, in the dTPCM, we apply motion analysis to transform the response to displacement. That is, the response field is now represented by the displacement field. Next, we approximate the displacement instead of the response by polynomial, since the displacement is more linear to the input parameter than the response. Finally, we randomly generate a sufficient number of displacement samples and transform them back to obtain response samples to estimate statistical properties. Through multiphase flow and solute transport examples, we demonstrate that the dTPCM provides much more accurate statistics than does the PCM, and requires considerably less computer time than does the Monte Carlo (MC) method.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000346654600020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Environmental SciencesLimnologyWater ResourcesSCI(E)EI3ARTICLEdxz@pku.edu.cn118736-87595