Benjamin Belfort

Addressing factors fixing setting from given data

This paper deals with global sensitivity analysis of computer model output. Given an independent input sample and associated model output vector with possibly the vector of output derivatives with respect to the input variables, we show that it is possible to evaluate the following global sensitivity measures: (i) the Sobol indices, (ii) the Borgonovos density-based sensitivity measure, and (iii) the derivative-based global sensitivity measure of Sobol and Kucherenko. We compare the efficiency of the different methods to address factors fixing setting, an important issue in global sensitivity analysis. First, global sensitivity analysis of the Ishigami function is performed with the different methods. Then, they are applied to two different responses of a soil drainage model. The results show that the polynomial chaos expansion for estimating Sobol indices is the most efficient approach. We compare several methods for global sensitivity analysis of model output.All the methods only require one single sample with input variables independently distributed.We study their efficiency to address factors fixing setting.The different methods are tested on the Ishigami function and a soil drainage model.Sobol indices via sparse PCE are found to be the most efficient approach.

A New Mass Lumping Scheme for the Mixed Hybrid Finite Element Method: Application to unsaturated water flow modelling

Abstract: Groundwater flow modelling is of interest in many sciences and engineering applications for scientific understanding and/or technological management. Accurate numerical simulation of infiltration in the vadose zone remains a challenge, especially when very sharp fronts are present. This study is focused principally on an alternatively numerical approaches referred to in the literature as the mixed hybrid finite element (MHFE) method. MHFE schemes simultaneously approximate both the pressure head and its gradient. For some problems of unsaturated water flow, the MHFE solutions contain oscillations. Various authors ( see [1]) suggest the use of a mass lumping procedure to avoid this unphysical phenomenon. An analyse of the resulting matrix system shows that the recommended technique differs from the standard mass-lumping well-established for Galerkin finite element methods. A “new” effective mass-lumping scheme adapted from [2] has been specially developed for the MHFE method. Its ability for eliminating oscillations have been tested in unsaturated conditions. Various test cases in a 2D domain, for homogeneous and heterogeneous dry porous media and subject to different boundary conditions are presented. References: [1] Farthing, M. W., C. E. Kees, and C. T. Miller. 2003. Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow. Adv. Water Resour. 26:373-394. [2] Younes A., Ackerer P. and Lehmann F., 2005.A new mass lumping scheme for the mixed hybrid finite element method, Int. J. Numer. Meth. Engng. (submitted).