On the use of stochastic spectral methods in deep excavation inverse problems

The back analysis or inverse analysis of the field instrumentation data is a common technique to ascertain the design parameter validity in deep excavation projects. That analysis is a process full of uncertainties and relies greatly on the expert judgement. Furthermore, deep excavation geotechnical models tend to be computationally very expensive making the inverse analysis a very lengthy process. In this paper, a Bayesian-type methodology to solve inverse problems which relies on the reduction of the numerical cost of the forward simulation through stochastic spectral surrogate models is presented. The proposed methodology is validated with three calibration examples.Canavate-Grimal, A.; Falcó, A.; Calderón García, PA.; Paya-Zaforteza, I. (2015). On the use of stochastic spectral methods in deep excavation inverse problems. Computers and Structures. 159:41-60. doi:10.1016/j.compstruc.2015.06.009S416015

A Multiscale Pressure Splitting of the Shallow-Water Equations: I. Formulation and 1D Tests

Direct representation of the free surface in ocean circulation models leads to a number of computational difficulties that are due to the fast time scales associated with free-surface waves. These fast time scales generally result in severe time-step restrictions when the free surface is advanced using an explicit scheme and may result in large phase errors when the free surface is treated implicitly with a large time step. A multiple-scale analysis of the shallow-water equations is used to analyze this stiffness and to guide the construction of a computational methodology that overcomes the associated difficulties. Specifically, we explore a class of fractional step methods that utilize coarsened grids in the propagation of long-wave data. The behavior of the corresponding schemes is examined in detail in light of one-dimensional model problems, based on finite-difference or spectral-element discretizations