Publications related to High-order collocation methods for differential equations with random inputs

A robust method for inverse transport modelling of atmospheric emissions using blind outlier detection

Martin Vetterli, Benjamin Bejar Haro, Marta Martinez-Camara

Emissions of harmful substances into the atmosphere are a serious environmental concern. In order to understand and predict their effects, it is necessary to estimate the exact quantity and timing of the emissions, from sensor measurements taken at differe ...

2014

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Alfio Quarteroni, Peng Chen

Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...

Elsevier Science Sa2013

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...

Siam Publications2013

A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices

Gianluigi Rozza, Andrea Manzoni, Denis Devaud

We consider a method to efficiently evaluate in a real-time context an output based on the numerical solution of a partial differential equation depending on a large number of parameters. We state a result allowing to improve the computational performance ...

Elsevier2013

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Gilles Brunner

In this project, we study and compare two methods to solve stochastic ordinary differential equations. The first is the Monte Carlo method and the second uses Polynomial Chaos. In the first part, we will solve a stochastic ordinary differential equation by ...

2013

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Alfio Quarteroni, Ricardo Esteban Ruiz Baier, Davide Baroli

In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed di ...

Springer Verlag2013

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Michaël Unser, Emrah Bostan, Ulugbek Kamilov, Masih Nilchian

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes, which specifies cont ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

Assyr Abdulle, Gilles Vilmart

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of It stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are show ...

2013

Estimation of A-type Piano Key weir rating curve

Anton Schleiss, Michael Pfister

The Piano Key weir (PKW) is a hydraulically attractive alternative to linear overflow weirs, increasing the unit discharge for similar heads and spillway widths. This advantage allows operating dam reservoirs on an increased level and provides thereby an e ...

Eds Erpicum et al., CRC Press, Boca Raton2013

High-order collocation methods for differential equations with random inputs

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A robust method for inverse transport modelling of atmospheric emissions using blind outlier detection

Accurate and efficient evaluation of failure probability for partial different equations with random input data

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

Estimation of A-type Piano Key weir rating curve

Accurate and efficient evaluation of failure probability for partial different equations with random input data

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

A combination between the reduced basis method and the ANOVA expansion: On the computation of sensitivity indices

Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

A robust method for inverse transport modelling of atmospheric emissions using blind outlier detection

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Estimation of A-type Piano Key weir rating curve

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity