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

Phase Retrieval by Using Transport-of-Intensity Equation and Differential Interference Contrast Microscopy

Michaël Unser, Daniel Sage, Benjamin Rappaz, Emrah Bostan, Emmanuel Augustin Julien Froustey

We present a variational reconstruction algorithm for the phase-retrieval problem by using the differential interference contrast microscopy. Principally, we rely on the transport-of-intensity equation that specifies the sought phase as the solution of a p ...

IEEE2014

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Fabio Nobile, Lorenzo Tamellini

In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number

N

of random inputs and an analytic dependence of the s ...

2014

Interface control domain decomposition methods for heterogeneous problems

Alfio Quarteroni, Marco Discacciati

This paper is concerned with the solution of heterogeneous problems by the interface control domain decomposition (ICDD) method, a strategy introduced for the solution of partial differential equations in computational domains partitioned into subdomains t ...

Wiley-Blackwell2014

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

Meiyue Shao

Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approxi ...

Siam Publications2014

Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid-structure interaction coupling problems

Gianluigi Rozza, Davide Forti

We present some recent advances and improvements in shape parametrisation techniques of interfaces for reduced-order modelling with special attention to fluid-structure interaction problems and the management of structural deformations, namely, to represen ...

Taylor & Francis2014

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

BPX-preconditioning for isogeometric analysis

Annalisa Buffa

We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or NURBS mapping which we assume to be regular. The numerical solution of the PDE is computed by ...

2013

Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems

Yun Bai

The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite elemen ...

EPFL2013

Optimal control for Partial Differential Equations

Antoine Giovanni Imboden

In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control pr ...

2013

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

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Phase Retrieval by Using Transport-of-Intensity Equation and Differential Interference Contrast Microscopy

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Interface control domain decomposition methods for heterogeneous problems

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid-structure interaction coupling problems

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

BPX-preconditioning for isogeometric analysis

Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems

Optimal control for Partial Differential Equations

Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems

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

Interface control domain decomposition methods for heterogeneous problems

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

BPX-preconditioning for isogeometric analysis

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Efficient geometrical parametrisation techniques of interfaces for reduced-order modelling: application to fluid-structure interaction coupling problems

Phase Retrieval by Using Transport-of-Intensity Equation and Differential Interference Contrast Microscopy

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

Optimal control for Partial Differential Equations