Publications related to MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

Isogeometric Analysis of Electrophysiological Models on Surfaces

In this project we numerically simulate electrophysiological models for cardiac applications by means of Isogeometric Analysis. Specifically, we aim at understanding the advantages of using high order continuous NURBS (Non-UniformRational B-Splines) basis ...

2014

Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012

This volume presents selected papers from the ninth International Conference on Spectral and High Order Methods (ICOSAHOM’12) conference that was held at Gammarth, Tunisia, during the week June 25–29, 2012. These selected papers were refereed by members of ...

Springer Verlag2014

Optimal control for power generating kites

Sanket Sanjay Diwale

Numerical solutions for optimal power generation in a pumping power cycle for Airborne Wind Energy is presented. The problem is essentially an infinite horizon optimal control problem which is then attempted to solve by three methods, finite time horizon a ...

2014

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

Comparison between reduced basis and stochastic collocation methods for elliptic problems

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

The stochastic collocation method has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method, primarily developed for solving parametric systems, has been recently used to deal with ...

Springer Verlag2014

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Fabio Nobile, Daniel Kressner, Christine Tobler, Rajesh Kumar

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

MATHICSE2014

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

Fabio Nobile, Annalisa Buffa, Francesca Bonizzoni

We study the mixed formulation of the stochastic Hodge-Laplace problem dened on a

n

-dimensional domain

D (n ≥ 1)

, with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. We ...

2014

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Fabio Nobile

In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assum ...

2014

Two-Level Discretization Techniques For Ground State Computations Of Bose-Einstein Condensates

Patrick Henning

This work presents a new methodology for computing ground states of Bose-Einstein condensates based on finite element discretizations on two different scales of numerical resolution. In a preprocessing step, a low-dimensional (coarse) generalized finite el ...

Society for Industrial and Applied Mathematics2014

MATHICSE Technical Report : Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

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Isogeometric Analysis of Electrophysiological Models on Surfaces

Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012

Optimal control for power generating kites

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

Interface control domain decomposition methods for heterogeneous problems

Comparison between reduced basis and stochastic collocation methods for elliptic problems

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Two-Level Discretization Techniques For Ground State Computations Of Bose-Einstein Condensates

Isogeometric Analysis of Electrophysiological Models on Surfaces

Comparison between reduced basis and stochastic collocation methods for elliptic problems

Optimal control for power generating kites

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

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012

Interface control domain decomposition methods for heterogeneous problems

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

Two-Level Discretization Techniques For Ground State Computations Of Bose-Einstein Condensates