Publications related to Stochastic partial differential equation

MATHICSE Technical Report : Low-rank updates and a divideand- conquer method for linear matrix equations

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

MATHICSE2017

Generalization of the Concept of Extents to Distributed Reaction Systems

Dominique Bonvin, Julien Léo Billeter, Diogo Filipe Mateus Rodrigues

In the chemical industry, a large class of processes involving reactions can be described by partial differential equations that depend on time and on one or more spatial coordinates. Examples of such distributed reaction systems are tubular reactors and r ...

Elsevier2017

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

MATHICSE2017

Numerical methods for random and stochastic partial differential equations

Fabio Nobile

Mathematical models involving partial differential equations (PDE) arise in numerous applications ranging from Natural Sciences and Engineering to Economics. Random and stochastic PDE models become very powerful (and sometimes unavoidable) extensions of de ...

2016

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

Alfio Quarteroni, Andrea Manzoni, Federico Negri

The numerical solution of partial differential equations (PDEs) depending on para- metrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this compu ...

MATHICSE2016

A posteriori error estimation for partial differential equations with random input data

Diane Sylvie Guignard

This thesis is devoted to the derivation of error estimates for partial differential equations with random input data, with a focus on a posteriori error estimates which are the basis for adaptive strategies. Such procedures aim at obtaining an approximati ...

EPFL2016

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Fabio Nobile, Lorenzo Tamellini

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...

2016

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

Giovanni Dietler, Andrzej Kulik, Fabrizio Benedetti, Dmitry Klinov

We performed dynamic force spectroscopy of single dextran and titin 127 molecules using small-amplitude and low-frequency (40-240 Hz) dithering of an atomic force microscope tip excited by a sine wave voltage fed onto the tip-carrying piezo. We show that f ...

Elsevier2016

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Alfio Quarteroni, Simone Deparis, Davide Forti

We are interested in the approximation of partial differential equations on domains decomposed into two (or several) subdomains featuring non-conforming interfaces. The non-conformity may be due to different meshes and/or different polynomial degrees used ...

Elsevier2016

Stochastic partial differential equation

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MATHICSE Technical Report : Low-rank updates and a divideand- conquer method for linear matrix equations

Generalization of the Concept of Extents to Distributed Reaction Systems

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Numerical methods for random and stochastic partial differential equations

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

A posteriori error estimation for partial differential equations with random input data

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Numerical methods for random and stochastic partial differential equations

MATHICSE Technical Report : Low-rank updates and a divideand- conquer method for linear matrix equations

Generalization of the Concept of Extents to Distributed Reaction Systems

A posteriori error estimation for partial differential equations with random input data

Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

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

INTERNODES: an accurate interpolation-based method for coupling the Galerkin solutions of PDEs on subdomains featuring non-conforming interfaces

Can Dissipative Properties of Single Molecules Be Extracted from a Force Spectroscopy Experiment?