Publications related to Numerical Integration of SDEs: A Short Tutorial

High order numerical approximation of the invariant measure of ergodic SDEs

We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then pre ...

Society for Industrial and Applied Mathematics2014

Pipelined Numerical Integration on Reduced Accuracy Architectures for Power System Transient Simulations

Maher Kayal, Georgios Lilis, Theodoros Kyriakidis, Guillaume Olivier Lanz

This work concerns a dedicated mixed-signal power system dynamic simulator. The equations that describe the behavior of a power system can be decoupled in a large linear system that is handled by the analog part of the hardware, and a set of differential e ...

IEEE2014

Isogeometric Analysis of Electrophysiological Models on Surfaces

Alessandro Samuele Patelli

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

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Assyr Abdulle, Gilles Vilmart

A fully discrete analysis of the finite element heterogeneous multiscale method for a class of nonlinear elliptic homogenization problems of nonmonotone type is proposed. In contrast to previous results obtained for such problems in dimension

d\leq2

for ...

Amer Mathematical Soc2014

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

Antoine Giovanni Imboden

In this report, we first introduce operator splitting as a way to solve nonlinear reaction-diffusion PDEs. We then present a flux-limiting technique for anisotropic diffusion problems that allows to recover the discrete maximum principle. Finally, we imple ...

2014

Stable multi-domain spectral penalty methods for fractional partial differential equations

Jan Sickmann Hesthaven

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any ord ...

Elsevier2014

Solving the infinite-horizon constrained LQR problem using splitting techniques

Colin Neil Jones, Milan Korda, Georgios Stathopoulos

This paper presents a method to solve the constrained infinite-time linear quadratic regulator (LQR) problem. We use an operator splitting technique, namely the alternating minimization algorithm (AMA), to split the problem into an unconstrained LQR proble ...

2014

Solving the infinite-horizon constrained LQR problem using splitting techniques

Colin Neil Jones, Milan Korda, Georgios Stathopoulos

This paper presents a method to solve the constrained infinite-time linear quadratic regulator (LQR) problem. We use an operator splitting technique, namely the alternating minimization algorithm (AMA), to split the problem into an unconstrained LQR proble ...

Elsevier2014

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

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

Numerical Integration of SDEs: A Short Tutorial

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High order numerical approximation of the invariant measure of ergodic SDEs

Pipelined Numerical Integration on Reduced Accuracy Architectures for Power System Transient Simulations

Isogeometric Analysis of Electrophysiological Models on Surfaces

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

Stable multi-domain spectral penalty methods for fractional partial differential equations

Solving the infinite-horizon constrained LQR problem using splitting techniques

Solving the infinite-horizon constrained LQR problem using splitting techniques

BPX-preconditioning for isogeometric analysis

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

High order numerical approximation of the invariant measure of ergodic SDEs

Isogeometric Analysis of Electrophysiological Models on Surfaces

Stable multi-domain spectral penalty methods for fractional partial differential equations

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

BPX-preconditioning for isogeometric analysis

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Pipelined Numerical Integration on Reduced Accuracy Architectures for Power System Transient Simulations

Solving the infinite-horizon constrained LQR problem using splitting techniques

Solving the infinite-horizon constrained LQR problem using splitting techniques

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions