Publications related to Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty

MATHICSE Technical Report : An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient

Fabio Nobile, Lorenzo Tamellini, Francesco Tesei

In this work we build on the classical adaptive sparse grid algorithm (T. Gerstner and M. Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version capable of using non-nested collocation points, and supporting quadrature and in ...

MATHICSE2015

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. Moreover, we discuss extensions to non-unif ...

MATHICSE2014

Discrete Stochastic Microfacet Models

Wenzel Alban Jakob

This paper investigates rendering glittery surfaces, ones which exhibit shifting random patterns of glints as the surface or viewer moves. It applies both to dramatically glittery surfaces that contain mirror-like flakes and also to rough surfaces that exh ...

ACM2014

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

A higher-order numerical framework for stochastic simulation of chemical reaction systems

Background: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulatio ...

Biomed Central Ltd2012

Certified reduced basis method for electromagnetic scattering and radar cross section estimation

Jan Sickmann Hesthaven, Yvon Maday

We study nontrivial applications of the reduced basis method (RBM) for electromagnetic applications with an emphasis on scattering and the estimation of radar cross section (RCS). The method and several extensions are explained with two examples with diffe ...

Elsevier2012

Efficient algorithms for computing Sommerfeld integral tails

Juan Ramon Mosig, Ruzica Golubovic

Sommerfeld-integrals (SIs) are ubiquitous in the analysis of problems involving antennas and scatterers embedded in planar multilayered media. It is well known that the oscillating and slowly decaying nature of their integrands makes the numerical evaluati ...

Institute of Electrical and Electronics Engineers2012

Numerical Study Of An Anisotropic Error Estimator In The L-2(H-1) Norm For The Finite Element Discretization Of The Wave Equation

Marco Picasso

An anisotropic a posteriori error estimate is derived for a finite element discretization of the wave equation in two space dimensions. Only the error due to space discretization is considered, and the error estimates are derived in the nonnatural L-2(0, T ...

2010

Hybrid Numerical Solution of the Chemical Master Equation

Maria-Emanuela-Canini Mateescu, Verena Wolf

We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the const ...

2010

Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty

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MATHICSE Technical Report : An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Discrete Stochastic Microfacet Models

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

A higher-order numerical framework for stochastic simulation of chemical reaction systems

Certified reduced basis method for electromagnetic scattering and radar cross section estimation

Efficient algorithms for computing Sommerfeld integral tails

Numerical Study Of An Anisotropic Error Estimator In The L-2(H-1) Norm For The Finite Element Discretization Of The Wave Equation

Hybrid Numerical Solution of the Chemical Master Equation

A higher-order numerical framework for stochastic simulation of chemical reaction systems

Numerical Study Of An Anisotropic Error Estimator In The L-2(H-1) Norm For The Finite Element Discretization Of The Wave Equation

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

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

Certified reduced basis method for electromagnetic scattering and radar cross section estimation

Discrete Stochastic Microfacet Models

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

MATHICSE Technical Report : An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient

Hybrid Numerical Solution of the Chemical Master Equation

Efficient algorithms for computing Sommerfeld integral tails