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Spectral methods for multiscale stochastic differential equations

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Spectral Methods for Hyperbolic Problems

Jan Sickmann Hesthaven

We review spectral methods for the solution of hyperbolic problems. To keep the discussion concise, we focus on Fourier spectral methods and address key issues of accuracy, stability, and convergence of the numerical approximations. Polynomial methods are ...

Elsevier Publishing2016

MATHICSE Technical Report : Analysis of the internodes method for non-conforming discretizations of elliptic equations

Alfio Quarteroni

INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transfering the Diri ...

MATHICSE2016

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In this paper, we study a single-sensor imaging system that uses a multispectral filter array to spectrally sample the scene. Our system captures information in both visible and near-infrared bands of the electromagnetic spectrum. Due to manufacturing limi ...

2016

In this work we apply the discontinuous Galekin (dG) spectral element method on meshes made of simplicial elements for the approximation of the elastodynamics equation. Our approach combines the high accuracy of spectral methods, the geometrical flexibilit ...

Springer Verlag2016

Higher order and spectral methods have been used with success for elliptic and parabolic initial and boundary value problems with smooth solutions. On the other hand, higher order methods have been applied to hyperbolic problems with less success, as highe ...

Society for Industrial and Applied Mathematics2015

Many applied problems, like transport processes in porous media or ferromagnetism in composite materials, can be modeled by partial differential equations (PDEs) with heterogeneous coefficients that rapidly vary at small scales. To capture the effective be ...

EPFL2015

In this work we present a simple method to reconstruct the complex spectral wave function of a biphoton, and hence gain complete information about the spectral and temporal properties of a photon pair. The technique, which relies on quantum interference, i ...

Amer Physical Soc2015

Singular spectrum analysis is a natural generalization of principal component methods for time series data. In this paper we propose an imputation method to be used with singular spectrum-based techniques which is based on a weighted combination of the for ...

Elsevier2013

A multilevel Monte Carlo (MLMC) method for mean square stable stochastic differential equations with multiple scales is proposed. For such problems, that we call stiff, the performance of MLMC methods based on classical explicit methods deteriorates becaus ...

Academic Press Inc Elsevier Science2013

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...

2012