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In this paper, we develop a nodal discontinuous Galerkin method for solving the time-dependent Maxwell's equations when metamaterials are involved. Both semi- and fully-discrete schemes are constructed. Numerical stability and error estimate are proved for ...
We propose a discontinuous Galerkin method for convection-subdiffusion equations with a fractional operator of order alpha [1,2] defined through the fractional Laplacian. The fractional operator of order alpha is expressed as a composite of first order der ...
Society for Industrial and Applied Mathematics2014
In this paper, a new high-order multiscale finite element method is developed for elliptic problems with highly oscillating coefficients. The method is inspired by the multiscale finite element method developed in [3], but a more explicit multiscale finite ...
Society for Industrial and Applied Mathematics2014
We propose two new and enhanced algorithms for greedy sampling of high- dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the devel- opment ...
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 ...
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
We propose a modified parallel-in-time - parareal-multi-level time integration method that, in contrast to previously proposed methods, employs a coarse solver based on a reduced model, built from the information obtained from the fine solver at each itera ...
In this paper, a parareal method is proposed for the parallel-in-time integration of time-fractional differential equations (TFDEs). It is a generalization of the original parareal method, proposed for classic differential equations. To match the global fe ...
This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational e ...
In this paper we develop and study numerically a model to describe some aspects of sound propagation in the human lung, considered as a deformable and viscoelastic porous medium (the parenchyma) with millions of alveoli filled with air. Transmission of sou ...
