Numerical homogenization beyond scale separation
Numerical homogenization is a methodology for the computational solution of multiscale
partial differential equations. It aims at reducing complex large-scale problems to simplified …
partial differential equations. It aims at reducing complex large-scale problems to simplified …
Variational multiscale stabilization and the exponential decay of fine-scale correctors
D Peterseim - Building bridges: connections and challenges in …, 2016 - Springer
This paper reviews the variational multiscale stabilization of standard finite element methods
for linear partial differential equations that exhibit multiscale features. The stabilization is of …
for linear partial differential equations that exhibit multiscale features. The stabilization is of …
Eliminating the pollution effect in Helmholtz problems by local subscale correction
D Peterseim - Mathematics of Computation, 2017 - ams.org
We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of
the Helmholtz equation with large wave number $\kappa $ in bounded domains in $\mathbb …
the Helmholtz equation with large wave number $\kappa $ in bounded domains in $\mathbb …
Localized orthogonal decomposition techniques for boundary value problems
P Henning, A Målqvist - SIAM Journal on Scientific Computing, 2014 - SIAM
In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial
differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For …
differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For …
Stable multiscale Petrov–Galerkin finite element method for high frequency acoustic scattering
D Gallistl, D Peterseim - Computer Methods in Applied Mechanics and …, 2015 - Elsevier
We present and analyze a pollution-free Petrov–Galerkin multiscale finite element method
for the Helmholtz problem with large wave number κ as a variant of Peterseim (2014). We …
for the Helmholtz problem with large wave number κ as a variant of Peterseim (2014). We …
Efficient implementation of the localized orthogonal decomposition method
In this paper we present algorithms for an efficient implementation of the Localized
Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical …
Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical …
A high-order approach to elliptic multiscale problems with general unstructured coefficients
R Maier - SIAM Journal on Numerical Analysis, 2021 - SIAM
We propose a multiscale approach for an elliptic multiscale setting with general unstructured
diffusion coefficients that is able to achieve high-order convergence rates with respect to the …
diffusion coefficients that is able to achieve high-order convergence rates with respect to the …
Localized orthogonal decomposition method for the wave equation with a continuum of scales
A Abdulle, P Henning - Mathematics of Computation, 2017 - ams.org
This paper is devoted to numerical approximations for the wave equation with a multiscale
character. Our approach is formulated in the framework of the Localized Orthogonal …
character. Our approach is formulated in the framework of the Localized Orthogonal …
An online generalized multiscale discontinuous Galerkin method (GMsDGM) for flows in heterogeneous media
Offline computation is an essential component in most multiscale model reduction
techniques. However, there are multiscale problems in which offline procedure is insufficient …
techniques. However, there are multiscale problems in which offline procedure is insufficient …
Two-level discretization techniques for ground state computations of Bose-Einstein condensates
This work presents a new methodology for computing ground states of Bose--Einstein
condensates based on finite element discretizations on two different scales of numerical …
condensates based on finite element discretizations on two different scales of numerical …