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Localized Orthogonal Decomposition Techniques for Boundary Value Problems
TLDR
In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. Expand
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Oversampling for the Multiscale Finite Element Method
TLDR
This paper reviews standard oversampling strategies as performed in the multiscale finite element method (MsFEM). Expand
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Sobolev Gradient Flow for the Gross-Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency
TLDR
We propose a new normalized Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem based on an energy inner product that depends on time through the density of the flow itself. Expand
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Localized orthogonal decomposition method for the wave equation with a continuum of scales
TLDR
We propose and analyze a new multiscale method for the wave equation in a heterogeneous medium with multiple highly varying length-scales. Expand
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Numerical Homogenization of H(curl)-Problems
TLDR
If an elliptic differential operator associated with an ${ H}({curl})$-problem involves rough (rapidly varying) coefficients, then solutions to the corresponding ${H}({Curl}) $-problem admit typicall... Expand
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Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials
This paper analyzes the numerical solution of a class of nonlinear Schrodinger equations by Galerkin finite elements in space and a mass and energy conserving variant of the Crank–Nicolson method dueExpand
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A localized orthogonal decomposition method for semi-linear elliptic problems
In this paper we propose and analyze a localized orthogonal decomposition (LOD) method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. ThisExpand
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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 simulation of partialExpand
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Two-Level Discretization Techniques for Ground State Computations of Bose-Einstein Condensates
TLDR
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 resolution. Expand
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Multiscale Partition of Unity
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatzExpand
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