Related papers: Compressed Wannier modes found from an $L_1$ regul…
Wannier functions have become a powerful tool in the electronic structure calculations of extended systems. The generalized Pipek-Mezey Wannier functions exhibit appealing characteristics (e.g., reaching an optimal localization and the…
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit…
In a recent paper [Phys. Rev. Lett. \textbf{93}, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function $\psi$ to be a functional of…
The L1 norm has been tremendously popular in signal and image processing in the past two decades due to its sparsity-promoting properties. More recently, its generalization to non-Euclidean domains has been found useful in shape analysis…
Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…
We present a spin-dependent extension of the non-orthogonal generalized Wannier function (NGWF) formalism within the framework of linear-scaling density functional theory (LS-DFT) as implemented in the ONETEP code. In traditional LS-DFT…
We consider the numerical computation of a variational problem that arises from materials science. The target functional is a type of elastic energy that is influenced by obstacles and adhesion. Owing to its strong nonlinearity and…
The electronic ground state of a periodic crystalline solid is usually described in terms of extended Bloch orbitals; localized Wannier functions can alternatively be used. These two representations are connected by families of unitary…
We consider a randomization of a function on $\mathbb R^d$ that is naturally associated to the Wiener decomposition and, intrinsically, to the modulation spaces. Such randomized functions enjoy better integrability, thus allowing us to…
The paper introduces a general strategy for identifying strong local minimizers of variational functionals. It is based on the idea that any variation of the integral functional can be evaluated directly in terms of the appropriate…
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as…
Unsteady Aerodynamic Shape Optimization presents new challenges in terms of sensitivity analysis of time-dependent objective functions. In this work, we consider periodic unsteady flows governed by the URANS equations. Hence, the resulting…
We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is…
Bands with non-trivial topological indices have a topological obstruction preventing them from being represented by exponentially localized Wannier states. Here, we propose a procedure to construct exponentially localized Wannier functions…
We report one algorithm for simulating oxygen $K$-edge RIXS for weakly correlated systems, using maximally localized Wannier functions as the basis set. The $N$-electron wavefunction is formulated using the single Slater determinant, and…
Over the last two decades, following the early developments on maximally localized Wannier functions, an ecosystem of electronic-structure simulation techniques and software packages leveraging the Wannier representation has flourished.…
We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time…
We investigate the electronic structure of over-coordinated defects in amorphous silicon via density-functional total-energy calculations, with the aim of understanding the relationship between topological and electronic properties on a…
For the Hamiltonian operator H = -{\Delta}+V(x) of the Schr\"odinger Equation with a repulsive potential, the problem of local decay is considered. It is analyzed by a direct method, based on a new, L^2 bounded, propagation observable. The…
We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…