Related papers: Numerical Methods for Multilattices
Concurrent multiscale methods play an important role in modeling and simulating materials with defects, aiming to achieve the balance between accuracy and efficiency. Atomistic-to-continuum (a/c) coupling methods, a typical class of…
We present the speedup from a novel parallel implementation of the multicanonical method on the example of a lattice gas in two and three dimensions. In this approach, all cores perform independent equilibrium runs with identical weights,…
Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite element spaces. We present in this paper a class of such methods…
Lattice simulations are an important class of problems in crystalline solids, surface science, alloys, adsorption, absorption, separation, catalysis, to name a few. We describe a fast computational method for performing lattice…
The Quantum Monte Carlo (QMC) method can yield the imaginary-time dependence of a correlation function $C(\tau)$ of an operator $\hat O$. The analytic continuation to real-time proceeds by means of a "numerical inversion" of these data to…
The numerical sign problem remains one of the central challenges in computational physics. The Worldvolume Hybrid Monte Carlo (WV-HMC) method has recently been proposed as a reliable and computationally efficient algorithm that crucially…
We develop a method to entangle neutral atoms using cold controlled collisions. We analyze this method in two particular set-ups: optical lattices and magnetic micro-traps. Both offer the possibility of performing certain multi-particle…
As the size of a mechanical lattice with beam-modeled edges approaches zero, it undergoes homogenization into a continuum model, which exhibits unusual mechanical properties that deviate from classical Cauchy elasticity, named micropolar…
In this paper, we present a numerical homogenization scheme for indefinite, time-harmonic Maxwell's equations involving potentially rough (rapidly oscillating) coefficients. The method involves an $\mathbf{H}(\mathrm{curl})$-stable,…
We introduce a multigrid multilevel Monte Carlo method for stochastic trace estimation in lattice QCD based on orthogonal projections. This formulation extends the previously proposed oblique decomposition and it is assessed on three…
One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling…
We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…
When approximating the expectations of a functional of a solution to a stochastic differential equation, the numerical performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may…
We present a new hybrid numerical method for multiscale partial differential equations, which simultaneously captures the global macroscopic information and resolves the local microscopic events over regions of relatively small size. The…
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum…
A new method to construct quasicrystalline lattices is proposed. It is based on Landau crystallization theory. Like well-known cut and projection methods our approach deals with N dimensional crystallography, but we don't need any…
We present a general class of unbiased improved estimators for physical observables in lattice gauge theory computations which significantly reduces statistical errors at modest computational cost. The error reduction techniques, referred…
Quantum chromodynamics, most commonly referred to as QCD, is a relativistic quantum field theory for the strong interaction between subatomic particles called quarks and gluons. The most systematic way of calculating the strong interactions…
In this paper, we suggest a new Heterogeneous Multiscale Method (HMM) for the (time-harmonic) Maxwell scattering problem with high contrast. The method is constructed for a setting as in Bouchitt\'e, Bourel and Felbacq (C.R. Math. Acad.…
The calculation of physical quantities by lattice QCD simulations requires in some important cases the determination of the inverse of a very large matrix. In this article we describe how stochastic estimator methods can be applied to this…