arXiv subjects

Michele Ruggeri

Publications and source records attributed to Michele Ruggeri.

34 records · Page 2Linked to original sources

arXiv2018

Computational micromagnetics with Commics

We present our open-source Python module Commics for the study of the magnetization dynamics in ferromagnetic materials via micromagnetic simulations. It implements state-of-the-art unconditionally convergent finite element methods for the numerical integration of the Landau-Lifshitz-Gilbert equation. The implementation is based on the multiphysics finite element software Netgen/NGSolve. The simulation scripts are written in Python, which leads to very readable code and direct access to extensive post-processing. Together with documentation and example scripts, the code is freely available on GitLab.

physics.comp-ph↗

arXiv2018

Convergence of adaptive stochastic Galerkin FEM

We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite element approximations. The algorithms are driven by the energy error reduction estimates derived from two-level a posteriori error indicators for spatial approximations and hierarchical a posteriori error indicators for parametric approximations. The focus of this work is on the mathematical foundation of the adaptive algorithms in the sense of rigorous convergence analysis. In particular, we prove that the proposed algorithms drive the underlying energy error estimates to zero.

math.NA↗

arXiv2018

Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs

We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations (PDEs) with parametric or uncertain inputs. In the algorithm, the stochastic Galerkin finite element method (sGFEM) is used to approximate the solutions to primal and dual problems that depend on a countably infinite number of uncertain parameters. Adaptive refinement is guided by an innovative strategy that combines the error reduction indicators computed for spatial and parametric components of the primal and dual solutions. The key theoretical ingredient is a novel two-level a posteriori estimate of the energy error in sGFEM approximations. We prove that this error estimate is reliable and efficient. The effectiveness of the goal-oriented error estimation strategy and the performance of the goal-oriented adaptive algorithm are tested numerically for three representative model problems with parametric coefficients and for three quantities of interest (including the approximation of pointwise values).

math.NA↗

arXiv2018

Correlation energies of the high-density spin-polarized electron gas to meV accuracy

We present a novel combination of quantum Monte Carlo methods and a finite size extrapolation framework with which we calculate the thermodynamic limit of the exact correlation energy of the polarized electron gas at high densities to meV accuracy, $-40.44(5)$ and $-31.70(4)$ mHa at $r_{\rm s}=0.5$ and $1$, respectively. The fixed-node error is characterized and found to exceed $1$ mHa, and we show that the magnitude of the correlation energy of the polarized electron gas is underestimated by up to $6$ meV by the Perdew-Wang parametrization, for which we suggest improvements.

cond-mat.str-el↗

arXiv2018

Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics

The tangent plane scheme is a time-marching scheme for the numerical solution of the nonlinear parabolic Landau-Lifshitz-Gilbert equation (LLG), which describes the time evolution of ferromagnetic configurations. Exploiting the geometric structure of LLG, the tangent plane scheme requires only the solution of one linear variational form per time-step, which is posed in the discrete tangent space determined by the nodal values of the current magnetization. We develop an effective solution strategy for the arising constrained linear systems, which is based on appropriate Householder reflections. We derive possible preconditioners, which are (essentially) independent of the time-step, and prove that the preconditioned GMRES algorithm leads to linear convergence. Numerical experiments underpin the theoretical findings.

math.NA↗

arXiv2017

Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation

Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and [Praetorius et al. (Comput. Math. Appl., 2017)], we propose a numerical algorithm for the integration of the nonlinear and time-dependent Landau-Lifshitz-Gilbert (LLG) equation which is unconditionally convergent, formally (almost) second-order in time, and requires only the solution of one linear system per time-step. Only the exchange contribution is integrated implicitly in time, while the lower-order contributions like the computationally expensive stray field are treated explicitly in time. Then, we extend the scheme to the coupled system of the Landau-Lifshitz-Gilbert equation with the eddy current approximation of Maxwell equations (ELLG). Unlike existing schemes for this system, the new integrator is unconditionally convergent, (almost) second-order in time, and requires only the solution of two linear systems per time-step.

math.NA↗

arXiv2017

Convergence of an implicit-explicit midpoint scheme for computational micromagnetics

Based on lowest-order finite elements in space, we consider the numerical integration of the Landau-Lifschitz-Gilbert equation (LLG). The dynamics of LLG is driven by the so-called effective field which usually consists of the exchange field, the external field, and lower-order contributions such as the stray field. The latter requires the solution of an additional partial differential equation in full space. Following Bartels and Prohl (2006) (Convergence of an implicit finite element method for the Landau-Lifschitz-Gilbert equation. SIAM J. Numer. Anal. 44), we employ the implicit midpoint rule to treat the exchange field. However, in order to treat the lower-order terms effectively, we combine the midpoint rule with an explicit Adams-Bashforth scheme. The resulting integrator is formally of second-order in time, and we prove unconditional convergence towards a weak solution of LLG. Numerical experiments underpin the theoretical findings.

math.NA↗

arXiv2017

Nonlinear Network description for many-body quantum systems in continuous space

We show that the recently introduced iterative backflow renormalization can be interpreted as a general neural network in continuum space with non-linear functions in the hidden units. We use this wave function within Variational Monte Carlo for liquid $^4$He in two and three dimensions, where we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation of these energies to zero variance gives values in close agreement with the exact values. For two dimensional $^4$He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form -a feature shared with the Shadow Wave Function, but now joined by much higher accuracy. We also achieve significant progress for liquid $^3$He in three dimensions, improving previous variational and fixed-node energies for this very challenging fermionic system.

cond-mat.other↗

arXiv2016

A self-consistent spin-diffusion model for micromagnetics

We propose a three-dimensional micromagnetic model that dynamically solves the Landau-Lifshitz-Gilbert equation coupled to the full spin-diffusion equation. In contrast to previous methods, we solve for the magnetization dynamics and the electric potential in a self-consistent fashion. This treatment allows for an accurate description of magnetization dependent resistance changes. Moreover, the presented algorithm describes both spin accumulation due to smooth magnetization transitions and due to material interfaces as in multilayer structures. The model and its finite-element implementation are validated by current driven motion of a magnetic vortex structure. In a second experiment, the resistivity of a magnetic multilayer structure in dependence of the tilting angle of the magnetization in the different layers is investigated. Both examples show good agreement with reference simulations and experiments respectively.

physics.comp-ph↗

arXiv2016

Low-density phases of $^3$He monolayers adsorbed on graphite

Quantum Monte Carlo simulations at zero temperature of a $^3$He monolayer adsorbed on graphite, either clean or preplated with $^4$He, unexpectedly point to a gas-liquid phase transition at a very low areal density of the order of 0.01Å$^{-2}$. This result stems from an essentially unbiased calculation of the ground state energy for an infinite, defect-free substrate which interacts with He atoms via a realistic potential, whereas the interaction between two He atoms includes two- and three-body terms. The sensitivity of the gas-liquid coexistence region on the model Hamiltonian employed is discussed.

cond-mat.stat-mech↗

arXiv2015

A three-dimensional spin-diffusion model for micromagnetics

We implement a finite-element scheme that solves the Landau-Lifshitz-Gilbert equation coupled to a diffusion equation accounting for spin-polarized currents. The latter solves for the spin accumulation not only in magnetic materials but also in nonmagnetic conductors. The presented method incorporates the model by Slonczewski for the description of spin torque in magnetic multilayers as well as the model of Zhang and Li for the description of current driven domain-wall motion. Furthermore it is able to do both resolve the time evolution of the spin accumulation or treat it in an adiabatic fashion by the choice of sufficiently large time steps.

physics.comp-ph↗

arXiv2015

Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids

We show how a ground state trial wavefunction of a Fermi liquid can be systematically improved introducing a sequence of renormalized coordinates through an iterative backflow transformation. We apply this scheme to calculate the ground state energy of liquid $^3$He in two dimensions at freezing density using variational and fixed-node diffusion Monte Carlo. Comparing with exact transient estimate results for systems with small number of particles, we find that variance extrapolations provide accurate results for the true ground state together with stringent lower bounds. For larger systems these bounds can in turn be used to quantify the systematic bias of fixed-node calculations. These wave functions are size consistent and the scaling of their computational complexity with the number of particles is the same as for standard backflow wave functions.

cond-mat.str-el↗

arXiv2014

Spin-polarized transport in ferromagnetic multilayers: An unconditionally convergent FEM integrator

We propose and analyze a decoupled time-marching scheme for the coupling of the Landau-Lifshitz-Gilbert equation with a quasilinear diffusion equation for the spin accumulation. This model describes the interplay of magnetization and electron spin accumulation in magnetic and non-magnetic multilayer structures. Despite the strong nonlinearity of the overall PDE system, the proposed integrator requires only the solution of two linear systems per time-step. Unconditional convergence of the integrator towards weak solutions is proved.

math.NA↗

arXiv2014

Quantum Monte Carlo study of a two dimensional dipolar Bose gas in a harmonic trap

We present a Quantum Monte Carlo study of the ground state properties of a two dimensional system of Bose particle with dipole moment in a harmonic trap. The direction of the dipoles is assumed to be fixed by an external field. We study how the system behaves when the direction of the dipole moments is changed. Our analysis is made using Path Integral Monte Carlo simulations in the Grand Canonical ensemble, using the Worm Algorithm. We study systems of increasing size, focusing on the spatial distribution of the atoms inside the trap and on the superfluid fraction of the sample. We find that vertical dipoles form a crystal, characterized by a shell structure, while tilting the dipoles has the effect of inducing a striped structure. We find that similar behaviour can be found in the analogue classical system. Vertical dipoles display nonclassical inertia while a strong tilting decreases superfluidity.

cond-mat.quant-gas↗

arXiv2014

Multiscale modeling in micromagnetics: existence of solutions and numerical integration

Various applications ranging from spintronic devices, giant magnetoresistance sensors, and magnetic storage devices, include magnetic parts on very different length scales. Since the consideration of the Landau-Lifshitz-Gilbert equation (LLG) constrains the maximum element size to the exchange length within the media, it is numerically not attractive to simulate macroscopic parts with this approach. On the other hand, the magnetostatic Maxwell equations do not constrain the element size, but cannot describe the short-range exchange interaction accurately. A combination of both methods allows to describe magnetic domains within the micromagnetic regime by use of LLG and also considers the macroscopic parts by a non-linear material law using the Maxwell equations. In our work, we prove that under certain assumptions on the non-linear material law, this multiscale version of LLG admits weak solutions. Our proof is constructive in the sense that we provide a linear-implicit numerical integrator for the multiscale model such that the numerically computable finite element solutions admit weak $H^1$-convergence (at least for a subsequence) towards a weak solution.

math.NA↗

arXiv2013

Quasi-2D Liquid He-3

Quantum Monte Carlo simulations at zero temperature of an ensemble of He-3 atoms adsorbed on Mg and Alkali substrates yield strong evidence of a thermodynamically stable liquid He-3 monolayer on all Alkali substrates, with the possible exception of Li. The effective 2D density is close to 0.02$ inverse square Angstroms on Na, making it the lowest density liquid in Nature. Its existence is underlain by zero-point atomic motion perpendicular to the substrate, whose effect is softening the short-range repulsion of the helium interatomic potential. The monolayer films should turn superfluid at a temperature of order 1 mK. No liquid film is predicted to form on Mg, or on stronger substrates such as graphite.

cond-mat.other↗