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Results for “RELAXATION METHOD”
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Nonlinear force-free extrapolation of the coronal magnetic field based on the magnetohydrodynamic relaxation method
We develop a nonlinear force-free field (NLFFF) extrapolation code based on the magnetohydrodynamic (MHD) relaxation method. We extend the classical MHD relaxation method in two important ways. First, we introduce an algorithm initially proposed by Dedner et al. to effectively clean the numerical errors associated with ∇ · B . Second, the multigrid type method is implemented in our NLFFF to perform direct analysis of the high-resolution magnetogram data. As a result of these two implementations, we successfully extrapolated the high resolution force-free field introduced by Low and Lou with better accuracy in a drastically shorter time. We also applied our extrapolation method to the MHD solution obtained from the flux-emergence simulation by Magara. We found that NLFFF extrapolation may be less effective for reproducing areas higher than a half-domain, where some magnetic loops are found in a state of continuous upward expansion. However, an inverse S-shaped structure consisting of the sheared and twisted loops formed in the lower region can be captured well through our NLFFF extrapolation method. We further discuss how well these sheared and twisted fields are reconstructed by estimating the magnetic topology and twist quantitatively.
A multigrid waveform relaxation method for solving the poroelasticity equations
In this work, a multigrid waveform relaxation method is proposed for solving a collocated finite difference discretization of the linear Biot’s model. This gives rise to the first space–time multigrid solver for poroelasticity equations in the literature. The waveform relaxation iteration is based on a point-wise Vanka smoother that couples the pressure variable at a grid-point with the displacements around it. A semi-algebraic mode analysis is proposed to theoretically analyze the convergence of the multigrid waveform relaxation algorithm. This analysis is novel since it combines the semi-algebraic analysis, suitable for parabolic problems, with the non-standard analysis for overlapping smoothers. The practical utility of the method is illustrated through several numerical experiments in one and two dimensions.
Force field preconditioned ab initio structure relaxation method
We present a general method to accelerate ab initio atomic structural relaxations. In this method, the conjugate gradient ab initio relaxation is preconditioned by a force field relaxation. This force field is constructed on-the-flight with the information of the ab initio forces and the current atomic configuration. At each ab initio relaxation step, the so-constructed force field is used to prerelax the system, with the relaxation direction as the preconditioned direction for the ab initio conjugated gradient method. The force field model and its parameters are rather general making this method applicable for a wide range of systems commonly used in material simulations. We report more than 80 different systems have been tested representing different cases in material simulations. Across the board, we find accelerations mostly over a factor of 2 and for some large systems with a factor of 6 ~ 9 . There is no case where the relaxation becomes worse. The code and lib for this method are provided, which can be used as a plugin in a standard ab initio atomic relaxation code.
Compact finite difference relaxation method for chaotic and hyperchaotic initial value systems
In this paper, we present a new application of higher order compact finite differences to solve nonlinear initial value problems exhibiting chaotic behaviour. The method involves dividing the domain of the problem into multiple sub-domains, with each sub-domain integrated using higher order compact finite difference schemes. The nonlinearity is dealt using a Gauss–Seidel-like relaxation. The method is, therefore, referred to as the multi-domain compact finite difference relaxation method (MD-CFDRM). In this new application, the MD-CFDRM is used to solve famous chaotic systems and hyperchaotic systems. The main advantage of the new approach is that it offers better accuracy on coarser grids which significantly improves the computational speed of the method. The results are compared with spectral-based multi-domain method.
A Study of Successive Over-relaxation Method Parallelization over Modern HPC Languages
Successive over-relaxation (SOR) is a computationally intensive, yet extremely important iterative solver for solving linear systems. Due to recent trends of exponential growth in amount of data generated and increasing problem sizes, serial platforms have proved to be insucient in providing the required computational power. In this paper, we present parallel implementations of red-black SOR method using three modern programming languages namely Chapel, D and Go. We employ SOR method for solving 2D steady-state heat conduction problem. We discuss the optimizations incorporated and the features of these languages which are crucial for improving the program performance. Experiments have been performed using 2, 4, and 8 threads and performance results are compared with serial execution. The analysis of results provides important insights into working of SOR method.
FORCED FIELD EXTRAPOLATION: TESTING A MAGNETOHYDRODYNAMIC (MHD) RELAXATION METHOD WITH A FLUX-ROPE EMERGENCE MODEL
We undertake an attempt to reconstruct the Sun's non-force-free magnetic field. The solar corona is often considered to be magnetohydrostatic. We solve the full MHD equations with a semi-realistic atmosphere model to attain this stationary state. Our method is tested with a Sun-like model which simulates the emergence of a magnetic flux rope passing from below the photosphere into the corona. Detailed diagnostics shows that our method can model the forced field more successfully than the optimization and potential method, but it still needs to be applied to real data.
A relaxation method for the energy and morphology of grain boundaries and interfaces
Not Available
A Single Compartment Relaxed Eddy Accumulation Method
The relaxed eddy accumulation (REA) method is a widely-known technique that measures turbulent fluxes of scalar quantities. The REA technique has been used to measure turbulent fluxes of various compounds, such as methane, ethene, propene, butene, isoprene, nitrous oxides, ozone, and others. The REA method requires the accumulation of scalar concentrations in two separate compartments that conditionally sample updrafts and downdraft events. It is demonstrated here that the assumptions behind the conventional or two-compartment REA approach allow for one-compartment sampling, therefore called a one compartment or 1-C-REA approach, thereby expanding its operational utility. The one-compartment sampling method is tested across various land cover types and atmospheric stability conditions, and it is found that the one-compartment REA can provide results comparable to those determined from conventional two-compartment REA. This finding enables rapid expansion and practical utility of REA in studies of surface-atmosphere exchanges, interactions, and feedbacks.
Halted-pendulum Relaxation: Application to White Dwarf Binary Initial Data
Studying compact-star binaries and their mergers is integral to determining progenitors for observable transients. Today, compact-star mergers are typically studied via state-of-the-art computational fluid dynamics codes. One such numerical technique, smoothed particle hydrodynamics (SPH), is frequently chosen for its excellent mass, energy, and momentum conservation. The natural treatment of vacuum and the ability to represent highly irregular morphologies make SPH an excellent tool for the study of compact-star binaries and mergers. For many scenarios, including binary systems, the outcome of simulations is only as accurate as the initial conditions. For SPH, it is essential to ensure that the particles are distributed regularly, representing the initial density profile but without long-range correlations. Particle noise in the form of high-frequency local motion and low-frequency global dynamics must be damped out. Damping the latter can be as computationally intensive as the actual simulation. We discuss a new and straightforward relaxation method, halted-pendulum relaxation (HPR), to remove global oscillation modes of SPH particle configurations. In combination with effective external potentials representing gravitational and orbital forces, we show that HPR has an excellent performance in efficiently relaxing SPH particles to the desired density distribution and removing global oscillation modes. We compare the method to frequently used relaxation approaches and test it on a white dwarf binary model at its Roche-lobe overflow limit. We highlight the importance of our method in achieving accurate initial conditions and its effect on achieving circular orbits and realistic accretion rates when compared with other general relaxation methods.
Analysis of Niobium Electropolishing Using a Generalized Distribution of Relaxation Times Method
Using electrochemical impedance spectroscopy, we have devised a method of sensing the microscopic surface conditions on the surface of niobium as it is undergoing an electrochemical polishing (EP) treatment. The method uses electrochemical impedance spectroscopy (EIS) to gather information on the surface state of the electrode without disrupting the polishing reaction. The EIS data is analyzed using a so-called distribution of relaxation times (DRT) method. Using DRT, the EIS data can be deconvolved into discrete relaxation time peaks without any a priori knowledge of the electrode dynamics. By analyzing the relaxation time peaks, we are able to distinguish two distinct modes of the EP reaction. As the polishing voltage is increased, the electrode transitions from the low voltage EP mode, characterized by a single relaxation time peaks, to the high voltage EP mode, characterized by two relaxation time peaks. We theorize that this second peak is caused by the formation of an oxide layer on the electrode. We also find that this oxide induced peak transitions from to a negative relaxation time, which is indicative of a blocking electrode process. By analyzing EPed samples, we show that samples polished in the low voltage mode have significantly higher surface roughness due to grain etching and faceting. We find that the surface roughness of the samples only improves when the oxide film peak is present and in the negative relaxation time region. This shows that EIS combined with DRT analysis can be used to predict etching on EPed Nb. This method can also be performed before or during the EP, which could allow for adjustment of polishing parameters to guarantee a smooth cavity surface finish.
Diffusion of point defects in crystalline silicon using the kinetic activation-relaxation technique method
We study point-defect diffusion in crystalline silicon using the kinetic activation-relaxation technique (k-ART), an off-lattice kinetic Monte Carlo method with on-the-fly catalog building capabilities based on the activation-relaxation technique (ART nouveau), coupled to the standard Stillinger-Weber potential. We focus more particularly on the evolution of crystalline cells with one to four vacancies and one to four interstitials in order to provide a detailed picture of both the atomistic diffusion mechanisms and overall kinetics. We show formation energies, activation barriers for the ground state of all eight systems, and migration barriers for those systems that diffuse. Additionally, we characterize diffusion paths and special configurations such as dumbbell complex, di-interstitial (IV-pair+2I) superdiffuser, tetrahedral vacancy complex, and more. In conclusion, this study points to an unsuspected dynamical richness even for this apparently simple system that can only be uncovered by exhaustive and systematic approaches such as the kinetic activation-relaxation technique.
A quantum energy transport model for semiconductor device simulation
This paper describes numerical methods for a quantum energy transport (QET) model in semiconductors, which is derived by using a diffusion scaling in the quantum hydrodynamic (QHD) model. We newly drive a four-moments QET model similar with a classical ET model. Space discretization is performed by a new set of unknown variables. Numerical stability and convergence are obtained by developing numerical schemes and an iterative solution method with a relaxation method. Numerical simulations of electron transport in a scaled MOSFET device are discussed. The QET model allows simulations of quantum confinement transport, and nonlocal and hot-carrier effects in scaled MOSFETs.
Advancing electrochemical impedance analysis through innovations in the distribution of relaxation times method
Electrochemical impedance spectroscopy (EIS) is a key tool across various scientific disciplines, including energy sciences, chemistry, and biology, enabling the analysis of electrochemical systems. However, conventional methods for interpreting EIS data are often complex and model dependent. The distribution of relaxation times (DRT) offers a non-parametric approach that simplifies the interpretation process by providing a timescale interpretation of EIS data. This article provides a comprehensive review of current methods for DRT inversion. Additionally, a survey of practitioners highlights key challenges in the field. Here, the findings underscore the need for standardized DRT analysis and benchmarks, as well as the development of automated analysis tools. These advancements would improve the usability and interpretability of EIS data. Ultimately, implementing these improvements could not only propel the field forward but also expand the application of DRT in scientific research by making it accessible to a broader range of researchers, including those without specialized expertise in programming or statistics.
SS{sub p}G: A strongly orthogonal geminal method with relaxed strong orthogonality
Strong orthogonality is an important constraint placed on geminal wavefunctions in order to make variational minimization tractable. However, strong orthogonality prevents certain, possibly important, excited configurations from contributing to the ground state description of chemical systems. The presented method lifts strong orthogonality constraint from geminal wavefunction by computing a perturbative-like correction to each geminal independently from the corrections to all other geminals. The method is applied to the Singlet-type Strongly orthogonal Geminals variant of the geminal wavefunction. Comparisons of this new SS{sub p}G method are made to the non-orthogonal AP1roG and the unconstrained Geminal Mean-Field Configuration Interaction method using small atomic and molecular systems. The correction is also compared to Density Matrix Renormalization Group calculations performed on long polyene chains in order to assess its scalability and applicability to large strongly correlated systems. The results of these comparisons demonstrate that although the perturbative correction is small, it may be a necessary first step in the systematic improvement of any strongly orthogonal geminal method.
Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem
Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applications. We first train a deep neural operator (DeepONet) to solve wave propagation problems described by the Helmholtz equation in a domain without scatterers but at different wavenumbers and with a complex absorbing boundary condition. We then design two classes of fast meta-solvers by combining DeepONet with either relaxation methods, such as Jacobi and Gauss-Seidel, or with Krylov methods, such as GMRES and BiCGStab, using the trunk basis of DeepONet as a coarse-scale preconditioner. We leverage the spectral bias of neural networks to account for the lower part of the spectrum in the error distribution while the upper part is handled inexpensively using relaxation methods or fine-scale preconditioners. The meta-solvers are then applied to solve scattering problems with different shape of scatterers, at no extra training cost. We first demonstrate that the resulting meta-solvers are shape-agnostic, fast, and robust, whereas the standard standalone solvers may even fail to converge without the DeepONet. We then apply both classes of meta-solvers to scattering from a submarine, a complex three-dimensional problem. We achieve very fast solutions, especially with the DeepONet-Krylov methods, which require orders of magnitude fewer iterations than any of the standalone solvers.
Metastable electronic states in uranium tetrafluoride
Here, the DFT+ U approach, where U is the Hubbard-like on-site Coulomb interaction, has successfully been used to improve the description of transition metal oxides and other highly correlated systems, including actinides. The secret of the DFT+ U approach is the breaking of d or f shell orbital degeneracy and adding an additional energetic penalty to non-integer occupation of orbitals. A prototypical test case, UO 2 , benefits from the + U approach whereby the bare LDA method predicts UO 2 to be a ferromagnetic metal, whereas LDA+ U correctly predicts UO 2 to be insulating. However, the concavity of the energetic penalty in the DFT+ U approach can lead to a number of convergent “metastable” electronic configurations residing above the ground state. Uranium tetrafluoride (UF 4 ) represents a more complex analogy to UO 2 in that the crystal field has lower symmetry and the unit cell contains two symmetrically distinct U atoms. We explore the metastable states in UF 4 using several different methods of selecting initial orbital occupations. Two methods, a “pre-relaxation” method wherein an initial set of orbital eigenvectors is selected via the self-consistency procedure and a crystal rotation method wherein the x, y, z axes are brought into alignment with the crystal field, are explored. We show that in the case of UF 4 , which has non-collinearity between its crystal axes and the U atoms' crystal field potentials, the orbital occupation matrices are much more complex and should be analyzed using a novel approach. In addition to demonstrating a complex landscape of metastable electronic states, UF 4 also shows significant hybridization in U–F bonding, which involves non-trivial contributions from s, p, d, and f orbitals.