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Accelerating Eigenvalue Computation for Nuclear Structure Calculations via Perturbative Corrections

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arXiv 2024年

作者： Roh, Dong Min Ng, Esmond Yang, Chao Lee, Dean Maris, Pieter Vary, James P. Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory United States Facility for Rare Isotope Beams Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Department of Physics and Astronomy Iowa State University AmesIA50011 United States

We present a new method for computing the lowest few eigenvalues and the corresponding eigenvectors of a nuclear many-body Hamiltonian represented in a truncated configuration interaction subspace, i.e., the no-core shell model (NCSM). The method uses the hierarchical structure of the NCSM Hamiltonian to partition the Hamiltonian as the sum of two matrices. The first matrix corresponds to the Hamiltonian represented in a small configuration space, whereas the second is viewed as the perturbation to the first matrix. Eigenvalues and eigenvectors of the first matrix can be computed efficiently. Perturbative corrections to the eigenvectors of the first matrix can be obtained from the solutions of a sequence of linear systems of equations defined in the small configuration space. These correction vectors can be combined with the approximate eigenvectors of the first matrix to construct a subspace from which more accurate approximations of the desired eigenpairs can be obtained. We call this method a Subspace Projection with Perturbative Corrections (SPPC) method. We show by numerical examples that the SPPC method can be more efficient than conventional iterative methods for solving large-scale eigenvalue problems such as the Lanczos, block Lanczos and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The method can also be combined with other methods to avoid convergence stagnation. © 2024, CC BY.

关键词： Matrix algebra

Interference between dielectronic and radiative recombination of Be-like highly charged ions

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Physical Review A 2023年第5期107卷 052801-052801页

作者： Xiao-Min Tong Xiang Gao Daiji Kato Nobuyuki Nakamura Center for Computational Sciences University of Tsukuba 1-1-1 Tennodai Tsukuba Ibaraki 305-8573 Japan Institute for Applied Physics and Computational Mathematics Beijing 100088 China National Institute for Fusion Science Toki Gifu 509-5292 Japan Interdisciplinary Graduate School of Engineering Sciences Kyushu University Fukuoka 816-8580 Japan Institute for Laser Science The University of Electro-Communications Tokyo 182-8585 Japan

We perform a systematical study for the polarization of x rays emitted when a free electron is captured by Be-like highly charged ions theoretically. We focus on the dielectronic recombination of the J=1/2→J=1/2 transition and its polarization is zero due to axial symmetry. Including the interference between the dielectronic and radiative recombinations, the polarization changes dramatically when the electron energy crosses the resonant energy. By comparing the simulations with or without certain interactions, we found that the Breit interaction is not important even for very high-Z ions. For low-Z ions, the configuration interaction of the dielectronic recombination states affects the polarization greatly, while for high-Z ions the configuration interaction of the ground state of Be-like ions plays an important role.

关键词： Autoionization & Auger processes Electronic excitation & ionization

A Pseudo-Spectral Scheme for Systems of Two-Point Boundary Value Problems with Left and Right Sided Fractional Derivatives and Related Integral Equations

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Computer Modeling in Engineering & Sciences 2021年第7期128卷 21-41页

作者： I.G.Ameen N.A.Elkot M.A.Zaky A.S.Hendy E.H.Doha Department of Mathematics Faculty of ScienceAl-Azhar UniversityCairoEgypt Department of Mathematics Faculty of ScienceCairo UniversityGiza12613Egypt Department of Applied Mathematics Physics DivisionNational Research CentreDokkiCairo12622Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and MathematicsUral Federal UniversityYekaterinburg620002Russia Department of Mathematics Faculty of ScienceBenha UniversityBenha13511Egypt

We target here to solve numerically a class of nonlinear fractional two-point boundary value problems involving left-and right-sided fractional *** main ingredient of the proposed method is to recast the problem into an equivalent system of weakly singular integral ***,a Legendre-based spectral collocation method is developed for solving the transformed ***,we can make good use of the advantages of the Gauss quadrature *** present the construction and analysis of the collocation *** results can be indirectly applied to solve fractional optimal control problems by considering the corresponding Euler–Lagrange *** numerical examples are given to confirm the convergence analysis and robustness of the scheme.

关键词： Spectral collocation method weakly singular integral equations two-point boundary value problems convergence analysis

Spin Transport Hydrodynamics of Polarized Deuterium-Tritium Fusion Plasma

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arXiv 2022年

作者： Hu, Ronghao Zhou, Hao Tao, Zhihao Zhang, Zhihao Lv, Meng Zou, Shiyang Ding, Yongkun College of Physics Sichuan University Chengdu610065 China Key Laboratory of High Energy Density Physics and Technology Ministry of Education Sichuan University Chengdu610064 China Institute of Applied Physics and Computational Mathematics Beijing100094 China

The spin transport equations for polarized deuterium-tritium (DT) fusion plasma are derived with the density matrix formulation, which are used to investigate the hydrodynamics of polarized DT-gas-filled targets during indirectly driven inertial confinement fusion implosions. The depolarization of DT ions by strong self-generated magnetic fields can be captured by the spin transport equation. The neutron yield, angular distribution and neutron beam polarization are obtained from three-dimensional spin transport hydrodynamics simulations of the target implosions. The simulation results indicate that an optimized spin alignment of the polarized target can reduce the depolarization of DT ions and the neutron beams induced by polar mode asymmetries in indirectly driven implosions. Copyright © 2022, The Authors. All rights reserved.

关键词： Depolarization

A NONLINEAR SCHR?DINGER EQUATION WITH COULOMB POTENTIAL

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Acta Mathematica Scientia 2022年第6期42卷 2230-2256页

作者：苗长兴张军勇郑继强 Institute of Applied Physics and Computational Mathematics Department of Mathematics Beijing Institute of Technology Department of Mathematics Cardiff University

In this paper,we study the Cauchy problem for the nonlinear Schr?dinger equations with Coulomb potential i?_tu+Δu+K/|x|u=-λ|u|p-1u with *** results reveal the influence of the long range potential K|x|-1on the existence and scattering theories for nonlinear Schrodinger *** particular,we prove the global existence when the Coulomb potential is attractive,i.e.,when K> 0,and the scattering theory when the Coulomb potential is repulsive,i.e.,when K <*** argument is based on the newlyestablished interaction Morawetz-type inequalities and the equivalence of Sobolev norms for the Laplacian operator with the Coulomb potential.

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Numerical analysis of the multiple scattering theory for electronic structure calculations

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arXiv 2021年

作者： Li, Xiaoxu Chen, Huajie Gao, Xingyu College of Education for the Future Beijing Normal University School of Mathematical Sciences Beijing Normal University Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics

The multiple scattering theory (MST) is one of the most widely used methods in electronic structure calculations. It features a perfect separation between the atomic configurations and site potentials, and hence provides an efficient way to simulate defected and disordered systems. This work studies the MST methods from a numerical point of view and shows the convergence with respect to the truncation of the angular momentum summations, which is a fundamental approximation parameter for all MST methods. We provide both rigorous analysis and numerical experiments to illustrate the efficiency of the MST methods within the angular momentum representations. Copyright © 2021, The Authors. All rights reserved.

关键词： Angular momentum

Effects of reflection distance on Richtmyer–Meshkov instability in the reshock process: A discrete Boltzmann study

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arXiv 2025年

作者： Lai, Huilin Lin, Chuandong Li, Demei Yang, Tao Gan, Yanbiao Lian, Lingyan Xu, Aiguo Fujian Normal University Fuzhou350117 China Sino-French Institute of Nuclear Engineering and Technology Sun Yat-sen University Zhuhai519082 China Key Laboratory for Thermal Science and Power Engineering of Ministry of Education Department of Energy and Power Engineering Tsinghua University Beijing100084 China Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle School of Liberal Arts and Sciences North China Institute of Aerospace Engineering Langfang065000 China National Key Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P. O. Box 8009-26 Beijing100088 China National Key Laboratory of Shock Wave and Detonation Physics Mianyang621999 China HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China State Key Laboratory of Explosion Science and Safety Protection Beijing Institute of Technology Beijing100081 China

The Richtmyer–Meshkov (RM) instability occurs when a perturbed interface between two fluids undergoes impulsive acceleration due to a shock wave. In this paper, a numerical investigation of the RM instability during the reshock process is conducted using the two-component discrete Boltzmann method. The influence of reflection distance on the RM instability, including both hydrodynamic and thermodynamic non-equilibrium effects, is explored in detail. The interaction time between the reflected shock wave and the material interface varies with different reflection distances. Larger reflection distances lead to a longer evolution time of the material interface before reshock, resulting in more complex effects on the interface deformation, the mixing extent of the fluid system, and non-equilibrium behaviors after reshock. Additionally, while the reflection distance has a minimal impact on mixing entropy before the secondary impact, a significant difference emerges after the secondary impact. This suggests that the secondary impact enhances the evolution of the RM instability. Furthermore, non-equilibrium behaviors or quantities exhibit complex dynamics due to the influence of the transmitted shock wave, transverse waves, rarefaction waves, material interfaces, and dissipation/diffusion processes. Copyright © 2025, The Authors. All rights reserved.

关键词： Shock waves

Retrieval of material properties of monolayer transition metal dichalcogenides from magnetoexciton energy spectra

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Physical Review B 2023年第20期107卷 205304-205304页

作者： Duy-Nhat Ly Dai-Nam Le Duy-Anh P. Nguyen Ngoc-Tram D. Hoang Ngoc-Hung Phan Hoang-Minh L. Nguyen Van-Hoang Le Computational Physics Key Laboratory K002 Department of Physics Ho Chi Minh City University of Education Ho Chi Minh City 72759 Vietnam Department of Physics University of South Florida Tampa Florida 33620 USA Institute of Applied Technology Thu Dau Mot University Thu Dau Mot City Binh Duong Province 75151 Vietnam

Reduced exciton mass, polarizability, and dielectric constant of the surrounding medium are essential properties for semiconducting materials, and they have been extracted recently from the magnetoexciton energies. However, the acceptable accuracy of the suggested method requires very high magnetic intensity. Therefore, in the present paper, we propose an alternative method of extracting these material properties from recently available experimental magnetoexciton s-state energies in monolayer transition metal dichalcogenides (TMDCs). The method is based on the high sensitivity of exciton energies to the material parameters in the Rytova-Keldysh model. It allows us to vary the considered material parameters to get the best fit of the theoretical calculation to the experimental exciton energies for the 1s, 2s, and 3s states. This procedure gives values of the exciton reduced mass and 2D polarizability. Then, the experimental magnetoexciton spectra compared to the theoretical calculation also determine the average dielectric constant. Concrete applications are presented only for monolayers WSe2 and WS2 from the recently available experimental data; however, the presented approach is universal and can be applied to other monolayer TMDCs. The mentioned fitting procedure requires a fast and effective method of solving the Schrödinger equation of an exciton in monolayer TMDCs with a magnetic field. Therefore, we also develop such a method in this paper for highly accurate magnetoexciton energies.

关键词： Excitons Microstructure Transition metal dichalcogenides Exact solutions for many-body systems

An extended plane wave framework for the electronic structure calculations of twisted bilayer material systems

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arXiv 2023年

作者： Dai, Xiaoying Zhou, Aihui Zhou, Yuzhi LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China

In this paper, we propose an extended plane wave framework to make the electronic structure calculations of the twisted bilayer 2D material systems practically feasible. Based on the foundation in [Y. Zhou, H. Chen, A. Zhou, J. Comput. Phys. 384, 99 (2019)], following extensions take place: (1) an tensor-producted basis set, which adopts PWs in the incommensurate dimensions, and localized basis in the interlayer dimension, (2) a practical application of a novel cutoff techniques we have recently developed, and (3) a quasi-band structure picture under the small twisted angles and weak interlayer coupling limits. With (1) and (2) now the dimensions of Hamiltonian matrix are reduced by about 2 orders of magnitude compared with the original framework. And (3) enables us to better organize the calculations and understand the results. For numerical examples, we study the electronic structures of the linear bilayer graphene lattice system with the magic twisted angle (∼ 1.05◦). The famous flat bands have been reproduced with their features in quantitative agreement with those from experiments and other theoretical calculations. Moreover, the extended framework has much less computational cost compared to the commensurate cell approximations, and is more extendable compared to the traditional model hamiltonians and tight binding models. Finally this framework can readily accommodate nonlinear models thus will laid the foundations for more effective yet accurate Density Functional Theory (DFT) calculations. © 2023, CC BY.

关键词： Electronic structure