首页期刊导航|Journal of scientific computing
期刊信息/Journal information
Journal of scientific computing
Plenum Press
Journal of scientific computing

Plenum Press

0885-7474

Journal of scientific computing/Journal Journal of scientific computingEISCIISTP
正式出版
收录年代

    A Multi-fidelity Adaptive Dynamical Low-Rank Based Optimization Algorithm for Fission Criticality Problems

    Carmela ScaloneLukas EinkemmerJonas KuschRyan G. McClarren...
    1.1-1.18页
    查看更多>>摘要：Abstract Computing the dominant eigenvalue is important in nuclear systems as it determines the stability of the system (i.e. whether the system is sub or supercritical). Recently, the work of Kusch et al. (J Comput Phys 470:111587, 2022) showed that performing a low-rank approximation can be very effective in reducing the high memory requirement and computational cost of such problems. In this work, we propose a rank adaptive approach that changes the rank during the inverse power iteration. This allows us to progressively increase the rank (i.e. changing the fidelity of the model) as we get closer to convergence, thereby further reducing computational cost. We then exploit this multi-fidelity approach to optimize a simplified nuclear reactor. In this case the system is parameterized and the values of the parameters that give criticality are sought.
      原文链接:
    • NETL
    • NSTL
    • Springer Nature

    An Accelerated Semi-Proximal ADMM with Applications to Multi-Block Sparse Optimization Problems

    Peng LiuLiang ChenMinru Bai
    1.1-1.30页
    查看更多>>摘要：Abstract As an extension of the alternating direction method of multipliers (ADMM), the semi-proximal ADMM (sPADMM) has been widely used in various fields due to its flexibility and robustness. In this paper, we first show that the two-block sPADMM algorithm can achieve an O(1/K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(1/\sqrt{K})$$\end{document} non-ergodic convergence rate. Then we propose an accelerated sPADMM (AsPADMM) algorithm by introducing extrapolation techniques and incrementing penalty parameters. The proposed AsPADMM algorithm is proven to converge globally to an optimal solution with a non-ergodic convergence rate of O(1/K). Furthermore, the AsPADMM can be extended and combined with the symmetric Gauss-Seidel decomposition to achieve an accelerated ADMM for multi-block problems. Finally, we apply the proposed AsPADMM to solving the multi-block subproblems in difference-of-convex algorithms for robust low-rank tensor completion problems and mixed sparse optimization problems. The numerical results suggest that the acceleration techniques bring about a notable improvement in the convergence speed.
      原文链接:
    • NETL
    • NSTL
    • Springer Nature

    AP-MIONet: Asymptotic-Preserving Multiple-Input Neural Operators for Capturing the High-Field Limits of Collisional Kinetic Equations

    Tian-ai ZhangShi Jin
    1.1-1.36页
    查看更多>>摘要：Abstract In kinetic equations, external fields play a significant role, particularly when their strength is sufficient to balance collision effects, leading to the so-called high-field regime. Two typical examples are the Vlasov-Poisson-Fokker-Planck (VPFP) system in plasma physics and the Boltzmann equation in semiconductor physics. In this paper, we propose a generic asymptotic-preserving multiple-input DeepONet (AP-MIONet) method for solving these two kinetic equations with variable parameters in the high-field regime. Our method aims to tackle two major challenges in this regime: the additional variable parameters introduced by electric fields, and the absence of an explicit local equilibrium, which is a key component of asymptotic-preserving (AP) schemes. We leverage the multiple-input DeepONet (MIONet) architecture to accommodate additional parameters, and formulate the AP loss function by incorporating both the mass conservation law and the original kinetic system. This strategy can avoid reliance on the explicit local equilibrium, preserve the mass and adapt to non-equilibrium states. We demonstrate the effectiveness and efficiency of the proposed method through extensive numerical examples.
      原文链接:
    • NETL
    • NSTL
    • Springer Nature

    Discontinuous Galerkin Finite Element Methods for Linear Port-Hamiltonian Dynamical Systems

    Xiaoyu ChengJ. J. W. van der VegtYan XuH. J. Zwart...
    1.1-1.47页
    查看更多>>摘要：Abstract In this paper, we present discontinuous Galerkin (DG) finite element discretizations for a class of linear hyperbolic port-Hamiltonian dynamical systems. The key point in constructing a port-Hamiltonian system is a Stokes-Dirac structure. Instead of following the traditional approach of defining the strong form of the Dirac structure, we define a Dirac structure in weak form, specifically in the input-state-output form. This is implemented within broken Sobolev spaces on a tessellation with polyhedral elements. After that, we state the weak port-Hamiltonian formulation and prove that it relates to a Poisson bracket. In our work, a crucial aspect of constructing the above-mentioned Dirac structure is that we provide a conservative relation between the boundary ports. Next, we state DG discretizations of the port-Hamiltonian system by using the weak form of the Dirac structure and broken polynomial spaces of differential forms, and we provide a priori error estimates for the structure-preserving port-Hamiltonian discontinuous Galerkin (PHDG) discretizations. The accuracy and capability of the methods developed in this paper are demonstrated by presenting several numerical experiments.
      原文链接:
    • NETL
    • NSTL
    • Springer Nature

    The Finite Element Method for the Navier–Stokes Equation with a Frictional Interface Condition

    Rui LuoPing ZengGuanyu Zhou
    1.1-1.27页
    查看更多>>摘要：Abstract This work deals with the finite element approximation of the non-stationary Navier–Stokes equations with a friction-type leak interface condition. We propose a fully discrete finite element scheme. The discrete variational inequality can be expressed equally as a Lagrange multiplier formulation. We demonstrate the stability and well-posedness of the discrete scheme and derive the error estimates. Additionally, we introduce the Uzawa algorithms and examine its convergence.Numerical examples are presented to confirm the theoretical results.
      原文链接:
    • NETL
    • NSTL
    • Springer Nature

    Semi and Fully Discrete Analysis of Extended Fisher–Kolmogorov Equation with Nonstandard FEMs for Space Discretisation

    Avijit DasNeela NatarajGopikrishnan Chirappurathu Remesan
    1.1-1.44页
    查看更多>>摘要：Abstract This article discusses lowest-order nonstandard finite element methods for space discretisation and backward Euler scheme for time discretisation of the extended Fisher–Kolmogorov equation with clamped boundary conditions. Spatial discretisation employs popular piecewise quadratic schemes based on triangles, namely, the Morley, the discontinuous Galerkin, and the C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^0$$\end{document} interior penalty schemes. Based on the smoother JIM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J I_{\textrm{M}}$$\end{document} defined for a piecewise smooth input function by a (generalized) Morley interpolation IM\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_\textrm{M}$$\end{document} followed by a companion operator J from Carstensen and Nataraj (ESAIM Math Model Numer Anal 56(1):41–78, 2022), a smoother based Ritz projection operator is defined. A set of abstract hypotheses establish the approximation properties of the Ritz projection operator. The approach allows for an elegant semidiscrete and fully discrete error analysis with minimal regularity assumption on the exact solution. Error estimates for both the semidiscrete and fully discrete schemes are presented. The numerical results validate the theoretical estimates and demonstrate the capability of the discontinuous Galerkin method to approximate the solution, even for non-smooth initial condition.
      原文链接:
    • NETL
    • NSTL
    • Springer Nature

    An Entropy Stable Pseudospectral Scheme for Shallow Water Equations in Skew-Symmetric Form on a Cubed Sphere

    Ting-An ChenChun-Hao Teng
    1.1-1.28页
    查看更多>>摘要：Abstract In this study we present a pseudospectral scheme for solving shallow water equations on a spherical surface. Our approach is based on formulating the equations in a skew-symmetric form, and then discretizing the resultant equations based on the Legendre method. The stability of the scheme can be established at the semi-discrete level. In addition, the scheme preserves mass conservation. The performance of the scheme is validated through several numerical examples, and the performance is as expected.
      原文链接:
    • NETL
    • NSTL
    • Springer Nature

    Correction To: A Posteriori Error Analysis of Hybrid High-Order Methods for the Elliptic Obstacle Problem

    Kamana PorwalRitesh Singla
    1.1-1.1页
      原文链接:
    • NETL
    • NSTL
    • Springer Nature

    Mittag-Leffler Interpolation Integrator for the Time-Fractional Allen–Cahn Equation

    Xing LiuYumeng Yang
    1.1-1.36页
    查看更多>>摘要：Abstract In this paper, a fully discrete scheme is presented for solving the time-fractional Allen–Cahn equation. The proposed scheme exhibits superlinear convergence in time. The space discretization is performed using the spectral Galerkin method. The time discretization is designed by combining the Mittag-Leffler function representation of the solution, the integrals of the Mittag-Leffler function and the piecewise polynomial interpolation method. Two methods have been developed to approximate the Mittag-Leffler function based on the Taylor series and the Wright function. The proposed time discretization is capable of achieving (1+α)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1+\alpha )$$\end{document}th order convergence, where the fractional order α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} ranges from 0 to 1. Numerical experiments are presented to verify our theoretical results.
      原文链接:
    • NETL
    • NSTL
    • Springer Nature

    A Balanced Augmented Lagrangian Method with Correction for Linearly Constrained Optimization

    Yanmei LiHaiwen XuWenxing Zhang
    1.1-1.29页
    查看更多>>摘要：Abstract Augmented Lagrangian method (ALM) is a quintessential prototype for linearly constrained optimization. However, a crude use of ALM is rarely possible due to the challenging augmented subproblem. A balanced ALM was recently innovated (He and Yuan, arXiv, 2021) by transferring some computational workloads from the augmented subproblem to the Lagrange multiplier. In this paper, by deploying the prediction-correction framework, we further ameliorate the balanced ALM by introducing a correction step. The O(1/N) convergence rates of the proposed method in both ergodic and nonergodic senses are established under some mild conditions. With the perspectives of spectral decomposition, we analyze the coefficients involving convergence rate of the proposed method. Numerical simulations on some image recovery problems demonstrate the compelling performance of the proposed method.
      原文链接:
    • NETL
    • NSTL
    • Springer Nature