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A Bound-Preserving and Positivity-Preserving Path-Conservative Discontinuous Galerkin Method for Solving Five-Equation Model of Compressible Two-Medium Flows 求解可压缩双介质流五方程模型的保界保正路径保守间断Galerkin方法
Pub Date : 2022-08-01 DOI: 10.1137/21m1444497
Jian Cheng, Fan Zhang
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引用次数: 3
Newton-Noda Iteration for Computing the Ground States of Nonlinear Schrödinger Equations 计算非线性Schrödinger方程基态的Newton-Noda迭代
Pub Date : 2022-08-01 DOI: 10.1137/21m1435793
Changgeng Du, Ching-Sung Liu
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引用次数: 3
Parallel-in-time preconditioner for the Sinc-Nyström systems Sinc-Nyström系统的并行实时预调节器
Pub Date : 2022-08-01 DOI: 10.1137/21m1462696
Jun Liu, Shulin Wu
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引用次数: 0
A Very Easy High-Order Well-Balanced Reconstruction for Hyperbolic Systems with Source Terms 具有源项的双曲型系统的一种非常简单的高阶良好平衡重构
Pub Date : 2022-08-01 DOI: 10.1137/21m1429230
C. Berthon, Solène Bulteau, F. Foucher, Meissa M'Baye, Victor Michel-Dansac
When adopting high-order finite volume schemes based on MUSCL reconstruction techniques to approximate the weak solutions of hyperbolic systems with source terms, the preservation of the steady states turns out to be very challenging. Indeed, the designed reconstruction must preserve the steady states under consideration in order to get the required well-balancedness property. A priori, to capture such a steady state, one needs to solve some strongly nonlinear equations. Here, we design a very easy correction to high-order finite volume methods. This correction can be applied to any scheme of order greater than or equal to 2, such as a MUSCL-type scheme, and ensures that this scheme exactly preserves the steady solutions. The main discrepancy with usual techniques lies in avoiding the inversion of the nonlinear function that governs the steady solutions. Moreover, for under-determined steady solutions, several nonlinear functions must be considered simultaneously. Since the derived correction only considers the evaluation of the governing nonlinear functions, we are able to deal with under-determined stationary systems. Several numerical experiments illustrate the relevance of the proposed well-balanced correction, as well as its main limitation, namely the fact that it may fail at being both well-balanced and more than second-order accurate for a specific class of initial conditions.
当采用基于MUSCL重构技术的高阶有限体积格式逼近带源项的双曲型系统弱解时,稳态的保持是非常具有挑战性的。实际上,所设计的重构必须保持所考虑的稳态,以获得所需的正平衡性。先验地,为了获得这样一个稳定状态,我们需要解一些强非线性方程。在这里,我们设计了一个非常容易的高阶有限体积方法的修正。这种修正可以应用于任何大于或等于2阶的格式,如muscl型格式,并确保该格式准确地保留稳定解。该方法与常用方法的主要区别在于避免了控制稳态解的非线性函数的反转。此外,对于欠定稳态解,必须同时考虑多个非线性函数。由于导出的修正只考虑控制非线性函数的评估,因此我们能够处理欠定的平稳系统。几个数值实验说明了所提出的良好平衡校正的相关性,以及它的主要局限性,即它可能无法在良好平衡和超过二阶精度的特定类别的初始条件。
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引用次数: 2
UGKS-Based Implicit Iterative Method for Multiscale Nonequilibrium Flow Simulations 基于ugks的多尺度非平衡流动模拟隐式迭代方法
Pub Date : 2022-08-01 DOI: 10.1137/21m1421398
Xiaocong Xu, Yajun Zhu, Chang Liu, K. Xu
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引用次数: 1
Robust Rational Approximations of Nonlinear Eigenvalue Problems 非线性特征值问题的鲁棒有理逼近
Pub Date : 2022-08-01 DOI: 10.1137/20m1380533
S. Güttel, G. Porzio, F. Tisseur
. We develop algorithms that construct robust (i.e., reliable for a given tolerance, and scaling independent) rational approximants of matrix-valued functions on a given subset of the complex plane. We consider matrix-valued functions provided in both split form (i.e., as a sum of scalar functions times constant coefficient matrices) and in black box form. We develop a new error analysis and use it for the construction of stopping criteria, one for each form. Our criterion for split forms adds weights chosen relative to the importance of each scalar function, leading to the weighted AAA algorithm, a variant of the set-valued AAA algorithm that can guarantee to return a rational approximant with a user-chosen accuracy. We propose two-phase approaches for black box matrix-valued functions that construct a surrogate AAA approximation in phase one and refine it in phase two, leading to the surrogate AAA algorithm with exact search and the surrogate AAA algorithm with cyclic Leja–Bagby refinement. The stopping criterion for black box matrix-valued functions is updated at each step of phase two to include information from the previous step. When convergence occurs, our two-phase approaches return rational approximants with a user-chosen accuracy. We select problems from the NLEVP collection that represent a variety of matrix-valued functions of different sizes and properties and use them to benchmark our algorithms.
. 我们开发了在复平面的给定子集上构造矩阵值函数的鲁棒(即,对给定容限可靠且与尺度无关)有理逼近的算法。我们考虑以分裂形式(即标量函数乘以常系数矩阵的和)和黑盒形式提供的矩阵值函数。我们开发了一种新的误差分析方法,并将其用于构建停止准则,每种形式一个停止准则。我们的分割表单标准添加了相对于每个标量函数的重要性所选择的权重,从而产生加权AAA算法,这是集值AAA算法的一种变体,可以保证以用户选择的精度返回有理近似值。我们提出了黑盒矩阵值函数的两阶段方法,该方法在第一阶段构建代理AAA近似,并在第二阶段对其进行细化,从而得到具有精确搜索的代理AAA算法和具有循环Leja-Bagby细化的代理AAA算法。在阶段二的每一步更新黑盒矩阵值函数的停止准则,以包含前一步的信息。当收敛发生时,我们的两阶段方法返回具有用户选择精度的有理近似值。我们从NLEVP集合中选择问题,这些问题代表了各种不同大小和性质的矩阵值函数,并使用它们对我们的算法进行基准测试。
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引用次数: 7
Active Neuron Least Squares: A Training Method for Multivariate Rectified Neural Networks 主动神经元最小二乘:一种多元校正神经网络的训练方法
Pub Date : 2022-08-01 DOI: 10.1137/21m1460764
M. Ainsworth, Yeonjong Shin
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引用次数: 3
Approximating Longest Common Subsequence in Linear Time: Beating the $sqrt{{n}}$ Barrier 在线性时间内逼近最长公共子序列:突破$sqrt{{n}}$障碍
Pub Date : 2022-08-01 DOI: 10.1137/19m1272068
M. Hajiaghayi, Masoud Seddighin, Saeed Seddighin, Xiaorui Sun
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引用次数: 0
Energy Stable and Mass Conservative Numerical Method for Gas Flow in Porous Media with Rock Compressibility 岩石可压缩性多孔介质中气体流动的能量稳定和质量守恒数值方法
Pub Date : 2022-08-01 DOI: 10.1137/21m1444461
Jisheng Kou, Xiuhua Wang, S. Du
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引用次数: 4
New Optimized Robin-Robin Domain Decomposition Methods using Krylov Solvers for the Stokes-Darcy System Stokes-Darcy系统基于Krylov求解器的Robin-Robin域分解新优化方法
Pub Date : 2022-08-01 DOI: 10.1137/21m1417223
Yingzhi Liu, Y. Boubendir, Xiaoming He, Yinnian He
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引用次数: 3
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