Journal of Computational and Applied Mathematics最新文献

英文中文

Fast convergence rates and trajectory convergence of a Tikhonov regularized inertial primal–dual dynamical system with time scaling and vanishing damping 具有时间缩放和阻尼消失的 Tikhonov 正则化惯性基元二元动力系统的快速收敛率和轨迹收敛性

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-22 DOI: 10.1016/j.cam.2024.116394

Ting Ting Zhu , Rong Hu , Ya Ping Fang

A Tikhonov regularized inertial primal-dual dynamical system with time scaling and vanishing damping is proposed for solving a linearly constrained convex optimization problem in Hilbert spaces. The system under consideration consists of two coupled second order differential equations and its convergence properties depend upon the decaying speed of the product of the time scaling parameter and the Tikhonov regularization parameter (named the rescaled regularization parameter) to zero. When the rescaled regularization parameter converges slowly to zero, the generated primal trajectory converges strongly to the minimal norm solution of the problem under suitable conditions. When the rescaled regularization parameter converges rapidly to zero, the system enjoys fast convergence rates in the primal–dual gap, the feasibility violation, the objective residual, and the gradient norm of the objective function along the trajectory, and the weak convergence of the trajectory to a primal–dual solution of the linearly constrained convex optimization problem. Finally, numerical experiments are performed to illustrate the theoretical findings.

为解决希尔伯特空间中的线性约束凸优化问题，提出了一种具有时间缩放和阻尼消失的 Tikhonov 正则化惯性原始二元动力系统。所考虑的系统由两个耦合二阶微分方程组成，其收敛特性取决于时间缩放参数与 Tikhonov 正则化参数（称为重标定正则化参数）的乘积衰减为零的速度。当重标定正则化参数缓慢收敛到零时，在合适的条件下，生成的基元轨迹会强烈收敛到问题的最小规范解。当重标定正则化参数快速收敛为零时，系统在原始-双重间隙、违反可行性、目标残差和目标函数梯度法等方面沿轨迹都有较快的收敛速度，并且轨迹弱收敛于线性约束凸优化问题的原始-双重解。最后，进行了数值实验来说明理论结论。

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引用次数: 0

Developing and analyzing a FDTD method for simulation of metasurfaces 开发和分析用于模拟超表面的 FDTD 方法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-21 DOI: 10.1016/j.cam.2024.116364

Yunqing Huang , Chanjie Li , Jichun Li

Metasurfaces as 2-D metamaterials have a subwavelength thickness. Direct simulation is very challenging since very fine meshes are needed around the metasurfaces. Here we develop the generalized sheet transition conditions (GSTCs) based finite-difference time-domain (FDTD) scheme by treating the metasurface as a zero-thickness plane. The effectiveness of the scheme is illustrated by three representative examples. We raise the open issue on how to establish the numerical stability of such GSTC-based FDTD scheme.

作为二维超材料的超表面具有亚波长厚度。由于超表面周围需要非常精细的网格，因此直接模拟非常具有挑战性。在这里，我们将超表面视为零厚度平面，开发了基于广义薄片过渡条件（GSTCs）的有限差分时域（FDTD）方案。我们通过三个具有代表性的例子说明了该方案的有效性。我们提出了如何建立这种基于 GSTC 的 FDTD 方案的数值稳定性这一未决问题。

引用次数: 0

On time integrators for Generalized Multiscale Finite Element Methods applied to advection–diffusion in high-contrast multiscale media 关于应用于高对比度多尺度介质中平流-扩散的广义多尺度有限元方法的时间积分器

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-19 DOI: 10.1016/j.cam.2024.116363

Wei Xie , Juan Galvis , Yin Yang , Yunqing Huang

Despite recent progress in dealing with advection–diffusion problems in high-contrast multiscale settings, there is still a need for methods that speed up calculations without compromising accuracy. In this paper, we consider the challenges of unsteady diffusion–advection problems in the presence of multiscale high-contrast media. We use the Generalized Multiscale Method (GMsFEM) as the space discretization and pay extra attention to the time solver. Traditional finite-difference methods’ accuracy and stability deteriorate in the presence of high contrast and also with an advection term. Following Contreras et al. (2023), we use exponential integrators to handle the time dependence, fully utilizing the advantages of the generalized multiscale method. For situations dominated by diffusion, our approach aligns with previous work. However, in cases where advection starts to dominate, we introduce a different local generalized eigenvalue problem to build the multiscale basis functions. This adjustment makes things more efficient since the basis functions retain more information related to the advection term. We present experiments to demonstrate the effectiveness of our proposed method.

尽管最近在处理高对比度多尺度环境下的平流-扩散问题方面取得了进展，但仍然需要在不影响精度的前提下加快计算速度的方法。在本文中，我们考虑了存在多尺度高对比度介质的非稳态扩散-平流问题所面临的挑战。我们使用广义多尺度法（GMsFEM）作为空间离散化方法，并对时间求解器给予了特别关注。传统有限差分法的精度和稳定性在高对比度和平流项的情况下会下降。继 Contreras 等人（2023 年）之后，我们使用指数积分器来处理时间依赖性，充分发挥了广义多尺度方法的优势。对于以扩散为主的情况，我们的方法与之前的工作一致。但是，在平流开始占主导地位的情况下，我们引入了一个不同的局部广义特征值问题来构建多尺度基础函数。由于基函数保留了更多与平流项相关的信息，因此这一调整提高了效率。我们将通过实验来证明我们提出的方法的有效性。

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引用次数: 0

A combined integer-valued autoregressive process with actuarial applications 具有精算应用价值的整数值自回归组合过程

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-19 DOI: 10.1016/j.cam.2024.116384

Xiang Hu , Jing Yao

This paper proposes a modification of a combined integer-valued autoregressive (CINAR) process based on binomial thinning, which is instrumental in modeling higher-order dependence between the number of claims in an insurance portfolio. The modified CINAR process is more general and enjoys stationarity and flexibility in higher-order serial dependence modeling. Two actuarial applications of the proposed process in risk theory and credibility model are explored. As an application to risk theory, we derive the distribution of aggregate claims under a discrete-time collective risk model and examine the effect of high-order dependence on the tail-related risk measures of the aggregate claims. Next, we apply the modified CINAR process to account for the unobserved gamma heterogeneity in determining the dynamics of the predictive credibility premium. A real data analysis shows that our approach provides a superior pattern to the predictive premium calculation when compared to the outcomes of several alternative models.

本文提出了一种基于二项稀疏化的组合整数值自回归（CINAR）过程的修正方法，该方法有助于对保险组合中索赔数量之间的高阶依赖性进行建模。改进后的 CINAR 过程更加通用，在高阶序列依赖性建模中具有静态性和灵活性。我们探讨了拟议过程在风险理论和可信度模型中的两种精算应用。在风险理论的应用中，我们推导了离散时间集体风险模型下的总索赔分布，并研究了高阶依赖性对总索赔尾部相关风险度量的影响。接下来，我们应用修正的 CINAR 过程来解释在确定预测可信溢价动态时未观察到的伽马异质性。实际数据分析表明，与其他几种模型的结果相比，我们的方法提供了更优越的预测溢价计算模式。

引用次数: 0

An immersed interface neural network for elliptic interface problems 用于椭圆界面问题的沉浸界面神经网络

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-19 DOI: 10.1016/j.cam.2024.116372

Xinru Zhang, Qiaolin He

In this paper, a new immersed interface neural network (IINN) is proposed for solving interface problems in a regular domain with jump discontinuities on an embedded irregular interface. This method is introduced in Poisson interface problems, which can also be generalized to solving Stokes interface problems and elliptic interface problems. The main idea is using neural network to approximate the extension of the known jump conditions along the normal lines of the interface and constructing a discontinuity capturing function. With such function, the interface problem with a non-smooth solution can be changed to the problem with a smooth solution. The numerical result is composed of the discontinuity capturing function and the smooth solution. There are four novel features in the present work: (i) the jump discontinuities can be accurately captured; (ii) it is not required to label the mesh around the interface and finding the correction term like Immersed Interface Method (IIM); (iii) it is completely mesh-free for training the discontinuity capturing function; (iv) it preserves second-order accuracy for the solution. The numerical results show that the IINN is comparable and behaves better than the traditional immersed interface method and other neural network methods.

本文提出了一种新的沉浸式界面神经网络 (IINN)，用于解决规则域中带有嵌入式不规则界面上跳跃不连续的界面问题。这种方法是在泊松界面问题中引入的，也可以推广到斯托克斯界面问题和椭圆界面问题的求解中。其主要思想是利用神经网络来近似沿界面法线延伸的已知跳跃条件，并构建一个不连续捕捉函数。有了这种函数，非光滑解的界面问题就可以转变为光滑解的问题。数值结果由不连续捕捉函数和光滑解组成。本研究有四个新特点：(i) 可以准确捕捉跳跃不连续；(ii) 不需要像沉浸界面法（IIM）那样标注界面周围的网格和寻找修正项；(iii) 在训练不连续捕捉函数时完全不需要网格；(iv) 保持了解的二阶精度。数值结果表明，IINN 与传统的沉入式界面方法和其他神经网络方法相比，具有可比性和更好的性能。

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引用次数: 0

A stochastic Bregman golden ratio algorithm for non-Lipschitz stochastic mixed variational inequalities with application to resource share problems 非 Lipschitz 随机混合变分不等式的随机布雷格曼黄金比率算法，应用于资源共享问题

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-19 DOI: 10.1016/j.cam.2024.116381

Xian-Jun Long, Jing Yang

In the study of stochastic mixed variational inequalities(SMVIs), Lipschitz is an indispensable assumption for the convergence analysis. However, practical applications may not satisfy this assumption. In this paper, we propose a stochastic Bregman golden ratio algorithm for solving non-Lipschitz SMVIs. Since our algorithm only requires to calculate one stochastic approximation of the expected mapping per iteration, the computations can be reduced. Under some moderate conditions, we prove the almost surely convergence of the iteration sequence and the

O (1 / K)

convergence rate, where

K

denotes the maximum iteration. Furthermore, we derive the probabilities of large deviation results, which provide a high probability guarantee for the convergence of the proposed algorithm. Numerical experiments on Logistic regression problems and modified entropy regularized LP boosting problems show that our algorithm is competitive compared with some existing algorithms. Finally, we apply our algorithm to solve a non-Lipschitz resource sharing problem.

在随机混合变分不等式（SMVI）的研究中，Lipschitz 是进行收敛分析不可或缺的假设。然而，实际应用中可能无法满足这一假设。本文提出了一种用于求解非 Lipschitz SMVI 的随机 Bregman 黄金比率算法。由于我们的算法每次迭代只需要计算一个预期映射的随机近似值，因此可以减少计算量。在一些适度条件下，我们证明了迭代序列几乎肯定收敛，收敛率为 O(1/K)，其中 K 表示最大迭代次数。此外，我们还推导出了大偏差概率结果，为所提算法的收敛性提供了高概率保证。在逻辑回归问题和修正熵正则化 LP 提升问题上的数值实验表明，与一些现有算法相比，我们的算法具有很强的竞争力。最后，我们应用我们的算法解决了一个非 Lipschitz 资源共享问题。

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引用次数: 0

Two sixth-order, L∞ convergent, and stable compact difference schemes for the generalized Rosenau-KdV-RLW equation 广义罗森诺-KdV-RLW方程的两种六阶、L∞收敛且稳定的紧凑差分方案

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-19 DOI: 10.1016/j.cam.2024.116382

Xin Zhang , Yiran Zhang , Qunzhi Jin , Yuanfeng Jin

In this paper, two sixth-order compact finite difference schemes for the generalized Rosenau-KdV-RLW equation are investigated, which utilize novel sixth-order operators. One is a two-level nonlinear difference scheme, while the other is a three-level linearized difference scheme. The schemes both achieve second-order and sixth-order accuracy in time and space, respectively. The proposed two schemes preserve key properties of the original equation in a discrete sense. Numerical results are presented to validate the theoretical findings, demonstrating the efficiency and reliability of the proposed compact approaches. Significantly, the proposed sixth-order operators can be extended to numerical algorithms for other equations.

本文利用新颖的六阶算子，研究了广义 Rosenau-KdV-RLW 方程的两种六阶紧凑有限差分方案。一个是两级非线性差分方案，另一个是三级线性化差分方案。这两种方案在时间和空间上都分别达到了二阶和六阶精度。所提出的两种方案在离散意义上保留了原始方程的关键特性。为了验证理论结论，我们给出了数值结果，证明了所提出的紧凑方法的效率和可靠性。值得注意的是，所提出的六阶算子可以扩展到其他方程的数值算法中。

引用次数: 0

An accelerated decentralized stochastic optimization algorithm with inexact model 具有不精确模型的加速分散随机优化算法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-18 DOI: 10.1016/j.cam.2024.116383

Xuexue Zhang , Sanyang Liu , Nannan Zhao

This paper considers the decentralized stochastic optimization problems where each node of network has only access to the local large data samples and local functions, which are distributed to the computational nodes. We extend the centralized fast adaptive gradient method with inexact model to deal with the large scale problem in the decentralized manner. Moreover, we propose an accelerated decentralized stochastic optimization algorithm with reconstructing parameter equations and defining new approximate local functions. Further, we provide the convergence analysis of the proposed algorithm and illustrate that our algorithm can achieve both the optimal stochastic oracle complexity and communication complexity that depend on the global condition number. Finally, the numerical experiments validate the convergence results of the proposed algorithm.

本文考虑的是分散式随机优化问题，即网络中的每个节点只能访问本地的大数据样本和本地函数，而这些样本和函数分布在计算节点上。我们扩展了具有不精确模型的集中式快速自适应梯度法，以分散方式处理大规模问题。此外，我们还提出了一种加速分散随机优化算法，该算法具有重构参数方程和定义新近似局部函数的功能。此外，我们还提供了所提算法的收敛性分析，并说明我们的算法可以同时实现取决于全局条件数的最优随机神谕复杂度和通信复杂度。最后，数值实验验证了所提算法的收敛结果。

引用次数: 0

H(curl2)-conforming triangular spectral element method for quad-curl problems 四曲面问题的 H(curl2)-符合三角谱元法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-17 DOI: 10.1016/j.cam.2024.116362

Lixiu Wang , Huiyuan Li , Qian Zhang , Zhimin Zhang

In this paper, we consider the

H ({curl}^{2})

-conforming triangular spectral element method to solve the quad-curl problems. We first explicitly construct the

H ({curl}^{2})

-conforming elements on triangles through the contravariant transform and the affine mapping from the reference element to physical elements. These constructed elements possess a hierarchical structure and can be categorized into the kernel space and non-kernel space of the curl operator. We then establish

H ({curl}^{2})

-conforming triangular spectral element spaces and the corresponding mixed formulated spectral element approximation scheme for the quad-curl problems and related eigenvalue problems. Subsequently, we present the best spectral element approximation theory in

H ({curl}^{2}; Ω)

-seminorms. Notably, the degrees of polynomials in the kernel space solely impact the convergence rate of the

{(L^{2} (Ω))}^{2}

-norm of

u_{h}

, without affecting the semi-norm of

H (curl; Ω)

and

H ({curl}^{2}; Ω)

. This observation enables us to derive eigenvalue approximations from either the upper or lower side by selecting different degrees of polynomials for the kernel space and non-kernel space of the curl operator. Finally, numerical results demonstrate the effectiveness and efficiency of our method.

在本文中，我们考虑用H(curl2)-conform三角谱元法来解决四曲面问题。我们首先通过从参考元素到物理元素的协变变换和仿射映射，在三角形上明确地构造出 H(curl2)-conforming 元素。这些构建的元素具有层次结构，可分为卷曲算子的核空间和非核空间。然后，我们为四卷问题和相关特征值问题建立了 H(curl2)-conforming 三角谱元空间和相应的混合配制谱元近似方案。随后，我们提出了 H(curl2;Ω)-seminorms 中的最佳谱元近似理论。值得注意的是，核空间中多项式的度数只影响 uh 的 (L2(Ω))2 准则的收敛速度，而不影响 H(curl;Ω) 和 H(curl2;Ω) 的半准则。这一观察结果使我们能够通过为卷曲算子的核空间和非核空间选择不同的多项式度，从上边或下边推导出特征值近似值。最后，数值结果证明了我们方法的有效性和效率。

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引用次数: 0

An alternating shifted higher order power method based algorithm for rank-R Hermitian approximation and solving Hermitian CP-decomposition problems 基于交替移位高阶幂方法的秩R赫米蒂近似算法和赫米蒂CP分解问题求解方法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-11-16 DOI: 10.1016/j.cam.2024.116385

Xiaofang Xin, Guyan Ni, Ying Li

The Hermitian tensor is a higher order extension of the Hermitian matrix that can be used to represent quantum mixed states and solve problems such as entanglement and separability of quantum mixed states. In this paper, we propose a novel numerical algorithm, an alternating shifted higher order power method (AS-HOPM), for rank-

R

Hermitian approximation, which can also be used to compute Hermitian Candecomp/Parafac (CP) decomposition. At the same time, for the choice of initial points, we give a Broyden–Fletcher–Goldfarb–Shanno (BFGS) method based on unconstrained optimization, and propose a BFGS-AS-HOPM algorithm for rank-

R

Hermitian approximation. For solving the Hermitian CP-decomposition problem, numerical experiments show that using the BFGS-AS-HOPM algorithm has a higher success rate than using the AS-HOPM algorithm alone.

赫米提张量是赫米提矩阵的高阶扩展，可用来表示量子混合态，解决量子混合态的纠缠和可分离性等问题。本文提出了一种新颖的数值算法--交替移位高阶幂方法（AS-HOPM），用于秩R赫米提近似，也可用于计算赫米提Candecomp/Parafac（CP）分解。同时，对于初始点的选择，我们给出了一种基于无约束优化的 Broyden-Fletcher-Goldfarb-Shanno (BFGS) 方法，并提出了一种用于秩-R 赫米提近似的 BFGS-AS-HOPM 算法。数值实验表明，在求解赫米蒂CP分解问题时，使用BFGS-AS-HOPM算法比单独使用AS-HOPM算法具有更高的成功率。

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