Journal of Computational and Applied Mathematics最新文献

英文中文

Detective generalized multiscale hybridizable discontinuous Galerkin(GMsHDG) method for porous media 探测多孔介质的广义多尺度可混合非连续伽勒金（GMsHDG）方法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-22 DOI: 10.1016/j.cam.2024.116320

Do Yang Park, Minam Moon

The Detective Generalized Multiscale Hybridizable Discontinuous Galerkin (Detective GMsHDG) method aims to further reduce the computational cost of the GMsHDG method. The GMsHDG method itself reduces the computational cost of the HDG method by employing an upscaled structure on a two-grid mesh. Given a PDE within a specified domain, we subdivide the domain into polygonal subdomains and transforms a HDG problem into globular and local problems. Globular problem concerns whether the solutions on smaller domains glue well to form a globular solution. The process involves generation of multiscale spaces, which is a vector space of functions defined on edges of the polygonal regions. A naive approximation by polynomials fails, especially in porous media, necessitating the generation of problem-specific spaces. The Detective GMsHDG method improves this process by replacing the generation of the multiscale space with the detective algorithm. The Detective GMsHDG method has two stages. First is called an offline stage. During the offline stage, we construct a detective function which, given a permeability distribution, it gives a multiscale space. Later stage is called the offline stage where, given the multiscale space, we use GMsHDG method to solve a given PDE numerically. We show numerical results to argue the liability of the solution using the detective GMsHDG method.

Detective Generalized Multiscale Hybridizable Discontinuous Galerkin（Detective GMsHDG）方法旨在进一步降低 GMsHDG 方法的计算成本。GMsHDG 方法本身通过在双网格上采用放大结构降低了 HDG 方法的计算成本。给定域内的一个 PDE，我们将域细分为多边形子域，并将 HDG 问题转化为球状问题和局部问题。全局问题涉及较小域上的解是否能很好地粘合以形成全局解。这一过程包括生成多尺度空间，即定义在多边形区域边缘上的函数向量空间。用多项式进行天真的近似是失败的，尤其是在多孔介质中，因此必须生成特定问题的空间。通过用侦探算法取代多尺度空间的生成，侦探式 GMsHDG 方法改进了这一过程。Detective GMsHDG 方法分为两个阶段。第一个阶段称为离线阶段。在离线阶段，我们构建一个侦探函数，在给定渗透率分布的情况下，给出一个多尺度空间。后一阶段称为离线阶段，在这一阶段，给定多尺度空间后，我们使用 GMsHDG 方法对给定的 PDE 进行数值求解。我们将展示数值结果，以论证使用 GMsHDG 侦探方法求解的可行性。

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引用次数: 0

A novel post-processed finite element method and its convergence for partial differential equations 新颖的后处理有限元方法及其对偏微分方程的收敛性

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-22 DOI: 10.1016/j.cam.2024.116319

Wenming He , Jiming Wu , Zhimin Zhang

In this article, by combining high-order interpolation on coarse meshes and low-order finite element solutions on fine meshes, we propose a novel approach to improve the accuracy of the finite element method. The new method is in general suitable for most partial differential equations. For simplicity, we use the second-order elliptic problem as an example to show how the novel approach improves the accuracy of the finite element method. Numerical tests are also conducted to validate the main theoretical results.

本文结合粗网格上的高阶插值和细网格上的低阶有限元求解，提出了一种提高有限元方法精度的新方法。新方法一般适用于大多数偏微分方程。为简单起见，我们以二阶椭圆问题为例，说明新方法如何提高有限元方法的精度。我们还进行了数值测试，以验证主要理论结果。

引用次数: 0

An efficient Newton-type matrix splitting algorithm for solving generalized absolute value equations with application to ridge regression problems 用于求解广义绝对值方程的高效牛顿型矩阵分割算法及其在脊回归问题中的应用

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-22 DOI: 10.1016/j.cam.2024.116329

Xuehua Li, Cairong Chen

A generalized Newton-based matrix splitting (GNMS) method is proposed for solving the generalized absolute value equations (GAVEs). Under mild conditions, the GNMS method converges to the unique solution of GAVEs. Moreover, we can obtain a few weaker convergence conditions for some existing methods. Numerical results verify the effectiveness of the proposed method.

本文提出了一种求解广义绝对值方程（GAVE）的基于牛顿的广义矩阵分割（GNMS）方法。在温和条件下，GNMS 方法能收敛到广义绝对值方程的唯一解。此外，我们还可以得到一些现有方法的较弱收敛条件。数值结果验证了所提方法的有效性。

引用次数: 0

Dimension reduction based on time-limited cross Gramians for bilinear systems 基于双线性系统的限时交叉格拉米安法降维

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-16 DOI: 10.1016/j.cam.2024.116302

Zhi-Hua Xiao , Yao-Lin Jiang , Zhen-Zhong Qi

The cross Gramian is a useful tool in model order reduction but only applicable to square dynamical systems. Throughout this paper, time-limited cross Gramians is firstly extended to square bilinear systems that satisfies a generalized Sylvester equation, and then concepts from decentralized control are used to approximate a cross Gramian for non-square bilinear systems. In order to illustrate these cross Gramians, they are calculated efficiently based on shifted Legendre polynomials and applied to dimension reduction, which leads to a lower dimensional model by truncating the states that are associated with smaller approximate generalized Hankel singular values. In combination of the dominant subspace projection method, our reduction procedure is modified to produce a bounded-input bounded-output stable-preserved reduced model under some certain conditions. At last, the performance of numerical experiments indicates the validity of our reduction methods.

交叉格拉米安是减少模型阶次的有用工具，但只适用于方形动力系统。本文首先将限时交叉格拉米安扩展到满足广义西尔维斯特方程的平方双线性系统，然后利用分散控制的概念来近似非平方双线性系统的交叉格拉米安。为了说明这些交叉格拉米安，我们基于移位 Legendre 多项式对其进行了有效计算，并将其应用于降维，通过截断与较小的近似广义汉克尔奇异值相关的状态，从而得到一个低维模型。结合主导子空间投影法，我们的降维程序经过修改，在某些特定条件下产生了有界输入有界输出的稳定保留降维模型。最后，数值实验结果表明我们的还原方法是有效的。

引用次数: 0

Numerical analysis of a thermoelastic problem of Moore–Gibson–Thompson type with history dependence in the thermal displacement 具有热位移历史依赖性的摩尔-吉布森-汤普森型热弹性问题的数值分析

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-16 DOI: 10.1016/j.cam.2024.116317

N. Bazarra , J.R. Fernández , R. Quintanilla

In this work, we study, from the numerical point of view, a heat conduction model which is described by the history dependent version of the Moore–Gibson–Thompson equation. First, we consider the thermal problem, introducing a fully discrete approximation by means of the finite element method and the implicit Euler scheme. The discrete stability of its solution is proved, and an a priori error analysis is provided, which leads to the linear convergence imposing suitable regularity conditions. Secondly, we deal with the natural extension to the thermoelastic case. Following the analysis of the thermal problem, similar results are shown. Finally, we present some one-dimensional numerical simulations for both problems which demonstrate the accuracy of the approximations and the behavior of the discrete energies and the solutions.

在这项工作中，我们从数值角度研究了一个热传导模型，该模型由与历史相关的摩尔-吉布森-汤普森方程版本描述。首先，我们考虑了热问题，通过有限元法和隐式欧拉方案引入了完全离散的近似方法。我们证明了其解的离散稳定性，并提供了先验误差分析，从而在适当的正则条件下实现线性收敛。其次，我们讨论了热弹性情况的自然扩展。根据对热问题的分析，我们得出了类似的结果。最后，我们介绍了这两个问题的一些一维数值模拟，证明了近似的准确性以及离散能量和解的行为。

引用次数: 0

Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D 针对二维奇异扰动四阶问题的 Shishkin 网格弱 Galerkin 有限元方法的收敛性分析

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-15 DOI: 10.1016/j.cam.2024.116324

Shicheng Liu , Xiangyun Meng , Qilong Zhai

In this paper, we apply the weak Galerkin (WG) finite element method to solve the singularly perturbed fourth-order boundary value problem in a 2D domain. A Shishkin mesh is used to ensure that the method exhibits uniform convergence, regardless of the singular perturbation parameter. Asymptotically optimal order error estimate in a

H^{2}

discrete norm is established for the corresponding WG solutions. Numerical tests are provided to verify the convergence theory.

本文采用弱 Galerkin（WG）有限元法求解二维域中的奇异扰动四阶边界值问题。我们使用 Shishkin 网格来确保该方法表现出均匀的收敛性，而不受奇异扰动参数的影响。为相应的 WG 解建立了 H2 离散规范下的渐近最优阶误差估计。提供了数值测试来验证收敛理论。

引用次数: 0

Non-Intrusive Reduced Basis two-grid method for flow and transport problems in heterogeneous porous media 用于解决异质多孔介质中的流动和传输问题的非侵入式还原基础双网格法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-15 DOI: 10.1016/j.cam.2024.116321

Wansheng Gao , Ludovic Chamoin , Insa Neuweiler

Due to its non-intrusive nature and ease of implementation, the Non-Intrusive Reduced Basis (NIRB) two-grid method has gained significant popularity in numerical computational fluid dynamics simulations. The efficiency of the NIRB method hinges on separating the procedure into offline and online stages. In the offline stage, a set of high-fidelity computations is performed to construct the reduced basis functions, which is time-consuming but is only executed once. In contrast, the online stage adapts a coarse-grid model to retrieve the expansion coefficients of the reduced basis functions. Thus it is much less costly than directly solving a high-fidelity model. However, coarse grids in heterogeneous porous media of flow models are often accompanied by upscaled hydraulic parameters (e.g. hydraulic conductivity), thus introducing upscaling errors. In this work, we introduce the two-scale idea to the existing NIRB two-grid method: when dealing with coarse-grid models, we also employ upscaled model parameters. Both the discretization and upscaling errors are compensated by the rectification post-processing. The numerical examples involve flow and heat transport problems in heterogeneous hydraulic conductivity fields, which are generated by self-affine random fields. Our research findings indicate that the modified NIRB method can effectively capture the large-scale features of numerical solutions, including pressure, velocity, and temperature. However, accurately retrieving velocity fields with small-scale features remains highly challenging.

由于其非侵入性和易于实施的特点，非侵入还原基（NIRB）双网格法在数值计算流体动力学模拟中大受欢迎。NIRB 方法的效率取决于将程序分为离线和在线两个阶段。在离线阶段，需要进行一系列高保真计算来构建还原基函数，虽然耗时，但只需执行一次。相比之下，在线阶段则通过调整粗网格模型来检索还原基函数的扩展系数。因此，它比直接求解高保真模型的成本要低得多。然而，异质多孔介质流动模型中的粗网格往往伴随着放大的水力参数（如水力传导率），从而引入放大误差。在这项工作中，我们在现有的 NIRB 双网格方法中引入了双尺度思想：在处理粗网格模型时，我们也采用了放大模型参数。离散化误差和放大误差都可以通过整流后处理得到补偿。数值示例涉及异质水力传导场中的流动和热量传输问题，这些问题由自线性随机场生成。研究结果表明，改进的 NIRB 方法能有效捕捉数值解的大尺度特征，包括压力、速度和温度。然而，精确获取具有小尺度特征的速度场仍然具有很大的挑战性。

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引用次数: 0

Analysis of dependent complementary competing risks data from a generalized inverted family of lifetime distributions under a maximum ranked set sampling procedure with unequal samples 在最大排序集抽样程序下，对来自广义倒置寿命分布族的依赖性互补竞争风险数据进行不等样分析

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-11 DOI: 10.1016/j.cam.2024.116309

Liang Wang , Chunfang Zhang , Yogesh Mani Tripathi , Yuhlong Lio

This paper explores analysis of a dependent complementary competing risks model when the failure causes are distributed by the proposed generalized inverted family of lifetime distributions. Under maximum ranked set sampling with unequal samples (MRSSU), statistical inference of model parameters and reliability indices is discussed under classical frequentist and Bayesian approaches, respectively. Maximum likelihood estimators along with their existence and uniqueness are obtained for model parameters, and associated approximate confidence intervals are constructed in consequence. Bayesian estimation is also performed with respect to general flexible priors, and the Markov Chain Monte Carlo (MCMC) algorithm is proposed for complex posterior computation. The study further examines classical and Bayesian estimations with order restriction of parameters when additional historical information is available in the MRSSU scenario. Finally, the performance of different results is evaluated through numerical simulations and a real data example is presented for demonstrating the application of our methods.

本文探讨了当故障原因按所提出的广义倒置寿命分布族分布时，对依赖性互补竞争风险模型的分析。在不等样本的最大排序集抽样（MRSSU）下，分别用经典的频数法和贝叶斯法讨论了模型参数和可靠性指数的统计推断。研究获得了模型参数的最大似然估计值及其存在性和唯一性，并由此构建了相关的近似置信区间。研究还针对一般灵活先验进行了贝叶斯估计，并提出了用于复杂后验计算的马尔可夫链蒙特卡罗（MCMC）算法。在 MRSSU 情景中，当有额外的历史信息时，研究进一步检验了带有参数阶次限制的经典估计和贝叶斯估计。最后，通过数值模拟对不同结果的性能进行了评估，并提供了一个真实数据示例来演示我们方法的应用。

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引用次数: 0

A mathematical model for the role of vaccination and treatment in measles transmission in Turkey 疫苗接种和治疗在土耳其麻疹传播中的作用数学模型

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-11 DOI: 10.1016/j.cam.2024.116308

Osman Rasit Isik , Necibe Tuncer , Maia Martcheva

A previously developed and analyzed deterministic model for the transmission dynamics of measles, which takes into account the possibility of vaccinated people also contracting the disease, has been developed for Turkey. The model consists of nine compartments. The structural identifiability of the model was examined using software and detailed tables are given assuming that the incidence is given for structural identifiability. As a result of this analysis, the model is found to be structurally identifiable if at least two parameters are given along with the incidence. The parameters in this non-autonomous model are determined by considering the 1970–2021 measles case numbers in Turkey. We realize that the changes in immigration rates in Turkey, especially since the early 2000s, the changes in vaccination rates from 1970 to the present, and the changes in the vaccination rates of susceptible individuals, are significant changes in terms of time, and so we assume that these three parameters are time dependent. The practical identifiability of the model with the determined parameters is examined and it is found that if two parameters are given, all parameters except five parameters are practical identifiable. Unidentified parameters are fixed to a value by taking reference sources into account, and a model with all parameters practically identifiable is achieved. With the obtained values, the associated reproduction number of the model was obtained as 1.07 which means that the disease will persist in Turkey.

先前为土耳其开发并分析了一个麻疹传播动态的确定性模型，该模型考虑到了接种过疫苗的人也有可能感染该疾病。该模型由九个部分组成。使用软件对模型的结构可识别性进行了检验，并提供了详细的表格，假定发病率为结构可识别性。分析结果表明，如果至少给出两个参数和发生率，模型在结构上是可识别的。这个非自主模型的参数是通过考虑 1970-2021 年土耳其麻疹病例数确定的。我们意识到，土耳其移民率的变化（尤其是自 21 世纪初以来）、1970 年至今疫苗接种率的变化以及易感人群疫苗接种率的变化都是时间方面的重大变化，因此我们假定这三个参数与时间相关。我们利用确定的参数对模型的实际可识别性进行了研究，结果发现，如果给出两个参数，则除五个参数外的所有参数都是实际可识别的。考虑到参考源，将无法识别的参数固定为一个值，这样就可以得到一个所有参数都可实际识别的模型。根据获得的数值，模型的相关繁殖数为 1.07，这意味着该疾病将在土耳其持续存在。

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引用次数: 0

Pricing of timer volatility-barrier options under Heston’s stochastic volatility model 赫斯顿随机波动率模型下的定时波动率障碍期权定价

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2024-10-11 DOI: 10.1016/j.cam.2024.116310

Mijin Ha , Donghyun Kim , Ji-Hun Yoon

Timer options are financial instruments that enable investors to exercise their rights on a random maturity date the realized variance reaches the level of variance budget. These options provide a stable investment opportunity for investors under the unpredictable and complex financial markets, such as global financial crisis or COVID-19 pandemic, which can induce the drastic changes of the volatility for the underlying asset. Meanwhile, in the financial markets, investors who invest in standard timer options may face the problems caused by the postponement of the exercising time for too low volatility, compared to standard vanilla options. In this regard, to overcome such disadvantages, we propose timer volatility-barrier options, which are activated and expired when the volatility arrives at a relatively low barrier level, with the original properties of the standard timer options. In this paper, by making use of the method of images, we derive an analytical formulas for the timer volatility-barrier options so that the volatility process can be driven by Heston stochastic volatility model, and verify the pricing accuracy of the timer options by comparing our solutions with those obtained from Monte Carlo simulations. Finally, we conduct numerical studies on the timer volatility-barrier options to examine the pricing sensitivities with respect to the various model parameters, and implement the discussion for pricing formula of double volatility barrier type of the timer options.

定时期权是一种金融工具，它使投资者能够在随机到期日行使其权利，即已实现的波动率达到波动率预算水平。在全球金融危机、COVID-19 大流行等不可预测的复杂金融市场环境下，这些期权为投资者提供了一个稳定的投资机会。同时，在金融市场中，与标准虚值期权相比，投资标准定时期权的投资者可能会面临因波动率过低而推迟行权时间的问题。为此，为了克服这种弊端，我们提出了定时波动率障碍期权，当波动率到达一个相对较低的障碍水平时，该期权被激活并到期，同时具有标准定时期权的原有特性。本文利用图像法推导出了定时波动率-障碍期权的解析公式，使波动率过程可以由 Heston 随机波动率模型驱动，并通过将我们的解与蒙特卡罗模拟得到的解进行比较，验证了定时期权的定价准确性。最后，我们对定时波动率壁垒期权进行了数值研究，以检验定价对各种模型参数的敏感性，并对定时期权双波动率壁垒类型的定价公式进行了讨论。

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