Computers & Mathematics with Applications最新文献

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Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the overlapping triangular finite elements 基于重叠三角形有限元的三相磁电弹性结构动力学分析

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.11.025

Cong Liu , Kaifu Li , Shaosong Min , Yingbin Chai

The conventional finite element method (FEM) usually fails to generate sufficiently fine numerical solutions in the analyses of Mageto-electro-elastic (MEE) structures in which three different types of physical fields are coupled together. To enhance the performance of the FEM in analyzing MEE structures, in this work a novel overlapping triangular finite element is introduced for dynamic analysis of MEE structures. In this new paradigm for finite element analysis, both local and global numerical approximations are used to construct the considered three-phase physical fields. The local numerical approximation is built by using the method of finite spheres (MFS) and the global numerical approximation is based on the traditional finite element interpolation. In the local numerical approximation, the polynomials or other specially-designed functions can be used as the nodal degrees of freedom. Free vibration and harmonic response analyses are carried out to show the abilities of the overlapping triangular elements in analyzing the three-phase MEE structures. It is demonstrated by the numerical solutions that the present overlapping triangular elements are much more effective to predict the dynamic behaviors of the MEE structures and more accurate solutions can be generated than the traditional FEM with the same mesh. Therefore, the present overlapping triangular elements embody great potential in analyzing various complicated MEE structures in practical engineering applications.

传统的有限元方法（FEM）在分析三种不同类型的物理场耦合在一起的磁-电弹性（MEE）结构时，往往不能得到足够精细的数值解。为了提高有限元法在MEE结构分析中的性能，本文引入了一种新的重叠三角形有限元法用于MEE结构的动力分析。在这种新的有限元分析范式中，使用局部和全局数值近似来构建所考虑的三相物理场。局部数值逼近采用有限球法（MFS），全局数值逼近采用传统有限元插值法。在局部数值逼近中，可以使用多项式或其他特殊设计的函数作为节点自由度。通过自由振动和谐波响应分析，证明了重叠三角形单元分析三相MEE结构的能力。数值计算结果表明，与传统有限元方法相比，采用重叠三角形单元法可以更有效地预测结构的动力特性，并能得到更精确的解。因此，目前的三角重叠单元在实际工程应用中对各种复杂MEE结构的分析具有很大的潜力。

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引用次数: 0

Finding minimal cubature rules for finite elements passing the patch test 寻找通过补丁测试的有限元素的最小曲率规则

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.11.030

Weizhu Wang, Stefanos-Aldo Papanicolopulos

Cubature, i.e. multivariate numerical integration, plays a core part in the finite-element method. For a given element geometry and interpolation, it is possible to choose different cubature rules, leading to concepts like full and reduced integration. These cubature rules are usually chosen from a rather small set of existing rules, which were not specifically derived for finite-element applications, and may therefore not be optimal.

We present a novel method to find element-specific cubature rules, based only on the requirement that the element passes the patch test. Starting from the monomial sets generating the displacement and geometry interpolations, the method computes the monomials that must be integrated exactly, and thus the moment equations that generate the required rules.

We use the presented method to compute rules for quadrilateral and hexahedral elements which try to minimise the number of integration points required, and test the resulting elements using a series of standard tests. The results show that, for higher-order interpolation, several of these new rules have an advantage over existing ones.

立体，即多元数值积分，是有限元法的核心部分。对于给定的元素几何和插值，可以选择不同的培养规则，从而产生完整和减少集成等概念。这些培养规则通常是从一组相当小的现有规则中选择的，这些规则并不是专门为有限元应用而衍生的，因此可能不是最优的。

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引用次数: 0

LRBF meshless methods for predicting soil moisture distribution in root zone 无网格LRBF法预测根区土壤水分分布

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.11.028

Mohamed Boujoudar , Abdelaziz Beljadid , Ahmed Taik

The main purpose of this study is to develop a numerical model of unsaturated flow in soils with plant root water uptake. The Richards equation and different sink term formulations are used in the numerical model to describe the distribution of soil moisture in the root zone. The Kirchhoff transformed Richards equation is used and the Gardner model is considered for capillary pressure. In the proposed numerical approach, we used localized radial basis function (LRBF) meshless techniques in space and the backward Euler scheme for temporal discretization to solve the system. The LRBF approach is an accurate and computationally efficient method that does not require mesh generation and is flexible in addressing high-dimensional problems. Furthermore, this method leads to a sparse matrix system, which avoids ill-conditioning issues. We implement the numerical model of infiltration and plant root water uptake for one, two, and three-dimensional soils. Numerical experiments are performed using nontrivial analytical solutions and available experimental data to validate the performance of the proposed numerical techniques. The results demonstrate the capability of the proposed numerical model to predict soil moisture dynamics in root zone.

本研究的主要目的是建立一个有植物根系吸水的土壤非饱和流动数值模型。数值模型采用理查兹方程和不同的汇项公式来描述根区土壤水分的分布。其中使用了基尔霍夫变换理查兹方程，并考虑了毛细管压力的加德纳模型。在拟议的数值方法中，我们采用了空间局部径向基函数（LRBF）无网格技术和时间离散化的后向欧拉方案来求解系统。LRBF 方法是一种精确且计算效率高的方法，无需生成网格，可灵活处理高维问题。此外，这种方法还能得到稀疏矩阵系统，从而避免了条件不良问题。我们为一维、二维和三维土壤建立了渗透和植物根系吸水的数值模型。我们利用非微观分析解和现有实验数据进行了数值实验，以验证所提数值技术的性能。结果表明，所提出的数值模型能够预测根区的土壤水分动态。

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引用次数: 0

Multi-resolution isogeometric analysis – efficient adaptivity utilizing the multi-patch structure 多分辨率等几何分析-利用多补丁结构的高效自适应

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.12.005

Stefan Takacs , Stefan Tyoler

Isogeometric Analysis (IgA) is a spline-based approach to the numerical solution of partial differential equations. The concept of IgA was designed to address two major issues. The first issue is the exact representation of domains generated from Computer-Aided Design (CAD) software. In practice, this can be realized only with multi-patch IgA, often in combination with trimming or similar techniques. The second issue is the realization of high-order discretizations (by increasing the spline degree) with a number of degrees of freedom comparable to low-order methods. High-order methods can deliver their full potential only if the solution to be approximated is sufficiently smooth; otherwise, adaptive methods are required. A zoo of local refinement strategies for splines has been developed in the last decades. Such approaches impede the utilization of recent advances that rely on tensor-product splines, e.g., matrix assembly and preconditioning. We propose a strategy for adaptive IgA that utilizes well-known approaches from the multi-patch IgA toolbox: using tensor-product splines locally, but allow for unstructured patch configurations globally. Our approach moderately increases the number of patches and utilizes different grid sizes for each patch. This allows reusing the existing code bases, recovers the convergence rates of other adaptive approaches, and increases the number of degrees of freedom only marginally. We provide an algorithm for the computation of a global basis and show that it works in any case. Additionally, we give approximation error estimates. Numerical experiments illustrate our results.

等距分析（IgA）是一种基于样条的偏微分方程数值解法。IgA 的概念旨在解决两个主要问题。第一个问题是精确表示计算机辅助设计 (CAD) 软件生成的域。在实践中，这只能通过多补丁 IgA 来实现，通常与修剪或类似技术相结合。第二个问题是实现高阶离散化（通过增加样条线度），其自由度数与低阶方法相当。只有当需要近似的解足够平滑时，高阶方法才能充分发挥其潜力；否则，就需要采用自适应方法。在过去的几十年中，已经开发出了一系列针对劈叉的局部细化策略。这些方法阻碍了对依赖于张量乘积劈叉的最新进展的利用，例如矩阵组装和预处理。我们提出的自适应 IgA 策略利用了多补丁 IgA 工具箱中众所周知的方法：局部使用张量乘积样条，但允许全局使用非结构补丁配置。我们的方法适度增加了补丁的数量，并为每个补丁使用了不同的网格尺寸。这样就可以重复使用现有的代码库，恢复其他自适应方法的收敛速度，而且自由度的增加幅度很小。我们提供了一种计算全局基础的算法，并证明它在任何情况下都有效。此外，我们还给出了近似误差估计值。数值实验说明了我们的结果。

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引用次数: 0

Convexification for a coefficient inverse problem for a system of two coupled nonlinear parabolic equations 两个耦合非线性抛物方程系统的系数反问题的凸化

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.12.004

Michael V. Klibanov , Jingzhi Li , Zhipeng Yang

A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called “Mean Field Games System” (MFGS), which is derived in the mean field games (MFG) theory. This theory has numerous applications in social sciences. The topic of Coefficient Inverse Problems (CIPs) in the MFG theory is in its infant age, both in theory and computations. A numerical method for this CIP is developed. Convergence analysis ensures the global convergence of this method. Numerical experiments are presented.

考虑两个时间方向相反的耦合非线性抛物型偏微分方程组。实际上，这就是所谓的“平均场博弈系统”（MFGS），它是在平均场博弈（MFG）理论中衍生出来的。这一理论在社会科学中有许多应用。系数逆问题（Coefficient Inverse Problems, CIPs）在MFG理论中的研究，无论是在理论上还是在计算上都处于起步阶段。提出了一种求解该CIP的数值方法。收敛性分析保证了该方法的全局收敛性。给出了数值实验结果。

引用次数: 0

Sparse tensor product finite elements for two scale elliptic and parabolic equations with discontinuous coefficients 具有不连续系数的两尺度椭圆型和抛物型方程的稀疏张量积有限元

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.11.018

Chen Hui Pang, Viet Ha Hoang

The paper develops the essentially optimal sparse tensor product finite element method for solving two scale elliptic and parabolic problems in a domain

D \subset R^{d}

d = 2, 3

, which is embedded with a periodic array of inclusions of microscopic sizes and spacing. The two scale coefficient is thus discontinuous in the fast variable. We obtain approximations for the solution of the homogenized equation and the scale interaction term, i.e. all the macroscopic and microscopic information, within a prescribed level of accuracy, using only an essentially optimal number of degrees of freedom, which is equal (apart from a possible logarithmic factor) to that required to solve one macroscopic scale problem in D. This is achieved by solving the two scale homogenized problem, and utilizing the regularity of the scale interaction term in all the slow and fast variables at the same time. However, unlike problems considered in the literature (e.g. Hoang and Schwab, 2004/05 [16]), the scale interaction term is only piecewise regular in the fast variable. We employ the discretization schemes developed for interface problems (Chen and Zou, 1998 [6], and Li et al., 2010 [20]) for the fast variable. Numerical correctors are developed from the finite element solutions with errors in terms of the finite element mesh size and the microscopic scale. Numerical examples that verify the theoretical convergence rates of the sparse tensor product finite elements are presented.

本文发展了本质上最优的稀疏张量积有限元方法，用于求解域D∧Rd， D =2,3上的两个尺度椭圆型和抛物型问题，该域内嵌有微观尺寸和间隔的内含物的周期阵列。因此，两个尺度系数在快速变量中是不连续的。我们仅使用本质上最优的自由度数（除去可能的对数因子），在规定的精度水平内获得均质化方程和尺度相互作用项的解的近似值，即所有宏观和微观信息，该自由度数等于d中解决一个宏观尺度问题所需的自由度（除了可能的对数因子）。同时在所有的慢速和快速变量中利用尺度相互作用项的规律性。然而，与文献中考虑的问题（如Hoang和Schwab， 2004/05[16]）不同，尺度相互作用项在快速变量中只是分段正则的。对于快速变量，我们采用针对界面问题开发的离散化方案（Chen and Zou, 1998 [6], Li et al., 2010[20]）。数值校正器是由有限元解发展而来的，其误差在有限元网格尺寸和微观尺度上。给出了数值算例，验证了稀疏张量积有限元的理论收敛速度。

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引用次数: 0

Direct sampling method for solving the inverse acoustic wave scattering problems in the time domain 直接采样法在时域上求解声波反散射问题

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.12.018

Hong Guo , Jin Huang , Zhaoxing Li

Based on the direct sampling method, this paper solves the inverse acoustic wave scattering problem from the transient scattered field. Two indicator functions can be obtained to reconstruct the shapes and the locations of the unknown scatterers, including the point-like scatterers and the extended scatterers. Our reconstruction method is easy to be implement because only the integrals need to be computed for the indicator functions. The asymptotic properties of the indicator function for the point-like scatterer are proved according to the Fourier-Laplace transform. Meanwhile, the effectiveness and the robustness of our method have been illustrated from two numerical examples.

基于直接采样法，从瞬态散射场出发，解决了声波反散射问题。可以得到两个指示函数来重建未知散射体的形状和位置，包括点状散射体和扩展散射体。我们的重建方法易于实现，因为只需要计算指示函数的积分。利用傅里叶-拉普拉斯变换证明了点状散射体的指示函数的渐近性质。同时，通过两个算例说明了该方法的有效性和鲁棒性。

引用次数: 0

A machine-learning enabled framework for quantifying uncertainties in parameters of computational models

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-30 DOI: 10.1016/j.camwa.2025.01.030

Taylor Roper , Harri Hakula , Troy Butler

This work presents novel extensions for combining two frameworks for quantifying both aleatoric (i.e., irreducible) and epistemic (i.e., reducible) sources of uncertainties in the modeling of engineered systems. The data-consistent (DC) framework poses an inverse problem and solution for quantifying aleatoric uncertainties in terms of pullback and push-forward measures for a given Quantity of Interest (QoI) map. Unfortunately, a pre-specified QoI map is not always available a priori to the collection of data associated with system outputs. The data themselves are often polluted with measurement errors (i.e., epistemic uncertainties), which complicates the process of specifying a useful QoI. The Learning Uncertain Quantities (LUQ) framework defines a formal three-step machine-learning enabled process for transforming noisy datasets into samples of a learned QoI map to enable DC-based inversion. We develop a robust filtering step in LUQ that can learn the most useful quantitative information present in spatio-temporal datasets. The learned QoI map transforms simulated and observed datasets into distributions to perform DC-based inversion. We also develop a DC-based inversion scheme that iterates over time as new spatial datasets are obtained and utilizes quantitative diagnostics to identify both the quality and impact of inversion at each iteration. Reproducing Kernel Hilbert Space theory is leveraged to mathematically analyze the learned QoI map and develop a quantitative sufficiency test for evaluating the filtered data. An illustrative example is utilized throughout while the final two examples involve the manufacturing of shells of revolution to demonstrate various aspects of the presented frameworks.

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引用次数: 0

Maximum principle-preserving, unconditionally energy-stable, and convergent method with second-order accuracy for the phase-field model of image inpainting

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-30 DOI: 10.1016/j.camwa.2025.01.032

Sheng Su, Junxiang Yang

Image inpainting is a technique for reconstructing missing or damaged regions of an image. In this paper, we propose a novel linear numerical method with second-order accuracy in both space and time for solving the modified Allen–Cahn equation applied to image inpainting. The proposed method is conditionally maximum principle-preserving, second-order accurate, and unconditionally energy-stable. A leap-frog finite difference scheme is employed to discretize the modified Allen–Cahn equation. Additionally, we present a comprehensive stability analysis and provide an error estimate for the method. Numerical experiments validate the effectiveness of the proposed method, demonstrating its accuracy, stability, expandability, and efficiency.

引用次数: 0

Unconditionally energy stable and second-order accurate one-parameter ESAV schemes with non-uniform time stepsizes for the functionalized Cahn-Hilliard equation

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-01-30 DOI: 10.1016/j.camwa.2025.01.027

Zengqiang Tan

This paper studies linear and unconditionally energy stable schemes for the functionalized Cahn-Hilliard (FCH) equation. Such schemes are built on the exponential scalar auxiliary variable (ESAV) approach and the one-parameter time discretizations as well as the extrapolation for the nonlinear term, and can arrive at second-order accuracy in time. It is shown that the derived schemes are uniquely solvable and unconditionally energy stable by using an algebraic identity derived by the method of undetermined coefficients. Importantly, such one-parameter ESAV schemes are extended to those with non-uniform time stepsizes, which are also shown to be unconditionally energy stable by an analogous algebraic identity. The energy stability results can be easily extended to the fully discrete schemes, where the Fourier pseudo-spectral method is employed in space. Moreover, based on the derived schemes with non-uniform time stepsizes, an adaptive time-stepping strategy is introduced to improve the computational efficiency for the long time simulations of the FCH equation. Several numerical examples are conducted to validate the computational accuracy and energy stability of our schemes as well as the effectiveness and computational efficiency of the derived adaptive time-stepping algorithm.

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引用次数: 0

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