Computers & Mathematics with Applications最新文献_第4页

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

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

{"title":"Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the overlapping triangular finite elements","authors":"Cong Liu , Kaifu Li , Shaosong Min , Yingbin Chai","doi":"10.1016/j.camwa.2024.11.025","DOIUrl":"10.1016/j.camwa.2024.11.025","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"179 ","pages":"Pages 148-177"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.11.030

Weizhu Wang, Stefanos-Aldo Papanicolopulos

{"title":"Finding minimal cubature rules for finite elements passing the patch test","authors":"Weizhu Wang, Stefanos-Aldo Papanicolopulos","doi":"10.1016/j.camwa.2024.11.030","DOIUrl":"10.1016/j.camwa.2024.11.030","url":null,"abstract":"<div><div>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.</div><div>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.</div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"179 ","pages":"Pages 1-16"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142804459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.11.028

Mohamed Boujoudar , Abdelaziz Beljadid , Ahmed Taik

{"title":"LRBF meshless methods for predicting soil moisture distribution in root zone","authors":"Mohamed Boujoudar , Abdelaziz Beljadid , Ahmed Taik","doi":"10.1016/j.camwa.2024.11.028","DOIUrl":"10.1016/j.camwa.2024.11.028","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"179 ","pages":"Pages 178-196"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.12.005

Stefan Takacs , Stefan Tyoler

{"title":"Multi-resolution isogeometric analysis – efficient adaptivity utilizing the multi-patch structure","authors":"Stefan Takacs , Stefan Tyoler","doi":"10.1016/j.camwa.2024.12.005","DOIUrl":"10.1016/j.camwa.2024.12.005","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"179 ","pages":"Pages 103-125"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142841381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.12.004

Michael V. Klibanov , Jingzhi Li , Zhipeng Yang

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

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.11.018

Chen Hui Pang, Viet Ha Hoang

{"title":"Sparse tensor product finite elements for two scale elliptic and parabolic equations with discontinuous coefficients","authors":"Chen Hui Pang, Viet Ha Hoang","doi":"10.1016/j.camwa.2024.11.018","DOIUrl":"10.1016/j.camwa.2024.11.018","url":null,"abstract":"<div><div>The paper develops the essentially optimal sparse tensor product finite element method for solving two scale elliptic and parabolic problems in a domain <span><math><mi>D</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mi>d</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></span>, 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 <em>D</em>. 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 <span><span>[16]</span></span>), 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 <span><span>[6]</span></span>, and Li et al., 2010 <span><span>[20]</span></span>) 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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"179 ","pages":"Pages 17-40"},"PeriodicalIF":2.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142804452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Computers & Mathematics with Applications Pub Date : 2025-02-01 DOI: 10.1016/j.camwa.2024.12.018

Hong Guo , Jin Huang , Zhaoxing Li

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

Computers & Mathematics with Applications Pub Date : 2025-01-30 DOI: 10.1016/j.camwa.2025.01.030

Taylor Roper , Harri Hakula , Troy Butler

{"title":"A machine-learning enabled framework for quantifying uncertainties in parameters of computational models","authors":"Taylor Roper , Harri Hakula , Troy Butler","doi":"10.1016/j.camwa.2025.01.030","DOIUrl":"10.1016/j.camwa.2025.01.030","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 184-212"},"PeriodicalIF":2.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Computers & Mathematics with Applications Pub Date : 2025-01-30 DOI: 10.1016/j.camwa.2025.01.032

Sheng Su, Junxiang Yang

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

Computers & Mathematics with Applications Pub Date : 2025-01-30 DOI: 10.1016/j.camwa.2025.01.027

Zengqiang Tan

{"title":"Unconditionally energy stable and second-order accurate one-parameter ESAV schemes with non-uniform time stepsizes for the functionalized Cahn-Hilliard equation","authors":"Zengqiang Tan","doi":"10.1016/j.camwa.2025.01.027","DOIUrl":"10.1016/j.camwa.2025.01.027","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"182 ","pages":"Pages 163-183"},"PeriodicalIF":2.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143097937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0