Applied Numerical Mathematics最新文献_第5页

An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, Part II. Piecewise-smooth interfaces 自动生成网格的椭圆界面问题的任意高阶非拟合有限元法，第二部分。片状光滑界面

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-20 DOI: 10.1016/j.apnum.2024.08.012

Zhiming Chen, Yong Liu

引用次数: 0

A thermodynamically consistent phase-field model and an entropy stable numerical method for simulating two-phase flows with thermocapillary effects 模拟具有热毛细管效应的两相流动的热力学一致相场模型和熵稳定数值方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-13 DOI: 10.1016/j.apnum.2024.08.010

Yanxiao Sun , Jiang Wu , Maosheng Jiang , Steven M. Wise , Zhenlin Guo

{"title":"A thermodynamically consistent phase-field model and an entropy stable numerical method for simulating two-phase flows with thermocapillary effects","authors":"Yanxiao Sun , Jiang Wu , Maosheng Jiang , Steven M. Wise , Zhenlin Guo","doi":"10.1016/j.apnum.2024.08.010","DOIUrl":"10.1016/j.apnum.2024.08.010","url":null,"abstract":"<div><p>In this study, we have derived a thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects. This model accommodates variations in physical properties such as density, viscosity, heat capacity, and thermal conductivity between the two components. The model equations encompass a Cahn-Hilliard equation with the volume fraction as the phase variable, a Navier-Stokes equation, and a heat equation, and meanwhile maintains mass conservation, energy conservation, and entropy increase simultaneously. Given the highly coupled and nonlinear nature of the model equations, we developed a semi-decoupled, mass-preserving, and entropy-stable time-discrete numerical method. We conducted several numerical tests to validate both our model and numerical method. Additionally, we have investigated the merging process of two bubbles under non-isothermal conditions and compared the results with those under isothermal conditions. Our findings reveal that temperature gradients influence bubble morphology and lead to earlier merging. Moreover, we have observed that the merging of bubbles slows down with increasing heat Peclect number <span><math><msub><mrow><mi>Pe</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span> when the initial temperature field increases linearly along the channel, while bubbles merge faster with heat Peclect number <span><math><msub><mrow><mi>Pe</mi></mrow><mrow><mi>T</mi></mrow></msub></math></span> when the initial temperature field decreases linearly along the channel.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142007007","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

Unconditionally energy stable high-order BDF schemes for the molecular beam epitaxial model without slope selection 无斜率选择的分子束外延模型的无条件能量稳定高阶 BDF 方案

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-12 DOI: 10.1016/j.apnum.2024.08.005

Yuanyuan Kang , Jindi Wang , Yin Yang

{"title":"Unconditionally energy stable high-order BDF schemes for the molecular beam epitaxial model without slope selection","authors":"Yuanyuan Kang , Jindi Wang , Yin Yang","doi":"10.1016/j.apnum.2024.08.005","DOIUrl":"10.1016/j.apnum.2024.08.005","url":null,"abstract":"<div><p>In this paper, we consider a class of k-order <span><math><mo>(</mo><mn>3</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>5</mn><mo>)</mo></math></span> backward differentiation formulas (BDF-k) for the molecular beam epitaxial (MBE) model without slope selection. Convex splitting technique along with k-th order Douglas-Dupont regularization term <span><math><msubsup><mrow><mi>τ</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>k</mi></mrow></msubsup><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>k</mi></mrow></msup><msub><mrow><munder><mrow><mi>D</mi></mrow><mo>_</mo></munder></mrow><mrow><mi>k</mi></mrow></msub><msup><mrow><mi>ϕ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> (<span><math><msub><mrow><munder><mrow><mi>D</mi></mrow><mo>_</mo></munder></mrow><mrow><mi>k</mi></mrow></msub></math></span> represents a truncated BDF-k formula) is added to the numerical schemes to ensure unconditional energy stability. The stabilized convex splitting BDF-k <span><math><mo>(</mo><mn>3</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>5</mn><mo>)</mo></math></span> methods are unique solvable unconditionally. Then the modified discrete energy dissipation laws are established by using the discrete gradient structures of BDF-k <span><math><mo>(</mo><mn>3</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>5</mn><mo>)</mo></math></span> formulas and processing k-th order explicit extrapolations of the concave term. In addition, based on the discrete energy technique, the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm stability and convergence of the stabilized BDF-k <span><math><mo>(</mo><mn>3</mn><mo>≤</mo><mi>k</mi><mo>≤</mo><mn>5</mn><mo>)</mo></math></span> schemes are obtained by means of the discrete orthogonal convolution kernels and the convolution type Young inequalities. Numerical results are carried out to verify our theory and illustrate the validity of the proposed schemes.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142011539","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

A multilevel Monte Carlo algorithm for stochastic differential equations driven by countably dimensional Wiener process and Poisson random measure 由可数维维纳过程和泊松随机测量驱动的随机微分方程的多级蒙特卡洛算法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-10 DOI: 10.1016/j.apnum.2024.08.007

Michał Sobieraj

{"title":"A multilevel Monte Carlo algorithm for stochastic differential equations driven by countably dimensional Wiener process and Poisson random measure","authors":"Michał Sobieraj","doi":"10.1016/j.apnum.2024.08.007","DOIUrl":"10.1016/j.apnum.2024.08.007","url":null,"abstract":"<div><p>In this paper, we investigate properties of standard and multilevel Monte Carlo methods for weak approximation of solutions of stochastic differential equations (SDEs) driven by infinite-dimensional Wiener process and Poisson random measure with Lipschitz payoff function. The error of the truncated dimension randomized numerical scheme, which depends on two parameters i.e., grid density <span><math><mi>n</mi><mo>∈</mo><mi>N</mi></math></span> and truncation dimension parameter <span><math><mi>M</mi><mo>∈</mo><mi>N</mi></math></span>, is of the order <span><math><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>δ</mi><mo>(</mo><mi>M</mi><mo>)</mo></math></span> such that <span><math><mi>δ</mi><mo>(</mo><mo>⋅</mo><mo>)</mo></math></span> is positive and decreasing to 0. We derive a complexity model and provide proof for the complexity upper bound of the multilevel Monte Carlo method which depends on two increasing sequences of parameters for both <em>n</em> and <em>M</em>. The complexity is measured in terms of upper bound for mean-squared error and is compared with the complexity of the standard Monte Carlo algorithm. The results from numerical experiments as well as Python and CUDA C implementation details are also reported.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142007006","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

Efficient simulation of complex Ginzburg–Landau equations using high-order exponential-type methods 利用高阶指数型方法高效模拟复杂的金兹堡-朗道方程

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-10 DOI: 10.1016/j.apnum.2024.08.009

Marco Caliari, Fabio Cassini

{"title":"Efficient simulation of complex Ginzburg–Landau equations using high-order exponential-type methods","authors":"Marco Caliari, Fabio Cassini","doi":"10.1016/j.apnum.2024.08.009","DOIUrl":"10.1016/j.apnum.2024.08.009","url":null,"abstract":"<div><p>In this paper, we consider the task of efficiently computing the numerical solution of evolutionary complex Ginzburg–Landau equations on Cartesian product domains with homogeneous Dirichlet/Neumann or periodic boundary conditions. To this aim, we employ for the time integration high-order exponential methods of splitting and Lawson type with constant time step size. These schemes enjoy favorable stability properties and, in particular, do not show restrictions on the time step size due to the underlying stiffness of the models. The needed actions of matrix exponentials are efficiently realized by using a tensor-oriented approach that suitably employs the so-called <em>μ</em>-mode product (when the semidiscretization in space is performed with finite differences) or with pointwise operations in Fourier space (when the model is considered with periodic boundary conditions). The overall effectiveness of the approach is demonstrated by running simulations on a variety of two- and three-dimensional (systems of) complex Ginzburg–Landau equations with cubic or cubic-quintic nonlinearities, which are widely considered in literature to model relevant physical phenomena. In fact, we show that high-order exponential-type schemes may outperform standard techniques to integrate in time the models under consideration, i.e., the well-known second-order split-step method and the explicit fourth-order Runge–Kutta integrator, for stringent accuracies.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168927424002058/pdfft?md5=91e2a12e99c9070a604eca3d527b8de9&pid=1-s2.0-S0168927424002058-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142089349","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

High-order reliable numerical methods for epidemic models with non-constant recruitment rate 非恒定招募率流行病模型的高阶可靠数值方法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-10 DOI: 10.1016/j.apnum.2024.08.008

Bálint Máté Takács , Gabriella Svantnerné Sebestyén , István Faragó

引用次数: 0

Efficient mapped Jacobi spectral method for integral equations with two-sided singularities 具有双面奇点的积分方程的高效映射雅可比谱法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-10 DOI: 10.1016/j.apnum.2024.08.003

Xiu Yang , Changtao Sheng

引用次数: 0

A posteriori error estimates for fully discrete finite difference method for linear parabolic equations 线性抛物方程全离散有限差分法的后验误差估计

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-08 DOI: 10.1016/j.apnum.2024.08.006

Mengli Mao , Wansheng Wang

引用次数: 0

High-order spline finite element method for solving time-dependent electromagnetic waves 用于求解时变电磁波的高阶样条线有限元法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-08 DOI: 10.1016/j.apnum.2024.08.002

Imad El-Barkani , Imane El-Hadouti , Mohamed Addam , Mohammed Seaid

{"title":"High-order spline finite element method for solving time-dependent electromagnetic waves","authors":"Imad El-Barkani , Imane El-Hadouti , Mohamed Addam , Mohammed Seaid","doi":"10.1016/j.apnum.2024.08.002","DOIUrl":"10.1016/j.apnum.2024.08.002","url":null,"abstract":"<div><p>In this paper we propose a high-order spline finite element method for solving a class of time-dependent electromagnetic waves and its associated frequency-domain approach. A Fourier transform and its inverse are used for the time integration of the wave problem. The spatial discretization is performed using a partitioned mesh with tensorial spline functions to form bases of the discrete solution in the variational finite element space. Quadrature methods such as the Gauss-Hermite quadrature are implemented in the inverse Fourier transform to compute numerical solutions of the time-dependent electromagnetic waves. In the present study we carry out a rigorous convergence analysis and establish error estimates for the wave solution in the relevant norms. We also provide a full algorithmic description of the method and assess its performance by solving several test examples of time-dependent electromagnetic waves with known analytical solutions. The method is shown to verify the theoretical estimates and to provide highly accurate and efficient simulations. We also evaluate the computational performance of the proposed method for solving a problem of wave transmission through non-homogeneous materials. The obtained computational results confirm the excellent convergence, high accuracy and applicability of the proposed spline finite element method.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141979538","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

The virtual element method for a contact problem with wear and unilateral constraint 具有磨损和单边约束的接触问题的虚拟元素法

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2024-08-06 DOI: 10.1016/j.apnum.2024.08.004

Bangmin Wu , Fei Wang , Weimin Han

引用次数: 0