Computers & Mathematics with Applications最新文献

{"title":"Direct reconstruction of a multidimensional heat equation","authors":"A. Boumenir","doi":"10.1016/j.camwa.2024.09.008","DOIUrl":"10.1016/j.camwa.2024.09.008","url":null,"abstract":"<div><div>We are concerned with a coefficient inverse problem of a multidimensional heat equation. The objective is to reconstruct the sought coefficient from a sequence of observations of the solution taken at a single point. To do so we first obtain an explicit formula for the sought coefficient, and then see how we can approximate it using few observations only. We also show that asymptotics of the solution help reduce the data processing to overcome the curse of dimensionality. This new and direct reconstruction method is fast and gives an alternative to iterative and Newton's type methods. Numerical examples are provided at the end.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311558","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}

{"title":"A linear edge finite element method for quad-curl problem","authors":"Chao Wang ,&nbsp;Jintao Cui ,&nbsp;Zhengjia Sun","doi":"10.1016/j.camwa.2024.09.015","DOIUrl":"10.1016/j.camwa.2024.09.015","url":null,"abstract":"<div><div>In this study, we explore for the application of a linear edge finite element method for the numerical solution of a quad-curl problem. We carefully construct a curl recovery operator, which serves to approximate the second order curl of the linear edge element function. The proposed scheme is creatively designed by integrating the constructed operator with the standard Ritz-Galerkin methods in a straightforward manner. We provide proof that the numerical solution derived from our proposed method converges optimally to the exact solution in both <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><mi>H</mi><mo>(</mo><mtext>curl</mtext><mo>,</mo><mi>Ω</mi><mo>)</mo></math></span> norms. Our analysis uncovers several intriguing properties of the curl recovery operator. To demonstrate the optimal convergence of our scheme, we construct a series of numerical experiments. The results provide compelling evidence of the effectiveness of our approach.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311559","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}

{"title":"Ultra-weak discontinuous Galerkin method with IMEX-BDF time marching for two dimensional convection-diffusion problems","authors":"Haijin Wang ,&nbsp;Lulu Jiang ,&nbsp;Qiang Zhang ,&nbsp;Yuan Xu ,&nbsp;Xiaobin Shi","doi":"10.1016/j.camwa.2024.09.009","DOIUrl":"10.1016/j.camwa.2024.09.009","url":null,"abstract":"<div><div>In this paper, we study the stability and error estimates of the fully discrete ultra-weak discontinuous Galerkin (UWDG) methods for solving two dimensional convection-diffusion problems, where the implicit-explicit backward difference formulas (IMEX-BDF) with order from one to five are considered in time discretization. By exploiting an extension of the multiplier technique applied in Wang et al. (2023) <span><span>[41]</span></span>, and by utilizing the symmetry and coercivity properties of the UWDG discretization for the diffusion term, we establish a general framework of unconditional stability analysis for the fully discrete schemes. In addition, by exploiting the ultra-weak projection proposed in Chen and Xing (2024) <span><span>[15]</span></span>, we obtain the optimal error estimates for the considered schemes. We also present some numerical results to verify the optimal accuracy of the considered schemes for both one and two dimensional convection-diffusion problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311557","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}

{"title":"A novel phase-field model for three-dimensional shape transformation","authors":"Seokjun Ham ,&nbsp;Hyundong Kim ,&nbsp;Youngjin Hwang ,&nbsp;Soobin Kwak ,&nbsp;Jyoti ,&nbsp;Jian Wang ,&nbsp;Heming Xu ,&nbsp;Wenjing Jiang ,&nbsp;Junseok Kim","doi":"10.1016/j.camwa.2024.09.006","DOIUrl":"10.1016/j.camwa.2024.09.006","url":null,"abstract":"<div><p>We present a simple and robust numerical technique for a novel phase-field model of three-dimensional (3D) shape transformation. Shape transformation has been achieved using phase-field models. However, previous phase-field models have intrinsic drawbacks, such as shrinkage due to motion by mean curvature and unwanted growth. To overcome these drawbacks associated with previous models, we propose a novel phase-field model that eliminates these shortcomings. The proposed phase-field model is based on the Allen–Cahn (AC) equation with nonstandard mobility and a nonlinear source term. To numerically and efficiently solve the proposed phase-field equation, we adopt an operator splitting method, which consists of the AC equation with a nonstandard mobility and a fidelity equation. The modified AC equation is solved using a fully explicit finite difference method with a time step that ensures stability. For solving the fidelity equation, we use a semi-implicit scheme with a frozen coefficient. We have performed several numerical experiments with various 3D sources and target shapes to verify the robustness and efficacy of our proposed mathematical model and its numerical method.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240738","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}

{"title":"Numerical simulation of a non-linear sublimation process with temperature-dependent permeability and volumetric heat source: A phase change problem","authors":"Vikas Chaurasiya","doi":"10.1016/j.camwa.2024.09.005","DOIUrl":"10.1016/j.camwa.2024.09.005","url":null,"abstract":"<div><p>Conventional freeze-drying takes a long drying time and makes the process expensive. High-quality biological materials, medicine, and vaccines may not find easy acceptance with this technology. To overcome the operative time, several engineering innovations are carried out. A long drying time during freeze-drying can be minimized by accelerating the sublimation rate. Obtaining a fast drying rate without harming the material properties is the prime focus of the accelerated freeze-drying (<em>AFD</em>) like-techniques. In connection with this, the study of temperature-dependent thermal-physical properties of the medium during sublimation is considered in this study. For example, a temperature-dependent volumetric heat source is assumed within the vapor region. An increase in the temperature field results in higher pressure. Therefore, a temperature-dependent specific heat of vapor pressure is also accounted for. Furthermore, the permeability of the medium and the specific heat of the water vapor are also assumed to be temperature-dependent. Exploring realistic theoretical models with variable-dependent characteristics and convection is essential since the experimental investigation of sublimation in a porous media may be challenging. Despite the previous available studies on sublimation heat and mass transfer, there is still a lack of mathematical modeling of this particular problem. To solve this non-linear sublimation problem, the Genocchi operational matrix of differentiation method (<span><math><mi>G</mi><mi>O</mi><mi>M</mi><mi>O</mi><mi>D</mi></math></span>) method is employed to obtain the numerical results. In case of full non-linear model, results obtained via current numerical technique are verified with finite-difference method (<em>FDM</em>). Furthermore, in a particular case, the accuracy test of the <span><math><mi>G</mi><mi>O</mi><mi>M</mi><mi>O</mi><mi>D</mi></math></span> method against <em>FDM</em> is presented, and it is found that the current numerical technique is more accurate than <em>FDM</em>. In the current study, it is found that a temperature-dependent heat source offers a faster sublimation rate than a constant one. Similarly, temperature-dependent specific heat of vapor pressure accelerates the pressure distribution within the sublimated region. With temperature-dependent permeability, the concentration distribution within the medium decreases. Moreover, the temperature-dependent specific heat of water vapor delayed the sublimation rate. Results found from this study are expected to aid in AFD techniques, food industry and pharmaceuticals.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240739","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}

{"title":"FEM-PIKFNN for underwater acoustic propagation induced by structural vibrations in different ocean environments","authors":"Qiang Xi ,&nbsp;Zhuojia Fu ,&nbsp;Wenzhi Xu ,&nbsp;Mi-An Xue ,&nbsp;Youssef F. Rashed ,&nbsp;Jinhai Zheng","doi":"10.1016/j.camwa.2024.09.007","DOIUrl":"10.1016/j.camwa.2024.09.007","url":null,"abstract":"<div><p>In this paper, a novel hybrid method based on the finite element method (FEM) and physics-informed kernel function neural network (PIKFNN) is proposed. The method is applied to predict underwater acoustic propagation induced by structural vibrations in diverse ocean environments, including the unbounded ocean, deep ocean, and shallow ocean. In the hybrid method, PIKFNN is regarded as an improved shallow physics-informed neural network (PINN) in which the activation function in the PINN is replaced with a physics-informed kernel function (PIKF). This ensures the integration of prior physical information into the neural network model. Moreover, PIKFNN circumvents embedding the governing equations into the loss function in the PINN and requires only training on boundary data. By using Green's function as PIKF and the structural-acoustic coupling response information obtained from the FEM as training data, PIKFNN can inherently capture the Sommerfeld radiation condition at infinity, which are naturally suitable for predicting ocean acoustic propagation. Numerical experiments demonstrate the accuracy and feasibility of FEM-PIKFNN in comparison with analytical solutions and finite element results.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240707","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}

{"title":"An elementary approach to splittings of unbounded operators","authors":"Arieh Iserles ,&nbsp;Karolina Kropielnicka","doi":"10.1016/j.camwa.2024.08.031","DOIUrl":"10.1016/j.camwa.2024.08.031","url":null,"abstract":"<div><p>Using elementary means, we derive the three most popular splittings of <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo></mrow></msup></math></span> and their error bounds in the case when <em>A</em> and <em>B</em> are (possibly unbounded) operators in a Hilbert space, generating strongly continuous semigroups, <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mi>A</mi></mrow></msup></math></span>, <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mi>B</mi></mrow></msup></math></span> and <span><math><msup><mrow><mi>e</mi></mrow><mrow><mi>t</mi><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo></mrow></msup></math></span>. The error of these splittings is bounded in terms of the norm of the commutators <span><math><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo></math></span>, <span><math><mo>[</mo><mi>A</mi><mo>,</mo><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo><mo>]</mo></math></span> and <span><math><mo>[</mo><mi>B</mi><mo>,</mo><mo>[</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>]</mo><mo>]</mo></math></span>.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142230559","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}

{"title":"On five-point equidistant stencils based on Gaussian function with application in numerical multi-dimensional option pricing","authors":"Tao Liu ,&nbsp;Ting Li ,&nbsp;Malik Zaka Ullah","doi":"10.1016/j.camwa.2024.09.003","DOIUrl":"10.1016/j.camwa.2024.09.003","url":null,"abstract":"<div><p>The purpose of this article is to study how the integrals of the Gaussian radial basis function can be employed to produce the coefficients of approximations under the radial basis function - finite difference solver. Here these coefficients are reported for a five-point stencil. Error equations are derived to demonstrate that the convergence rate is four for approximating the 1st and 2nd differentiations of a function. Then the coefficients are used in solving multi-dimensional option pricing problems, which are modeled as time-dependent variable-coefficients parabolic partial differential equations with non-smooth initial conditions. The numerical simulations support the applicability and usefulness of the presented method.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142230440","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}

{"title":"Finite element approximation for a delayed generalized Burgers-Huxley equation with weakly singular kernels: Part I Well-posedness, regularity and conforming approximation","authors":"Sumit Mahajan,&nbsp;Arbaz Khan,&nbsp;Manil T. Mohan","doi":"10.1016/j.camwa.2024.08.036","DOIUrl":"10.1016/j.camwa.2024.08.036","url":null,"abstract":"<div><p>In this study, we explore the theoretical and numerical aspects of the generalized Burgers-Huxley equation (a non-linear advection-diffusion-reaction problem) incorporating weakly singular kernels in a <em>d</em>-dimensional domain, where <span><math><mi>d</mi><mo>∈</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></span>. For the continuous problem, we provide an in-depth discussion on the existence and the uniqueness of weak solution using the Faedo-Galerkin approximation technique. Further, regularity results for the weak solution are derived based on assumptions of smoothness for both the initial data and the external forcing. Using the regularity of the solution, the uniqueness of weak solutions has been established. In terms of numerical approximation, we introduce a semi-discrete scheme using the conforming finite element method (CFEM) for space discretization and derive optimal error estimates. Subsequently, we present a fully discrete approximation scheme that employs backward Euler discretization in time and CFEM in space. A priori error estimates for both the semi-discrete and fully discrete schemes are discussed under minimal regularity assumptions. To validate our theoretical findings, we provide computational results that lend support to the derived conclusions.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142229743","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}

{"title":"An efficient computational framework for data assimilation of fractional-order dynamical system with sparse observations","authors":"Qinwu Xu","doi":"10.1016/j.camwa.2024.09.004","DOIUrl":"10.1016/j.camwa.2024.09.004","url":null,"abstract":"<div><p>We introduce an efficient computational framework for data assimilation of fractional dynamical systems, extending traditional data assimilation techniques to fractional models. This framework offers effective computational methods that eliminate the need for complex adjoint model derivations and algorithm redesign. We establish the fundamental problem formulation, develop both the AtD and DtA approaches, and derive adjoint forms and numerical schemes for each method. Additionally, we create a unified fractional-order variational data assimilation framework applicable to both linear and nonlinear models, incorporating both explicit and implicit discrete methods. Specific discretization schemes and gradient formulas are derived for three distinct types of fractional-order models. The method's reliability and convergence are verified, and the effect of observation sparsity and quality is examined through numerical examples.</p></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142172934","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}