Computers & Mathematics with Applications最新文献

{"title":"Fast evaluation and robust error analysis of the virtual element methods for time fractional diffusion wave equation","authors":"Jixiao Guo ,&nbsp;Yanping Chen ,&nbsp;Qin Liang","doi":"10.1016/j.camwa.2024.11.001","DOIUrl":"10.1016/j.camwa.2024.11.001","url":null,"abstract":"<div><div>The article is concerned with and analyzes the <em>α</em>-robust error bound for time-fractional diffusion wave equations with weakly singular solutions. Nonuniform <em>L</em>1-type time meshes are used to handle non-smooth systems, and the sum-of-exponentials (SOEs) approximation for the kernels function is adopted to reduce the memory storage and computational cost. Meanwhile, the virtual element method (VEM), which can deal with complex geometric meshes and achieve arbitrary order of accuracy, is constructed for spatial discretization. Based on the explicit factors and discrete complementary convolution kernels, the optimal error bound of the fully discrete SOEs-VEM scheme in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm is derived in detail and that is <em>α</em>-robust, i.e., the bounds will not explosive growth while <span><math><mi>α</mi><mo>→</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup></math></span>. Finally, some numerical experiments are implemented to verify the theoretical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"177 ","pages":"Pages 41-57"},"PeriodicalIF":2.9,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142673452","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":"Deep mixed residual method for solving PDE-constrained optimization problems","authors":"Jinjun Yong ,&nbsp;Xianbing Luo ,&nbsp;Shuyu Sun ,&nbsp;Changlun Ye","doi":"10.1016/j.camwa.2024.11.009","DOIUrl":"10.1016/j.camwa.2024.11.009","url":null,"abstract":"<div><div>The deep mixed residual method (DeepMRM) is a technique to solve partial differential equation. In this paper, it is applied to tackle PDE-constrained optimization problems (PDE-COPs). For a PDE-COP, we transform it into an optimality system, and then employ mixed residual method (MRM) on this system. By implementing the DeepMRM with three different network structures (fully connected neural network, residual network, and attention fully connected neural network), we successfully solve PDE-COPs including elliptic, semi-linear elliptic, and Navier-Stokes (NS) equation constrained optimization problems. Compared with the exact or high-fidelity solutions, the DeepMRM provides an effective approach for solving PDE-COPs using the three different network structures.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 510-524"},"PeriodicalIF":2.9,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660785","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":"Pure-positivity-preserving methods with an optimal sufficient CFL number for fifth-order MR-WENO schemes on structured meshes","authors":"Yan Tan,&nbsp;Jun Zhu","doi":"10.1016/j.camwa.2024.11.010","DOIUrl":"10.1016/j.camwa.2024.11.010","url":null,"abstract":"<div><div>In this paper, one-dimensional and two-dimensional pure-positivity-preserving (PPP) methods are proposed for fifth-order finite volume multi-resolution WENO (MR-WENO) schemes to solve some extreme problems on structured meshes. The MR-WENO spatial reconstruction procedures only require one five-cell, one three-cell, and one one-cell stencils for achieving uniform fifth-order accuracy in smooth regions and keeping essentially non-oscillatory property in non-smooth regions in one dimension. One redefines five new cell averages vectors after performing such spatial reconstructions and design one quartic polynomials vector and three quadratic polynomials vectors based on them. After that, a new detective process is used to examine the positivity of density and pressure of three quadratic polynomials vectors inside the whole target cell. If the negativity happens, a new compression limiter is carried out to enable the positivity of density and pressure of three quadratic polynomials vectors over the whole target cell and the positivity of density and pressure of one quartic polynomials vector at the midpoint of the target cell. It is a new way to design the positivity-preserving methods to keep fifth-order accuracy and the positivity over the target cell instead of only at some discrete Gauss-Lobatto quadrature points, since the precise minimum values of the density and pressure are now available. Then a theoretically proof is given to increase the optimal sufficient CFL number from 1/12 to 1/6 for the fifth-order WENO schemes. This methodology can be expanded to multi-dimensions easily. Unlike some classical positivity-preserving methods, the PPP methods could apply a special four-point Gauss-Lobatto quadrature formula or any other quadrature formulas on condition that their numerical precision is no smaller than four. Since the optimal CFL number of 1/6 is a sufficient but not necessary condition, the novelty PPP methods for fifth-order finite volume MR-WENO schemes with a larger practical CFL number of 0.6 are also available and robust enough when simulating some extreme problems without timely halving its value.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"177 ","pages":"Pages 1-22"},"PeriodicalIF":2.9,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142658865","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":"Simulation of fluid-structure interaction using the density smoothing B-spline material point method with a contact approach","authors":"Zheng Sun,&nbsp;Yunjun Hua,&nbsp;Yunqing Xu,&nbsp;Xiaomin Zhou","doi":"10.1016/j.camwa.2024.11.008","DOIUrl":"10.1016/j.camwa.2024.11.008","url":null,"abstract":"<div><div>Fluid-structure interaction (FSI) problems with strong nonlinearity and multidisciplinarity pose challenges for current numerical FSI algorithms. This work proposes a monolithic strategy for solving the equations of motion for both the fluid and structural domains under the unique Lagrangian framework of the B-spline material point method (BSMPM). A node-based density smoothing BSMPM (referred to as ds-BSMPM) is proposed to eliminate pressure instability and oscillation in the simulation of weakly compressible fluids, which is straightforwardly implemented using B-spline basis functions without the need for any sophisticated particle search algorithm. The interaction between the fluid and structure is conducted using the Lagrangian multiplier method on the tensor product grid, whose actual position is determined by the Greville abscissa and is used to detect contact. The proposed method is verified and validated against existing numerical approaches and experimental results, demonstrating the effectiveness of the proposed method in eliminating the oscillations of water pressure and solid stress, and avoiding premature and erroneous contact. In particular, this work presents a promising monolithic approach for achieving high-fidelity solutions to complex FSI problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 525-544"},"PeriodicalIF":2.9,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660786","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":"Positivity and bound preserving well-balanced high order compact finite difference scheme for Ripa and pollutant transport model","authors":"Baifen Ren ,&nbsp;Bao-Shan Wang ,&nbsp;Xiangxiong Zhang ,&nbsp;Zhen Gao","doi":"10.1016/j.camwa.2024.11.012","DOIUrl":"10.1016/j.camwa.2024.11.012","url":null,"abstract":"<div><div>We construct a fourth-order accurate compact finite difference scheme that is well-balanced, positivity-preserving of water height, and bound-preserving of temperature for Ripa and concentration for pollutant transport systems. The proposed scheme preserves the still-water steady state and the positivity of water height. It also maintains concentration bounds for pollutants across nonflat bottom topographies, regardless of the presence of a pollutant source. Our approach incorporates water height and pollutant concentration constraints within the same discretization, utilizing weak monotonicity and a simple bound-preserving limiter while preserving the well-balanced property. Through extensive numerical simulations encompassing Ripa and pollutant transport models, we demonstrate the effectiveness of our method, verifying its well-balanced property, high-order accuracy, positivity-preserving, and bound-preserving capabilities.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 545-563"},"PeriodicalIF":2.9,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660787","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 energy stable finite element method for the nonlocal electron heat transport model","authors":"Xiaodong Yuan ,&nbsp;Aimin Chen ,&nbsp;Rui Guo ,&nbsp;Maojun Li","doi":"10.1016/j.camwa.2024.11.011","DOIUrl":"10.1016/j.camwa.2024.11.011","url":null,"abstract":"<div><div>In this paper, the nonlocal electron heat transport model in one and two dimensions is considered and studied. An energy stability finite element method is designed to discretize the nonlocal electron heat transport model. For the nonlinear discrete system, both Newton iteration and implicit-explicit (IMEX) schemes are employed to solve it. Then the energy stability is proved in semi-discrete and fully-discrete schemes. Numerical examples are presented to verify the energy stability of the proposed schemes as well as the optimal convergence order in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>, <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"177 ","pages":"Pages 23-40"},"PeriodicalIF":2.9,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142658866","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":"Unconditional error estimate of linearly-implicit and energy-preserving schemes for nonlocal wave equations","authors":"Lingling Li ,&nbsp;Yayun Fu","doi":"10.1016/j.camwa.2024.11.002","DOIUrl":"10.1016/j.camwa.2024.11.002","url":null,"abstract":"<div><div>Compared to the classical wave equation, the nonlocal wave equation incorporates a nonlocal operator and can capture a broader range of practical phenomena. However, this nonlocal formulation significantly increases the computational cost in numerical simulations, necessitating the development of efficient and accurate time integration schemes. Inspired by the newly developed generalized scalar auxiliary variable (GSAV) method in Refs. <span><span>[8]</span></span>, <span><span>[24]</span></span> for dissipative systems, this paper uses the GSAV approach to construct linearly-implicit energy-preserving schemes for nonlocal wave systems. The developed numerical schemes only require solving linear equations with constant coefficients at each time step and are more efficient than the original SAV schemes <span><span>[30]</span></span> for wave equations. We also discuss the unique solvability, conduct a rigorous error analysis, and present numerical examples to demonstrate the accuracy, conservation and effectiveness of the obtained schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 492-509"},"PeriodicalIF":2.9,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660784","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 unconditional energy-stable finite element method for the electro-hydrodynamic equations","authors":"Mengmeng Li ,&nbsp;Guang-an Zou ,&nbsp;Min Zhang","doi":"10.1016/j.camwa.2024.11.003","DOIUrl":"10.1016/j.camwa.2024.11.003","url":null,"abstract":"<div><div>In this paper, we mainly focus on the numerical approximations of the electro-hydrodynamic system, which couples the Poisson-Nernst-Planck equations and the Navier-Stokes equations. A novel linear, fully-decoupled and energy-stable finite element scheme for solving this system is proposed and analyzed. The fully discrete scheme developed here is employed by the stabilizing strategy, implicit-explicit (IMEX) scheme and a rotational pressure-correction method. One particular feature of the scheme is adding a stabilization term artificially in the conservation of charge density equation to decouple the computations of velocity field from electric field, which can be treated as a first-order perturbation term for balancing the explicit treatment of the coupling term. We rigorously prove the unique solvability, unconditional energy stability and error estimates of the proposed scheme. Finally, some numerical examples are provided to verify the accuracy and stability of the developed numerical scheme.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 447-468"},"PeriodicalIF":2.9,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660256","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 comparative study of numerical methods for approximating the solutions of a macroscopic automated-vehicle traffic flow model","authors":"George Titakis ,&nbsp;Iasson Karafyllis ,&nbsp;Dionysios Theodosis ,&nbsp;Ioannis Papamichail ,&nbsp;Markos Papageorgiou","doi":"10.1016/j.camwa.2024.11.007","DOIUrl":"10.1016/j.camwa.2024.11.007","url":null,"abstract":"<div><div>In this paper, a particle method is used to approximate the solutions of a “fluid-like” macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the macroscopic traffic model: mass is preserved, the mechanical energy is decaying and an energy functional is also decaying. To demonstrate the advantages of the particle method under consideration, a comparison with other numerical methods for viscous compressible fluid models is provided. Since the solutions of the macroscopic traffic model can be approximated by the solutions of a reduced model consisting of a single nonlinear heat-type partial differential equation, the numerical solutions produced by the particle method are also compared with the numerical solutions of the reduced model. Finally, a traffic simulation scenario and a comparison with the Aw-Rascle-Zhang (ARZ) model are provided, illustrating the advantages of the use of automated vehicles.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 469-490"},"PeriodicalIF":2.9,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660783","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":"Modelling and simulation of radiative heat transfer in non-grey absorbing and emitting media under phase change","authors":"Fatima-Ezzahrae Moutahir ,&nbsp;Youssef Belhamadia ,&nbsp;Mohammed Seaid ,&nbsp;Mofdi El-Amrani","doi":"10.1016/j.camwa.2024.11.005","DOIUrl":"10.1016/j.camwa.2024.11.005","url":null,"abstract":"<div><div>A class of mathematical models are proposed for modelling and numerical simulation of coupled radiative and conductive heat transfer in non-grey absorbing and emitting media under phase change. Progress in this area of mathematical modelling would contribute to a sustainable future manufacturing involving high temperature and phase change. Accurately predicting phase-change interface is the crucial step for these applications in non-grey semi-transparent media. In the present study, the conduction and radiation effects are analyzed by a set of nonlinear partial differential equations and a linear integral equation, respectively. The proposed model forms a system of nonlinear integro-differential equations and it accounts for both thermal radiation and phase change in the design. For non-grey media, the spectrum is divided into a sequence of finite intervals of frequency bands with averaged absorption coefficients resulting in coupled systems to be solved for each frequency band. The coupled equations are approximated using a second-order method in both time and space. Using discrete ordinates for the angular discretization of the integral equation for the radiation effects, a Newton-type algorithm is used to deal with the nonlinear systems. Numerical results are presented for several test problems in both grey and non-grey media, and comparisons to simulations without radiation are also shown in this study. The findings here could be used to understand effects of thermal radiation in non-grey absorbing and emitting media under phase change.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 432-446"},"PeriodicalIF":2.9,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142660257","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}