Computers & Mathematics with Applications最新文献

{"title":"Block ω-circulant preconditioners for parabolic equations","authors":"Po Yin Fung, Sean Y. Hon","doi":"10.1016/j.camwa.2025.01.019","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.019","url":null,"abstract":"In this study, a novel class of block <ce:italic>ω</ce:italic>-circulant preconditioners is developed for the all-at-once linear system that emerges from solving parabolic equations using first and second order discretization schemes for time. We establish a unifying preconditioning framework for <ce:italic>ω</ce:italic>-circulant preconditioners, extending and modifying the preconditioning approach recently proposed in (Zhang and Xu, 2024 <ce:cross-ref ref>[27]</ce:cross-ref>) and integrating some existing results in the literature. The proposed preconditioners leverage fast Fourier transforms for efficient diagonalization, facilitating parallel-in-time execution. Theoretically, these preconditioners ensure that eigenvalue clustering around ±1 is achieved, fostering fast convergence under the minimal residual method. Furthermore, when using the generalized minimal residual method, the effectiveness of these preconditioners is supported by the singular value clustering at unity. Numerical experiments validate the performance of the developed preconditioning strategies.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"30 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020141","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 staggered discontinuous Galerkin method for solving SN transport equation on arbitrary polygonal grids","authors":"Deng Wang, Zupeng Jia","doi":"10.1016/j.camwa.2025.01.018","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.018","url":null,"abstract":"This paper proposes a staggered discontinuous Galerkin (SDG) method for solving the 2D <mml:math altimg=\"si1.svg\"><mml:msub><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msub></mml:math> transport equation on arbitrary polygonal mesh. The new method allows rough grids such as highly distorted quadrilateral grids and general polygonal grids. More importantly, it is numerical flux free, different from the standard discontinuous Galerkin (DG) method using upwind flux, and thus gains the advantage of not demanding a sweeping algorithm to determine the computational ordering of all elements. The sweeping process not only requires a significant amount of computation, but also encounters deadlocks due to the presence of cycles in the corresponding directed graph on deformed three-dimensional polyhedral meshes. Additionally, there are challenges with sweeping stability on curved meshes. Our method naturally avoids these problems such that it can be generalized to high-order schemes on curved meshes. Convergence of the new method is analyzed in the linear case, and we have shown that it is optimally convergent for sufficiently smooth transport solution and appropriate total cross section. Numerical results are consistent with the theoretical analysis. The tests also show that our method employing linear elements can maintain second-order accuracy on rough grids mentioned earlier, demonstrating good robustness, and be able to model material interfaces with sharp changes of the angular flux. Moreover, the asymptotic-preserving property can be observed by scaling the cross section parameter in the thick diffusive limit problem. A test employing quadratic elements is also provided, which preliminarily demonstrates the feasibility and effectiveness of our method in higher-order scenarios.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"33 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020191","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 handy tool for assessing tetrahedron-based finite-cell methods and for numerical simulations in spheroidal domains","authors":"Andrés León Baldelli, Vitoriano Ruas, Marco Antonio Silva Ramos","doi":"10.1016/j.camwa.2025.01.017","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.017","url":null,"abstract":"A straightforward procedure is presented for the generation of finite-cell meshes consisting of tetrahedrons for curved domains, whose boundary can be expressed in spherical coordinates with origin at a suitable location in its interior. Besides the equation of the boundary, the generation of the mesh depends only on an integer parameter, whose value is associated with its degree of refinement. Several examples indicate that the meshes of a given domain form a quasi-uniform family of partitions, as the value of the integer parameter increases. Mesh quality is optimal in the case of a ball but it remains quite correct as the shape of the domain moves away from perfect sphericity, with a gradual but in all natural downgrade. The procedure is a handy tool for an a priori order-checking of a new finite-cell method, as applied to a given type of boundary value problem posed in curved domains. A MATLAB code was developed to implement this tetrahedrization procedure for domains with three symmetry planes.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"25 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020142","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 cartesian cut-cell technique for modeling turbulent flow in asymmetric diffusers using various turbulence models","authors":"A.S. Dawood, A.S. Amer, R.M. Abumandour, W.A. El-Askary","doi":"10.1016/j.camwa.2025.01.015","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.015","url":null,"abstract":"The process of accurately predicting the behavior of the separated turbulent flow requires extraordinary efforts, whether it is choosing the appropriate computational mesh or using the appropriate turbulence model for that. The present study introduces a comparative numerical investigation for predicting the behavior of turbulent-separated flow in asymmetric diffusers. Numerical simulation using a finite volume approach of incompressible Reynolds Averaged Navier Stokes equations (RANS) with three turbulence models (Standard <mml:math altimg=\"si31.svg\"><mml:mrow><mml:mi>k</mml:mi><mml:mo linebreak=\"goodbreak\">−</mml:mo><mml:mrow><mml:mi>ε</mml:mi></mml:mrow></mml:mrow></mml:math>, Chen-kim, and modified Chen-kim) is here performed in a self-developed FORTRAN code. The treatment of asymmetric diffusers poses challenges due to the complex flow behavior and geometry. To address this, a developed cartesian cut-cell technique is employed, which provides compatibility with solid boundaries and efficiently handles complex geometries This developed cut-cell technique is checked to treat its ability to predict complex turbulent flow with the presence of strong pressure gradient for correctness and convergence, as well as testing the proposed turbulence-models performance. So, verifications are performed by comparing the present computational results of asymmetric-diffuser flow characteristics with available experimental and LES data. The proposed models reveal acceptable agreements in most cases, especially the modified Chen-kim model, which shows a great match with the experimental and LES results for all flow characteristics. The standard k-ε model fails to predict the flow-separation well in most comparisons. Extended computational studies are also introduced to investigate the effects of diffuser cant angles (4 to 15°) and area ratio (2.4 to 7) on the diffuser flow behavior using the successfully modified Chen-kim turbulence model. The parametric study reveals that these two factors strongly affect the diffuser performance, where the pressure recovery, skin friction coefficients, and separation bubble size are provided.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"32 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020188","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":"Analysis of the Picard-Newton finite element iteration for the stationary incompressible inductionless MHD equations","authors":"Xiaodi Zhang, Meiying Zhang, Xianghai Zhou","doi":"10.1016/j.camwa.2025.01.016","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.016","url":null,"abstract":"In this paper, we propose and analyze the Picard-Newton finite element iteration for the stationary incompressible inductionless magnetohydrodynamics (MHD) equations. In finite element discretization, the hydrodynamic unknowns are approximated by stable finite element pairs, and the electromagnetic system is discretized by using the face-volume pairs. To solve the nonlinear discretized problem efficiently, our method consists of first applying the Picard iteration and then applying the Newton iteration. The Picard-Newton iteration is proved to be globally stable under the uniqueness condition and quadratically convergent under the stronger uniqueness condition. Thanks to the improved stability property, this solver has a larger convergence basin than the usual Newton iteration. Numerical tests confirm our theoretical analysis and show that the Picard-Newton iteration dramatically excels both the Picard and Newton iterations in several benchmark problems.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"9 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020189","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":"Efficient reliability analysis method for non-linear truss structures using machine learning-based uncertainty quantification","authors":"Trung-Hieu Nguyen, Truong-Thang Nguyen, Duc-Minh Hoang, Viet-Hung Dang, Xuan-Dat Pham","doi":"10.1016/j.camwa.2025.01.014","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.014","url":null,"abstract":"Truss structures typically involve a large number of similar elements; hence, it is necessary to employ reliability analysis algorithms that can handle high-dimensional problems to analyze the reliability of truss structures. Moreover, when considering non-linear behaviors in terms of both material properties and geometry, developing such an algorithm is challenging. For this purpose, this study proposes a novel method, named t-LQR that combines the advancements from three domains: i) a high-performance gradient boosting model from machine learning for a highly accurate prediction model, ii) an active learning process from reliability analysis for adaptively improving the prediction model, and iii) quantile regression for uncertainty quantification from probabilistic information to identify the relevant candidates used to refine the prediction model. The validity and robustness of the proposed method are verified through planar and spatial truss structures, showing that t-LQR significantly reduces the computational time of structural analysis-up to 25 times-compared to the conventional Monte Carlo methods. Furthermore, t-LQR outperforms competing Kirging-based models in terms of accuracy for non-linear problems.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"59 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020190","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":"Analysis of tumor metastasis model in microenvironment based on coupled fractional reaction diffusion equation","authors":"Yating Huang, Zhenyou Wang","doi":"10.1016/j.camwa.2025.01.012","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.012","url":null,"abstract":"This paper explores the licensing stage in tumor metastasis, focusing on the mathematical relationships between the tumor microenvironment and cells. Building on Academician Cao's insights, we develop a fractional order spatiotemporal model using a reaction-diffusion approach, solving it numerically to account for tumor metastasis memory and heritability. Our analysis identifies causal relationships during this stage, providing essential theoretical support and tools for advancing cancer treatment research. This study aims to innovate tumor therapy methods, offering new insights and strategies.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"74 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020192","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 numerical method for 2D elliptic singularly perturbed systems with different magnitude parameters in the diffusion and the convection terms","authors":"Carmelo Clavero, Ram Shiromani","doi":"10.1016/j.camwa.2025.01.011","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.011","url":null,"abstract":"In this work we are interested in constructing a uniformly convergent method to solve a 2D elliptic singularly perturbed weakly system of convection-diffusion type. We assume that small positive parameters appear at both the diffusion and the convection terms of the partial differential equation. Moreover, we suppose that both the diffusion and the convection parameters can be distinct and also they can have a different order of magnitude. Then, the nature of the overlapping regular or parabolic boundary layers, which, in general, appear in the exact solution, is much more complicated. To solve the continuous problem, we use the classical upwind finite difference scheme, which is defined on piecewise uniform Shishkin meshes, which are given in a different way depending on the value and the ratio between the four singular perturbation parameters which appear in the continuous problem. So, the numerical algorithm is an almost first order uniformly convergent method. The numerical results obtained with our algorithm for a test problem are presented; these results corroborate in practice the good behavior and the uniform convergence of the algorithm, aligning with the theoretical results.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"137 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143020193","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 family of second-order time stepping methods for a nonlinear fluid-fluid interaction model","authors":"Yiru Chen, Yun-Bo Yang, Lijie Mei","doi":"10.1016/j.camwa.2025.01.010","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.010","url":null,"abstract":"In this paper, we present a fully discrete finite element scheme for the nonlinear fluid-fluid interaction model, which consists of two Navier-Stokes equations coupled by some nonlinear interface. The presented fully discrete scheme is based on a type of implicit-explicit (IMEX) second-order time-stepping schemes in temporal discretization and mixed finite element in spatial discretization. The scheme is a combination of a linearization treatment for the advection term, explicit treatment for nonlinear interface conditions by a scalar auxiliary variable method, together with stabilization terms which are proportional to discrete curvature of the solutions in both velocity and pressure. Because of the scalar auxiliary variable method, we only require solving a sequence of linear differential equation with constant coefficients at each time step. Unconditional stability is proved and convergence analysis is derived. Finally, the derived theoretical results are supported by three numerical examples.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"74 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986207","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 time-fractional optimal transport: Formulation and algorithm","authors":"Yiqun Li, Hong Wang, Wuchen Li","doi":"10.1016/j.camwa.2025.01.009","DOIUrl":"https://doi.org/10.1016/j.camwa.2025.01.009","url":null,"abstract":"The time-fractional optimal transport (OT) models are developed to describe the anomalous transport of the agents such that their densities are transported from the initial density distribution to the terminal one with the minimal cost. The general-proximal primal-dual hybrid gradient (G-prox PDHG) algorithm is applied to solve the OT formulations, in which a preconditioner induced by the numerical approximation to the time-fractional PDE is derived to accelerate the convergence of the algorithm. Numerical experiments for OT problems between Gaussian distributions are carried out to investigate the performance of the OT formulations. Those numerical experiments also demonstrate the effectiveness and flexibility of our proposed algorithm.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"14 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142986208","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}