Computers & Mathematics with Applications最新文献_第3页

Design and time-domain finite element analysis of a carpet thermal concentrator in metamaterials

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-25 DOI: 10.1016/j.camwa.2025.03.016

Bin He , Shouzhu Bao

引用次数: 0

Fully consistent lowest-order finite element methods for generalised Stokes flows with variable viscosity 粘性可变的广义斯托克斯流的完全一致的最低阶有限元方法

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-25 DOI: 10.1016/j.camwa.2025.03.013

Felipe Galarce , Douglas R.Q. Pacheco

引用次数: 0

A lattice-Boltzmann inspired finite volume solver for compressible flows

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-20 DOI: 10.1016/j.camwa.2025.03.007

Jinhua Lu, Song Zhao, Pierre Boivin

{"title":"A lattice-Boltzmann inspired finite volume solver for compressible flows","authors":"Jinhua Lu, Song Zhao, Pierre Boivin","doi":"10.1016/j.camwa.2025.03.007","DOIUrl":"10.1016/j.camwa.2025.03.007","url":null,"abstract":"<div><div>The lattice Boltzmann method (LBM) for compressible flow is characterized by good numerical stability and low dissipation, while the conventional finite volume solvers have intrinsic conversation and flexibility in using unstructured meshes for complex geometries. This paper proposes a strategy to combine the advantages of the two kinds of solvers by designing a finite volume solver to mimic the LBM algorithm. It assumes an ideal LBM that can recover all desired higher-order moments. Time-discretized moment equations with second-order temporal accuracy and physically consistent dissipation terms are derived from the ideal LBM. By solving the recovered moment equations, a finite volume solver that can be applied to nonuniform meshes naturally, enabling body-fitted mass-conserving simulations, is proposed. Numerical tests show that the proposed solver can achieve good numerical stability from subsonic to hypersonic flows, and low dissipation for a long-distance entropy spot convection. For the challenging direct simulations of acoustic waves, its dissipation can be significantly reduced compared with the Lax-Wendroff solver of the same second-order spatial and temporal accuracy, while only remaining higher than that of the LBM on coarse meshes. The analysis implies that approximations of third-order temporal accuracy are required to recover the low dissipation of LBM further.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 50-71"},"PeriodicalIF":2.9,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143666522","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 decoupled, convergent and fully linear algorithm for the Landau–Lifshitz–Gilbert equation with magnetoelastic effects

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-18 DOI: 10.1016/j.camwa.2025.03.008

Hywel Normington , Michele Ruggeri

{"title":"A decoupled, convergent and fully linear algorithm for the Landau–Lifshitz–Gilbert equation with magnetoelastic effects","authors":"Hywel Normington , Michele Ruggeri","doi":"10.1016/j.camwa.2025.03.008","DOIUrl":"10.1016/j.camwa.2025.03.008","url":null,"abstract":"<div><div>We consider the coupled system of the Landau–Lifshitz–Gilbert equation and the conservation of linear momentum law to describe magnetic processes in ferromagnetic materials including magnetoelastic effects in the small-strain regime. For this nonlinear system of time-dependent partial differential equations, we present a decoupled integrator based on first-order finite elements in space and an implicit one-step method in time. We prove unconditional convergence of the sequence of discrete approximations towards a weak solution of the system as the mesh size and the time-step size go to zero. Compared to previous numerical works on this problem, for our method, we prove a discrete energy law that mimics that of the continuous problem and, passing to the limit, yields an energy inequality satisfied by weak solutions. Moreover, our method does not employ a nodal projection to impose the unit length constraint on the discrete magnetisation, so that the stability of the method does not require weakly acute meshes. Furthermore, our integrator and its analysis hold for a more general setting, including body forces and traction, as well as a more general representation of the magnetostrain. Numerical experiments underpin the theory and showcase the applicability of the scheme for the simulation of the dynamical processes involving magnetoelastic materials at submicrometer length scales.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 1-29"},"PeriodicalIF":2.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143666523","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

Spatiotemporal numerical simulation of breast cancer tumors in one-dimensional nonlinear moving boundary models via temporal-spatial spectral collocation method

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-18 DOI: 10.1016/j.camwa.2025.03.006

Yin Yang , Sayyed Ehsan Monabbati , Emran Tohidi , Atena Pasban

{"title":"Spatiotemporal numerical simulation of breast cancer tumors in one-dimensional nonlinear moving boundary models via temporal-spatial spectral collocation method","authors":"Yin Yang , Sayyed Ehsan Monabbati , Emran Tohidi , Atena Pasban","doi":"10.1016/j.camwa.2025.03.006","DOIUrl":"10.1016/j.camwa.2025.03.006","url":null,"abstract":"<div><div>In this research article, we have simulated the solutions of three types of (classical) moving boundary models in ductal carcinoma in situ by an efficient temporal-spatial spectral collocation method. In all of these three classical models, the associated fixed (spatial) boundary equations are localized by the numerical scheme. In the numerical scheme, Laguerre polynomials and Hermite polynomials are implemented to approximate the temporal and spatial variables (of unknown solutions), respectively. Then, as a generalization of the first classical model, we have considered a space-fractional moving boundary model and then transformed it, again, to the corresponding fixed boundary space-fractional equation for a straightforward discretization. Due to the impossibility of transforming of the time-fractional moving boundary model into its fixed boundary variant, we localized the time-fractional moving boundary model directly by the proposed method. The results in this category are also very satisfactory and the accuracy is again in a spectral rate. Moreover, (temporal) multi-step version of our method is applied for the considered models and the results are very accurate with respect to the single-step one, especially when the boundary of tumor is diverging in practice. In this regard, an adaptive strategy is connected to the temporal multi-step approach for a better simulation. Extensive test problems are provided to verify the accuracy of the method, with full consideration given to iterative tools for solving the final system of nonlinear algebraic equations.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"187 ","pages":"Pages 30-49"},"PeriodicalIF":2.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143666524","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

Primal-mixed finite element methods for the coupled Biot and Poisson–Nernst–Planck equations

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-12 DOI: 10.1016/j.camwa.2025.03.004

Gabriel N. Gatica , Cristian Inzunza , Ricardo Ruiz-Baier

{"title":"Primal-mixed finite element methods for the coupled Biot and Poisson–Nernst–Planck equations","authors":"Gabriel N. Gatica , Cristian Inzunza , Ricardo Ruiz-Baier","doi":"10.1016/j.camwa.2025.03.004","DOIUrl":"10.1016/j.camwa.2025.03.004","url":null,"abstract":"<div><div>We propose mixed finite element methods for the coupled Biot poroelasticity and Poisson–Nernst–Planck equations (modeling ion transport in deformable porous media). For the poroelasticity, we consider a primal-mixed, four-field formulation in terms of the solid displacement, the fluid pressure, the Darcy flux, and the total pressure. In turn, the Poisson–Nernst–Planck equations are formulated in terms of the electrostatic potential, the electric field, the ionized particle concentrations, their gradients, and the total ionic fluxes. The weak formulation, posed in Banach spaces, exhibits the structure of a perturbed block-diagonal operator consisting of perturbed and generalized saddle-point problems for the Biot equations, a generalized saddle-point system for the Poisson equations, and a perturbed twofold saddle-point problem for the Nernst–Planck equations. One of the main novelties here is the well-posedness analysis, hinging on the Banach fixed-point theorem along with small data assumptions, the Babuška–Brezzi theory in Banach spaces, and a slight variant of recent abstract results for perturbed saddle-point problems, again in Banach spaces. The associated Galerkin scheme is addressed similarly, employing the Banach fixed-point theorem to yield discrete well-posedness. A priori error estimates are derived, and simple numerical examples validate the theoretical error bounds, and illustrate the performance of the proposed schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 53-83"},"PeriodicalIF":2.9,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600613","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

Multi-material topology optimization of thermoelastic structures by an ordered SIMP-based phase field model

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-12 DOI: 10.1016/j.camwa.2025.03.005

Minh Ngoc Nguyen , Nhon Nguyen-Thanh , Shunhua Chen , Tinh Quoc Bui

{"title":"Multi-material topology optimization of thermoelastic structures by an ordered SIMP-based phase field model","authors":"Minh Ngoc Nguyen , Nhon Nguyen-Thanh , Shunhua Chen , Tinh Quoc Bui","doi":"10.1016/j.camwa.2025.03.005","DOIUrl":"10.1016/j.camwa.2025.03.005","url":null,"abstract":"<div><div>This paper presents a phase field approach to multi-material topology optimization of thermo-elastic structures. Based on the ordered Solid Isotropic Material with Penalization (ordered SIMP) model, the phase field variable is interpreted as the normalized density, which is used as the design variable in topology optimization. The material properties are interpolated in each interval of the normalized density. The advantage of ordered SIMP is that the number of design variables does not depend on the number of materials. In the proposed method, phase field evolution is governed by one Allen-Cahn type equation, with the introduction of a multiple-well potential function to take into account multiple material phases. This feature makes the current approach different from previous works, where numerous phase field evolution equations are needed. In contrast to the original ordered SIMP model, which was developed for structures subjected to only mechanical load, the current approach incorporates interpolation schemes to account for both thermal conductivity and thermal stress coefficient. An assessment of the feasibility and performance of the developed method is conducted via various benchmark examples and comparison with available reference results in the literature.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 84-100"},"PeriodicalIF":2.9,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143600614","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

Superconvergnce analysis of an energy-stable implicit scheme with variable time steps and anisotropic spatial nonconforming finite elements for the nonlinear Sobolev equations

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-10 DOI: 10.1016/j.camwa.2025.03.002

Lifang Pei , Ruixue Li , Jiwei Zhang , Yanmin Zhao

{"title":"Superconvergnce analysis of an energy-stable implicit scheme with variable time steps and anisotropic spatial nonconforming finite elements for the nonlinear Sobolev equations","authors":"Lifang Pei , Ruixue Li , Jiwei Zhang , Yanmin Zhao","doi":"10.1016/j.camwa.2025.03.002","DOIUrl":"10.1016/j.camwa.2025.03.002","url":null,"abstract":"<div><div>A fully discrete implicit scheme is presented and analyzed for the nonlinear Sobolev equations, which combines an anisotropic spatial nonconforming FEM with the variable-time-step BDF2 such that nonuniform meshes can be adopted in both time and space simultaneously. We prove that the fully discrete scheme is uniquely solvable, possesses the modified discrete energy dissipation law, and achieves second-order accuracy in both temporal and spatial directions under mild meshes conditions (adjacent time-step ratio condition <span><math><mn>0</mn><mo><</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>:</mo><mo>=</mo><mfrac><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo><</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>max</mi></mrow></msub><mo>≈</mo><mn>4.8645</mn></math></span> and anisotropic space meshes). The analysis approach involves a priori boundedness of the finite element solution, anisotropic properties of the element, energy projection error, DOC kernels and a modified discrete Grönwall inequality. Theoretical results reveal that the error in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm is sharp in time and optimal or even superconvergent in space. Abundant numerical experiments verify the theoretical results, and demonstrate the efficiency and accuracy of the proposed fully discrete scheme.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 37-52"},"PeriodicalIF":2.9,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579259","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

Conservative primal hybrid finite element method for weakly damped Klein-Gordon equation

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-10 DOI: 10.1016/j.camwa.2025.03.003

Sanjib K. Acharya , Amiya K. Pani , Ajit Patel , Ravina Shokeen

{"title":"Conservative primal hybrid finite element method for weakly damped Klein-Gordon equation","authors":"Sanjib K. Acharya , Amiya K. Pani , Ajit Patel , Ravina Shokeen","doi":"10.1016/j.camwa.2025.03.003","DOIUrl":"10.1016/j.camwa.2025.03.003","url":null,"abstract":"<div><div>Based on the primal hybrid finite element method (FEM) to discretize spatial variables, a semi-discrete scheme is obtained for the weakly damped Klein-Gordon equation. It is shown that this method is energy-conservative, and optimal error estimates in the energy norm are proved with the help of a modified elliptic projection. Moreover, a superconvergence result is derived, and as a consequence, the maximum norm estimate is obtained. Then, a non-standard type argument shows optimal error analysis in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>-norm with reduced regularity assumption on the solution. Further, the optimal order of convergence for the Lagrange multiplier is also established, and a superconvergence result for the gradient of the error between the modified elliptic projection and the primal hybrid finite element solution in maximum norm is derived. For a complete discrete scheme, an energy-conservative finite difference method is applied in the temporal direction, and the well-posedness of the discrete system is shown using a variant of the Brouwer fixed point theorem. The optimal rate of convergence for the primal variable in energy and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm for the fully discrete problem are established. Both semidiscrete and fully discrete schemes are analyzed for polynomial non-linearity, which is of the locally Lipschitz type. Finally, some numerical experiments are conducted to validate our theoretical findings.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 16-36"},"PeriodicalIF":2.9,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579258","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

Explicit solution of high-dimensional parabolic PDEs: Application of Kronecker product and vectorization operator in the Haar wavelet method

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-07 DOI: 10.1016/j.camwa.2025.03.001

Masood Ahmad , Muhammad Ahsan , Zaheer Uddin

{"title":"Explicit solution of high-dimensional parabolic PDEs: Application of Kronecker product and vectorization operator in the Haar wavelet method","authors":"Masood Ahmad , Muhammad Ahsan , Zaheer Uddin","doi":"10.1016/j.camwa.2025.03.001","DOIUrl":"10.1016/j.camwa.2025.03.001","url":null,"abstract":"<div><div>In this paper, we propose a numerically stable and efficient method based on Haar wavelets for solving high-dimensional second-order parabolic partial differential equations (PDEs). In the proposed framework, the spatial second-order derivatives in the governing equation are approximated using the Haar wavelet series. These approximations are subsequently integrated to obtain the corresponding lower-order derivatives. By substituting these expressions into the governing equation, the PDE is transformed into a system of first-order ordinary differential equations. This resulting system is then advanced in time using Euler's scheme.</div><div>Conventional Haar wavelet methods transform the given PDEs into a system with a large number of equations, which makes them computationally expensive. In contrast, the present Haar wavelets method (HWM) significantly reduces the number of algebraic equations. Moreover, the incorporation of the Kronecker product and vectorization operator properties in the HWM substantially decreases the computational cost compared to existing Haar wavelet methods in the literature (e.g., <span><span>[25]</span></span>, <span><span>[34]</span></span>, <span><span>[35]</span></span>). The HWM achieves second-order accuracy in spatial variables. We demonstrate the effectiveness of the HWM through various multi-dimensional problems, including two-, three-, four-, and ten-dimensional cases. The numerical results confirm the accuracy and efficiency of the proposed approach.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"186 ","pages":"Pages 1-15"},"PeriodicalIF":2.9,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562047","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