Computers & Mathematics with Applications最新文献_第9页

Spatiotemporal numerical simulation of breast cancer tumors in one-dimensional nonlinear moving boundary models via temporal-spatial spectral collocation method 基于时空谱配点法的一维非线性移动边界模型中乳腺癌肿瘤的时空数值模拟

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

Multi-material topology optimization of thermoelastic structures by an ordered SIMP-based phase field model 基于有序simp相场模型的多材料热弹性结构拓扑优化

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

Primal-mixed finite element methods for the coupled Biot and Poisson–Nernst–Planck equations 耦合Biot方程和泊松-能-普朗克方程的原始混合有限元方法

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

Superconvergnce analysis of an energy-stable implicit scheme with variable time steps and anisotropic spatial nonconforming finite elements for the nonlinear Sobolev equations 非线性Sobolev方程各向异性空间非协调有限元变时间步长能量稳定隐式格式的超收敛分析

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 弱阻尼Klein-Gordon方程的保守原始混合有限元法

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 高维抛物型偏微分方程的显式解：Kronecker积和向量化算子在Haar小波方法中的应用

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

Novel connection of spectral scheme and one-step of s-order approaches for MHD flows enclosed a duct 封闭管道的 MHD 流动的光谱方案与 s 阶一步法之间的新联系

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-04 DOI: 10.1016/j.camwa.2025.02.016

Muhammad Hamid , Muhammad Usman , Zhenfu Tian

{"title":"Novel connection of spectral scheme and one-step of s-order approaches for MHD flows enclosed a duct","authors":"Muhammad Hamid , Muhammad Usman , Zhenfu Tian","doi":"10.1016/j.camwa.2025.02.016","DOIUrl":"10.1016/j.camwa.2025.02.016","url":null,"abstract":"<div><div>A challenging and common problem that frequently arises in the fields of physics and engineering, two-dimensional (2D) incompressible, viscous MHD duct flows have significant theoretical and practical significance due to their numerous and widespread applications in astrophysics, geology, power generation, MHD generators, electromagnetic pumps, accelerators, blood flow measurements, drug delivery, and other areas. Therefore, a robust solution to such a problem becomes a challenging task for the research community. This framework develops a novel connection to inspect the accurate and rapid convergent solutions of a coupled system of convection-diffusion equations arising in 2D unsteady MHD flows. This coupling is based on one-step <em>s</em>-stage/order methods to approximate the temporal variable with the Vieta-Fibonacci polynomials-based spectral method to estimate the spatial variables. The spatial derivative terms given in the problem under discussion are replaced by new operational matrices of integer order. The paper incorporates related theorems to provide a mathematical validation of the techniques. Additionally, we conduct a study on convergence and error bonds to verify the computational algorithm's mathematical formulation. A thorough comparison analysis illustrates the validity, correctness, and dependability of the computational approach that is now recommended. Novel investigation includes the spectral technique coupled with the fourth-order Runge-Kutta method handles the nonlinear issue very well to investigate the exact smooth solutions to physical problems. The suggested schemes are discovered to have an exponential order of convergence in the spatial direction, and the COC in the temporal direction confirms the findings of previous research.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"184 ","pages":"Pages 185-220"},"PeriodicalIF":2.9,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143534326","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

Optimizing Variational Physics-Informed Neural Networks Using Least Squares 利用最小二乘法优化变分物理信息神经网络

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-01 DOI: 10.1016/j.camwa.2025.02.022

Carlos Uriarte , Manuela Bastidas , David Pardo , Jamie M. Taylor , Sergio Rojas

{"title":"Optimizing Variational Physics-Informed Neural Networks Using Least Squares","authors":"Carlos Uriarte , Manuela Bastidas , David Pardo , Jamie M. Taylor , Sergio Rojas","doi":"10.1016/j.camwa.2025.02.022","DOIUrl":"10.1016/j.camwa.2025.02.022","url":null,"abstract":"<div><div>Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a least squares solver for the weights of the last layer of the neural network, we improve the convergence of the loss during training in most practical scenarios. This work analyzes the computational cost of the resulting hybrid least-squares/gradient-descent optimizer and explains how to implement it efficiently. In particular, we show that a traditional implementation based on backward-mode automatic differentiation leads to a prohibitively expensive algorithm. To remedy this, we propose using either forward-mode automatic differentiation or an ultraweak-type scheme that avoids the differentiation of trial functions in the discrete weak formulation. The proposed alternatives are up to one hundred times faster than the traditional one, recovering a computational cost-per-iteration similar to that of a conventional gradient-descent-based optimizer alone. To support our analysis, we derive computational estimates and conduct numerical experiments in one- and two-dimensional problems.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"185 ","pages":"Pages 76-93"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519112","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

Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization 基于Galerkin/最小二乘稳定的平流扩散方程的时空有限元分析

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-03-01 DOI: 10.1016/j.camwa.2025.02.020

Biswajit Khara , Kumar Saurabh , Robert Dyja , Anupam Sharma , Baskar Ganapathysubramanian

引用次数: 0

An asymptotic preserving scheme for the Euler-Poisson-Boltzmann system in the quasineutral limit 欧拉-泊松-玻尔兹曼系统在拟中性极限下的渐近保持格式

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2025-02-27 DOI: 10.1016/j.camwa.2025.02.021

K.R. Arun , R. Ghorai

引用次数: 0