Applied Numerical Mathematics最新文献

英文中文

Boundary corrections for splitting methods in the time integration of multidimensional parabolic problems

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-12-06 DOI: 10.1016/j.apnum.2024.12.002

S. González-Pinto, D. Hernández-Abreu

This work considers two boundary correction techniques to mitigate the reduction in the temporal order of convergence in PDE sense (i.e., when both the space and time resolutions tend to zero independently of each other) of d dimension space-discretized parabolic problems on a rectangular domain subject to time dependent boundary conditions. We make use of the MoL approach (method of lines) where the space discretization is made with central differences of order four and the time integration is carried out with s-stage AMF-W-methods. The time integrators are of ADI-type (alternating direction implicit by using a directional splitting) and of higher order than the usual ones appearing in the literature which only reach order two. Besides, the techniques here explained also work for most of splitting methods when directional splitting is used. A remarkable fact is that with these techniques the time integrators recover the temporal order of PDE-convergence at the level of time-independent boundary conditions.

引用次数: 0

A numerical approach for a 1D tumor-angiogenesis simulations model

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-12-06 DOI: 10.1016/j.apnum.2024.11.017

P. De Luca , A. Galletti , G. Giunta , L. Marcellino

Angiogenesis, the formation of new blood vessels, is critical in both normal and pathological contexts, especially cancer. This process involves complex interactions among endothelial cells, tumor angiogenic factors, matrix metalloproteinases, angiogenic inhibitors, and neoplastic tissues. Different mathematical and computational models have been proposed for representing the tumor angiogenesis process. Among these, we focus on partial differential equations models which are able to capture the dynamic and spatial complexities in tumor growing. Our starting point is a PDE system which mimics the angiogenesis evolution. The aim of this work is to combine both spatial and time discretization methods for designing a matrix-based model. This approach allows us to observe some error properties of numerical schema proposed, by deducing the cumulative error among space and time. Experimental tests include convergence studies, for validating the reliability of the method. Results confirm our approach is useful for addressing real angiogenesis problem.

引用次数: 0

Error analysis of an ADI scheme for the two-dimensional fractal mobile/immobile transport equation with weakly singular solutions

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-12-05 DOI: 10.1016/j.apnum.2024.12.001

Weizhi Liu , Hu Chen , Mahmoud Zaky

In this work, we consider a numerical approximation for the two-dimensional fractal mobile/immobile transport equation with weakly singular solutions, where the time first-order derivative is discretized by the backward Euler method, and the Caputo fractional derivative is approximated by the L1 scheme on a uniform mesh. The fully discrete ADI scheme is established by adding a high-order term. The stability and the convergence analyses of the fully discrete ADI scheme are analyzed in

L^{2}

-norm and

H^{1}

-norm. The numerical results show that the error estimates are sharp.

引用次数: 0

Error analysis of implicit-explicit weak Galerkin finite element method for time-dependent nonlinear convection-diffusion problem

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-11-29 DOI: 10.1016/j.apnum.2024.11.016

Wenjuan Li , Fuzheng Gao , Jintao Cui

This paper focuses on the exploration of an implicit-explicit (IMEX) weak Galerkin finite element method (WG-FEM) applied to a one-dimensional nonlinear convection-diffusion equation. Based on a special weak form featuring two built-in parameters, we propose the fully implicit-explicit discrete WG finite element scheme. The diffusion term is treated implicitly, while the nonlinear convection term is treated explicitly. The WG-FEM utilizes locally piecewise polynomials of degree k to approximate the primal variable within the element interiors, along with piecewise polynomials of degree

k + 1

for the weak derivatives. Optimal error estimates in the

L^{2}

norm for the fully discrete scheme are derived in the theoretical analysis. Furthermore, we conduct numerical experiments to illustrate the effectiveness and accuracy of the proposed scheme.

引用次数: 0

Numerical analysis of evolutionary mixed variational problems: Applications in modeling asphalt pavements with interlayer frictional contact conditions

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-11-28 DOI: 10.1016/j.apnum.2024.11.015

Zhizhuo Zhang , Mikaël Barboteu , Xiaobing Nie , Jinde Cao

In this study, we address the numerical approximation of a class of evolutionary mixed variational problems and its application to the modeling of multi-layer viscoelastic contact systems. The specificity of this problem resides in the introduction of a dual multiplier to decouple and describe the nonlinear unilateral constraint, which renders it advantageous in the study and numerical computation of numerous contact problems. By imposing appropriate regularity conditions, we prove the approximation properties of the solution to its corresponding discrete problem and proceed to discuss its application in asphalt pavement mechanics modeling based on multi-layer contact systems. Particularly, the introduction of time-dependent dual constraint conditions realizes the simulation of time-dependent interlayer contact states, making the model more in line with the evolution process of actual pavement. Several numerical experiments conducted in both two and three dimensions illustrate the nonlinear displacement characteristics within the contact zones and validate conclusions related to error convergence. Furthermore, these experiments demonstrate the effectiveness of this approach in modeling pavement mechanics.

{"title":"Numerical analysis of evolutionary mixed variational problems: Applications in modeling asphalt pavements with interlayer frictional contact conditions","authors":"Zhizhuo Zhang , Mikaël Barboteu , Xiaobing Nie , Jinde Cao","doi":"10.1016/j.apnum.2024.11.015","DOIUrl":"10.1016/j.apnum.2024.11.015","url":null,"abstract":"<div><div>In this study, we address the numerical approximation of a class of evolutionary mixed variational problems and its application to the modeling of multi-layer viscoelastic contact systems. The specificity of this problem resides in the introduction of a dual multiplier to decouple and describe the nonlinear unilateral constraint, which renders it advantageous in the study and numerical computation of numerous contact problems. By imposing appropriate regularity conditions, we prove the approximation properties of the solution to its corresponding discrete problem and proceed to discuss its application in asphalt pavement mechanics modeling based on multi-layer contact systems. Particularly, the introduction of time-dependent dual constraint conditions realizes the simulation of time-dependent interlayer contact states, making the model more in line with the evolution process of actual pavement. Several numerical experiments conducted in both two and three dimensions illustrate the nonlinear displacement characteristics within the contact zones and validate conclusions related to error convergence. Furthermore, these experiments demonstrate the effectiveness of this approach in modeling pavement mechanics.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 208-231"},"PeriodicalIF":2.2,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145558","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 frozen Levenberg-Marquardt-Kaczmarz method with convex penalty terms and two-point gradient strategy for ill-posed problems 带凸惩罚项和两点梯度策略的冷冻莱文伯格-马尔卡特-卡茨马尔兹方法，用于解决难题

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-11-26 DOI: 10.1016/j.apnum.2024.11.014

Xiaoyan Zhang, Guangyu Gao, Zhenwu Fu, Yang Li, Bo Han

In this paper, we present a frozen iteratively regularized approach for solving ill-posed problems and conduct a thorough analysis of its performance. This method involves incorporating Nesterov's acceleration strategy into the Levenberg-Marquardt-Kaczmarz method and maintaining a constant Fréchet derivative of

F_{i}

at an initial approximation solution

x_{0}

throughout the iterative process, which called the frozen strategy. Moreover, convex functions are employed as penalty terms to capture the distinctive features of solutions. We establish convergence and regularization analysis by leveraging some classical assumptions and properties of convex functions. These theoretical findings are further supported by a number of numerical studies, which demonstrate the efficacy of our approach. Additionally, to verify the impact of initial values on the accuracy of reconstruction, the data-driven strategy is adopted in the third numerical example for comparison.

在本文中，我们提出了一种用于求解问题的冻结迭代正则化方法，并对其性能进行了深入分析。该方法将涅斯捷罗夫加速策略融入 Levenberg-Marquardt-Kaczmarz 方法中，并在整个迭代过程中保持 Fi 在初始近似解 x0 处的弗雷谢特导数不变，这就是所谓的冻结策略。此外，还采用凸函数作为惩罚项，以捕捉解的显著特征。我们利用凸函数的一些经典假设和特性，建立了收敛性和正则化分析。这些理论结论得到了大量数值研究的进一步支持，证明了我们方法的有效性。此外，为了验证初始值对重建精度的影响，我们在第三个数值示例中采用了数据驱动策略进行比较。

{"title":"A frozen Levenberg-Marquardt-Kaczmarz method with convex penalty terms and two-point gradient strategy for ill-posed problems","authors":"Xiaoyan Zhang, Guangyu Gao, Zhenwu Fu, Yang Li, Bo Han","doi":"10.1016/j.apnum.2024.11.014","DOIUrl":"10.1016/j.apnum.2024.11.014","url":null,"abstract":"<div><div>In this paper, we present a frozen iteratively regularized approach for solving ill-posed problems and conduct a thorough analysis of its performance. This method involves incorporating Nesterov's acceleration strategy into the Levenberg-Marquardt-Kaczmarz method and maintaining a constant Fréchet derivative of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> at an initial approximation solution <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> throughout the iterative process, which called the frozen strategy. Moreover, convex functions are employed as penalty terms to capture the distinctive features of solutions. We establish convergence and regularization analysis by leveraging some classical assumptions and properties of convex functions. These theoretical findings are further supported by a number of numerical studies, which demonstrate the efficacy of our approach. Additionally, to verify the impact of initial values on the accuracy of reconstruction, the data-driven strategy is adopted in the third numerical example for comparison.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 187-207"},"PeriodicalIF":2.2,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142722723","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

New adaptive low-dissipation central-upwind schemes 新的自适应低耗散中央上风方案

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-11-20 DOI: 10.1016/j.apnum.2024.11.010

Shaoshuai Chu , Alexander Kurganov , Igor Menshov

We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU schemes employ the recently proposed LDCU numerical fluxes computed using the point values reconstructed with the help of adaptively selected nonlinear limiters. To this end, we use a smoothness indicator to detect “rough” parts of the computed solution, where the piecewise linear reconstruction is performed using an overcompressive limiter, which leads to extremely sharp resolution of shock and contact waves. In the “smooth” areas, we use a more dissipative limiter to prevent appearance of artificial kinks and staircase-like structures there. In order to avoid oscillations, we perform the reconstruction in the local characteristic variables obtained using the local characteristic decomposition. We use a smoothness indicator from Löhner (1987) [34] and apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics. The obtained numerical results clearly demonstrate that the new adaptive LDCU schemes outperform the original ones.

我们为一维和二维双曲守恒定律系统引入了新的二阶自适应低耗散中央上风（LDCU）方案。新的自适应 LDCU 方案采用了最近提出的 LDCU 数值通量，该通量是利用自适应选择的非线性限幅器重建的点值计算得出的。为此，我们使用平滑度指标来检测计算解的 "粗糙 "部分，在这些部分中，分片线性重构是使用超压缩限制器进行的，这导致冲击波和接触波的分辨率极高。在 "光滑 "区域，我们使用耗散性更强的限制器，以防止出现人为的扭结和阶梯状结构。为了避免振荡，我们使用局部特征分解得到的局部特征变量进行重建。我们使用 Löhner (1987) [34] 提出的平滑度指标，并将所开发的方案应用于气体动力学的一维和二维欧拉方程。得到的数值结果清楚地表明，新的自适应 LDCU 方案优于原始方案。

{"title":"New adaptive low-dissipation central-upwind schemes","authors":"Shaoshuai Chu , Alexander Kurganov , Igor Menshov","doi":"10.1016/j.apnum.2024.11.010","DOIUrl":"10.1016/j.apnum.2024.11.010","url":null,"abstract":"<div><div>We introduce new second-order adaptive low-dissipation central-upwind (LDCU) schemes for the one- and two-dimensional hyperbolic systems of conservation laws. The new adaptive LDCU schemes employ the recently proposed LDCU numerical fluxes computed using the point values reconstructed with the help of adaptively selected nonlinear limiters. To this end, we use a smoothness indicator to detect “rough” parts of the computed solution, where the piecewise linear reconstruction is performed using an overcompressive limiter, which leads to extremely sharp resolution of shock and contact waves. In the “smooth” areas, we use a more dissipative limiter to prevent appearance of artificial kinks and staircase-like structures there. In order to avoid oscillations, we perform the reconstruction in the local characteristic variables obtained using the local characteristic decomposition. We use a smoothness indicator from Löhner (1987) <span><span>[34]</span></span> and apply the developed schemes to the one- and two-dimensional Euler equations of gas dynamics. The obtained numerical results clearly demonstrate that the new adaptive LDCU schemes outperform the original ones.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"209 ","pages":"Pages 155-170"},"PeriodicalIF":2.2,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142697462","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

An adaptive DtN-FEM for the scattering problem from orthotropic media 正交各向同性介质散射问题的自适应 DtN-FEM

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-11-20 DOI: 10.1016/j.apnum.2024.11.013

Lei Lin , Junliang Lv , Tian Niu

This paper is concerned with scattering of electromagnetic waves by an orthotropic infinite cylinder. Such a scattering problem is modeled by a orthotropic media scattering problem. By constructing the Dirichlet-to-Neumann (DtN) operator and introducing a transparent boundary condition, the orthotropic media problem is reformulated as a bounded boundary value problem. An a posteriori error estimate is derived for the finite element method with the truncated DtN boundary operator. The a posteriori error estimate contains the finite element approximation error and the truncation error of the DtN boundary operator, where the latter decays exponentially with respect to the truncation parameter. Based on the a posteriori error estimate, an adaptive finite element algorithm is proposed for solving the orthotropic media problem. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed method.

本文研究正交无限圆柱体对电磁波的散射。这种散射问题被模拟为正交介质散射问题。通过构造 Dirichlet-to-Neumann (DtN) 算子并引入透明边界条件，正交介质问题被重新表述为有界边界值问题。利用截断的 DtN 边界算子，得出了有限元方法的后验误差估计值。后验误差估计包含有限元近似误差和 DtN 边界算子的截断误差，后者与截断参数成指数衰减。根据后验误差估计，提出了一种自适应有限元算法，用于求解各向同性介质问题。通过数值示例证明了所提方法的有效性和稳健性。

引用次数: 0

Convergence, divergence, and inherent oscillations in MAS solutions of 2D Laplace-Neumann problems 二维拉普拉斯-诺伊曼问题 MAS 解的收敛、发散和固有振荡

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-11-20 DOI: 10.1016/j.apnum.2024.11.012

Georgios D. Kolezas, George Fikioris, John A. Roumeliotis

The method of auxiliary sources (MAS), also known as the method of fundamental solutions (MFS), is a well-known computational method for the solution of boundary-value problems. The final solution (“MAS solution”) is obtained once we have found the amplitudes of N auxiliary “MAS sources.” Past studies have shown that it is possible for the MAS solution to converge to the true solution even when the N auxiliary sources diverge and oscillate. Here, we extend the past studies by demonstrating this possibility within the context of Laplace's equation with Neumann boundary conditions. The correct solution can thus be obtained from sources that, when N is large, must be considered unphysical. We carefully explain the underlying reasons for the unphysical results, distinguish from other difficulties that might concurrently arise, and point to significant differences with time-dependent problems studied in the past.

辅助源法（MAS），又称基本解法（MFS），是一种著名的边界值问题求解计算方法。当我们找到 N 个辅助 "MAS 源 "的振幅后，就得到了最终解（"MAS 解"）。过去的研究表明，即使 N 个辅助源发散和振荡，MAS 解也有可能收敛到真解。在这里，我们扩展了过去的研究，在具有新曼边界条件的拉普拉斯方程中证明了这种可能性。因此，可以从 N 较大时必须被视为非物理的源中获得正确的解。我们仔细解释了非物理结果的根本原因，区分了可能同时出现的其他困难，并指出了与过去研究的时间相关问题的显著区别。

引用次数: 0

A priori error estimates for a coseismic slip optimal control problem 同震滑移优化控制问题的先验误差估计

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics

Pub Date : 2024-11-19 DOI: 10.1016/j.apnum.2024.11.011

Jorge Aguayo , Rodolfo Araya

This article presents an a priori error estimation for a finite element discretization applied to an optimal control problem governed by a mixed formulation for linear elasticity equations, where weak symmetry is imposed for the stress tensor. The optimal control is given by a discontinuity jump in displacements, representing the coseismic slip along a fault plane. Inferring the fault slip during an earthquake is crucial for understanding earthquake dynamics and improving seismic risk mitigation strategies, making this optimal control problem scientifically significant. We establish an a priori error estimate using appropriate finite element spaces for control and states. Our theoretical convergence rates were validated through numerical experiments.

本文介绍了应用于线性弹性方程混合表述的最优控制问题的有限元离散化的先验误差估计，其中对应力张量施加了弱对称性。最优控制由位移的不连续跳跃给出，代表沿断层面的共震滑移。推断地震期间的断层滑移对于理解地震动力学和改进地震风险缓解策略至关重要，因此这一最优控制问题具有重要的科学意义。我们利用适当的有限元空间为控制和状态建立了先验误差估计。我们的理论收敛率通过数值实验得到了验证。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Applied Numerical Mathematics

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀