Journal of Computational and Applied Mathematics最新文献_第4页

Preconditioned FEM-based neural networks for solving incompressible fluid flows and related inverse problems 求解不可压缩流体流动及相关逆问题的预条件有限元神经网络

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-05 DOI: 10.1016/j.cam.2025.116663

Franziska Griese, Fabian Hoppe, Alexander Rüttgers, Philipp Knechtges

{"title":"Preconditioned FEM-based neural networks for solving incompressible fluid flows and related inverse problems","authors":"Franziska Griese, Fabian Hoppe, Alexander Rüttgers, Philipp Knechtges","doi":"10.1016/j.cam.2025.116663","DOIUrl":"10.1016/j.cam.2025.116663","url":null,"abstract":"<div><div>The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A comparatively new approach in this context is to combine the good approximation properties of neural networks (for parameter dependence) with the classical finite element method (for discretization). However, instead of considering the solution mapping of the PDE from the parameter space into the FEM-discretized solution space as a purely data-driven regression problem, so-called physically informed regression problems have proven to be useful. In these, the equation residual is minimized during the training of the neural network, i.e. the neural network “learns” the physics underlying the problem. In this paper, we extend this approach to saddle-point and non-linear fluid dynamics problems, respectively, namely stationary Stokes and stationary Navier–Stokes equations. In particular, we propose a modification of the existing approach: Instead of minimizing the plain vanilla equation residual during training, we minimize the equation residual modified by a preconditioner. By analogy with the linear case, this also improves the condition in the present non-linear case. Our numerical examples demonstrate that this approach significantly reduces the training effort and greatly increases accuracy and generalizability. Finally, we show the application of the resulting parameterized model to a related inverse problem.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116663"},"PeriodicalIF":2.1,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792139","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

An efficient temporal multiscale algorithm for simulating a long-term plaque growth problem in relation to power-law blood flows 模拟与幂律血流有关的长期斑块生长问题的高效时间多尺度算法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-04 DOI: 10.1016/j.cam.2025.116666

Xinyu Li , Ping Lin , Weifeng Zhao

{"title":"An efficient temporal multiscale algorithm for simulating a long-term plaque growth problem in relation to power-law blood flows","authors":"Xinyu Li , Ping Lin , Weifeng Zhao","doi":"10.1016/j.cam.2025.116666","DOIUrl":"10.1016/j.cam.2025.116666","url":null,"abstract":"<div><div>This paper discusses the problem of non-Newtonian fluids with time multiscale characteristics, especially considering the type of power-law blood flow in a narrowed blood vessel due to plaque growth. In the vessel, the blood flow is considered as a fast-scale periodic motion, while the vessel wall grows on a slow scale. We use an auxiliary temporal periodic problem and an effective time-average equation to approximate the original problem. The approximation error is analyzed only for a largely simplified linear system, where the simple front-tracking technique is used to update the slow vessel wall growth. An effective multiscale method is then designed based on the approximation problem. The front-tracking technique also makes the implementation of the multiscale algorithm easier. Compared with the traditional direct solving process, this method shows a strong acceleration effect. Finally, we present a concrete numerical example. Through comparison, the relative error between the results of the multi-scale algorithm and the direct solving process is small, which is consistent with the theoretical analysis.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116666"},"PeriodicalIF":2.1,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143783945","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 structured spectral gradient methods for nonlinear least squares with application in robotic motion control problems 非线性最小二乘的结构谱梯度新方法及其在机器人运动控制中的应用

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-04 DOI: 10.1016/j.cam.2025.116671

Aliyu Muhammed Awwal , Nuttapol Pakkaranang

引用次数: 0

Space–time non-local multi-continua multiscale method for channelized-media parabolic equations 通道介质抛物方程的时空非局部多连续多尺度方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-04 DOI: 10.1016/j.cam.2025.116669

Jiuhua Hu , Wing Tat Leung , Eric Chung

{"title":"Space–time non-local multi-continua multiscale method for channelized-media parabolic equations","authors":"Jiuhua Hu , Wing Tat Leung , Eric Chung","doi":"10.1016/j.cam.2025.116669","DOIUrl":"10.1016/j.cam.2025.116669","url":null,"abstract":"<div><div>In this paper, we consider a parabolic problem with time-dependent heterogeneous coefficients. Many applied problems have coupled spatial and temporal heterogeneities. Their homogenization or upscaling requires cell problems that are formulated in space–time representative volumes for problems with scale separation. In problems without scale separation, local problems include multiple macroscopic variables and oversampled local problems, where these macroscopic parameters are computed. These approaches, called Non-local multi-continua, are proposed for problems with complex spatial heterogeneities in a number of previous papers. In this paper, we extend this approach to handle space–time heterogeneities, by identifying macroscopic parameters in space–time regions. Our proposed method space–time Non-local multi-continua (space–time NLMC) offers an efficient numerical solver to deal with time-dependent heterogeneous coefficients. It provides a flexible and systematic approach to construct multiscale basis functions, enabling accurate approximation of the solution. The construction of these multiscale basis functions involves solving local energy minimization problems within the oversampled space–time regions. The resulting basis functions exhibit exponential decay outside the selected domain. Unlike the classical time-stepping methods combined with full-discretization technique, our space–time NLMC efficiently constructs the multiscale basis functions in the space–time domain, resulting in computational savings compared to space-only approaches as discussed in the paper. We present two numerical experiments that demonstrate the accuracy and effectiveness of the proposed approach.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116669"},"PeriodicalIF":2.1,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808167","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

Meshfree phase-field modeling of three-phase flow using smoothed particle hydrodynamics with differential reproducing kernels and artificial compressibility 基于微分再现核和人工可压缩性的光滑颗粒流体力学三相流无网格相场建模

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-03 DOI: 10.1016/j.cam.2025.116654

Adam Y. Ghoneim

{"title":"Meshfree phase-field modeling of three-phase flow using smoothed particle hydrodynamics with differential reproducing kernels and artificial compressibility","authors":"Adam Y. Ghoneim","doi":"10.1016/j.cam.2025.116654","DOIUrl":"10.1016/j.cam.2025.116654","url":null,"abstract":"<div><div>This paper presents a meshfree approach for phase-field (PF) modeling of three-phase flow using Smoothed Particle Hydrodynamics (SPH) with Differential Reproducing Kernels (DRK). In this method, the constructed approximating weight functions and their gradients satisfy the reproducibility condition. The computational domain is discretized into particles and a diffuse interface is assumed between three immiscible fluid phases. The propagation of the diffuse interface is handled by solving a Cahn-Hilliard (CH) equation based on the Helmholtz free energy functional minimization. We employ an artificial compressibility method based on the General Pressure Equation (GPE), exhibiting a stabilizing dissipative pressure term for solving the Navier–Stokes (NS) equations. As such, we depart from the density-based Equation of State (EOS) typically used in weakly-compressible SPH. The proposed PF-SPH method for solving the Cahn-Hilliard-Navier–Stokes (CHNS) system of equations was found to be particularly effective in handling the non-trivial surface tension effects at the fluid interfaces, where more than two immiscible fluid phases co-exist. Additionally, particle shifting was found to be critical in ensuring successful construction of the DRK weight functions. We present the mathematical formulation and discuss the results of numerical simulations conducted in both 2D and 3D, as well as in both Lagrangian and Eulerian frameworks, demonstrating the versatility and applicability of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116654"},"PeriodicalIF":2.1,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143792138","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

Crank–Nicolson alternative direction implicit method for two-dimensional variable-order space-fractional diffusion equations with nonseparable coefficients 具有不可分系数的二维变阶空间分数扩散方程的Crank-Nicolson交替方向隐式方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-02 DOI: 10.1016/j.cam.2025.116655

Qiu-Ya Wang , Cui-Yun Lin , Cheng-Xue Lao

引用次数: 0

Nonsymmetric product integration rules for Chebyshev weight functions with Chebyshev abscissae 具有切比雪夫横坐标的切比雪夫权函数的非对称积积分规则

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-02 DOI: 10.1016/j.cam.2025.116668

Sotirios E. Notaris, Nikolaos J. Theodorakopoulos

{"title":"Nonsymmetric product integration rules for Chebyshev weight functions with Chebyshev abscissae","authors":"Sotirios E. Notaris, Nikolaos J. Theodorakopoulos","doi":"10.1016/j.cam.2025.116668","DOIUrl":"10.1016/j.cam.2025.116668","url":null,"abstract":"<div><div>We study four product integration rules, two for the Chebyshev weight of the first-kind based on the Chebyshev abscissae of the third or fourth-kind, and another two for the Chebyshev weight of the second-kind based again on the Chebyshev abscissae of the third or fourth-kind. The new rules are shown to have positive weights given by explicit formulae. Furthermore, we determine the precise degree of exactness and we compute the variance of the quadrature formulae, we examine their definiteness or nondefiniteness, and we obtain asymptotically optimal error bounds for these formulae by Peano kernel methods. In addition, the convergence of the quadrature formulae is shown not only for Riemann integrable functions on <span><math><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>, but also for functions having a monotonic singularity at one or both endpoints of <span><math><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>. Interestingly enough, the rules for the Chebyshev weight of the second-kind based on the Chebyshev abscissae of the third or fourth-kind have the best possible degree of exactness for an interpolatory formula not of Gauss type.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116668"},"PeriodicalIF":2.1,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808166","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

On adaptive anisotropic mesh optimization for convection–diffusion problems 对流扩散问题的自适应各向异性网格优化

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-02 DOI: 10.1016/j.cam.2025.116661

Petr Knobloch , René Schneider

{"title":"On adaptive anisotropic mesh optimization for convection–diffusion problems","authors":"Petr Knobloch , René Schneider","doi":"10.1016/j.cam.2025.116661","DOIUrl":"10.1016/j.cam.2025.116661","url":null,"abstract":"<div><div>Numerical solution of convection-dominated problems requires the use of layer-adapted anisotropic meshes. Since a priori construction of such meshes is difficult for complex problems, it is proposed to generate them in an adaptive way by moving the node positions in the mesh such that an a posteriori error estimator of the overall error of the approximate solution is reduced. This approach is formulated for a SUPG finite element discretization of a stationary convection–diffusion problem defined in a two-dimensional polygonal domain. The optimization procedure is based on the discrete adjoint technique and a SQP method using the BFGS update. The optimization of node positions is applied to a coarse grid only and the resulting anisotropic mesh is then refined by standard adaptive red-green refinement. Four error estimators based on the solution of local Dirichlet problems are tested and it is demonstrated that an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm based error estimator is the most robust one. The efficiency of the proposed approach is demonstrated on several model problems whose solutions contain typical boundary and interior layers.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116661"},"PeriodicalIF":2.1,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143783944","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

High-order bound-preserving finite difference methods for incompressible two-phase flow in porous media 多孔介质中不可压缩两相流的高阶保界有限差分方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-01 DOI: 10.1016/j.cam.2025.116658

Hui Guo , Kaixuan Wang , Jian Huang , Yang Yang

{"title":"High-order bound-preserving finite difference methods for incompressible two-phase flow in porous media","authors":"Hui Guo , Kaixuan Wang , Jian Huang , Yang Yang","doi":"10.1016/j.cam.2025.116658","DOIUrl":"10.1016/j.cam.2025.116658","url":null,"abstract":"<div><div>In this paper, we develop high-order bound-preserving (BP) finite difference (FD) methods for solving the incompressible and immiscible two-phase flow problem with capillary pressure in porous media. We use the implicit pressure explicit saturation (IMPES) scheme to solve for the pressure, auxiliary variables, and saturations of each phase in the coupled system. The boundedness of the saturations of the two phases, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>w</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, between 0 and 1 is an important physical characteristic. Applying non-physical numerical approximations may lead to significant oscillations in the numerical results and cause instability in the simulation. We apply high-order FD method and BP technique to maintain the high-order accuracy and the boundary of saturations. In the BP technique, the main idea is to choose an appropriate time step and apply positivity-preserving (PP) technique to <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>w</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, respectively, and ensure that <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>w</mi></mrow></msub><mo>+</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mn>1</mn></mrow></math></span>. In addition, the high-order accuracy is obtained by the parameterized flux limiter. Numerical examples are presented to demonstrate the high-order accuracy of the scheme and the effectiveness of the BP technique.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116658"},"PeriodicalIF":2.1,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808153","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 recipe for learning Variably Scaled Kernels via Discontinuous Neural Networks 一个通过不连续神经网络学习变尺度核的方法

IF 2.1 2区数学

Journal of Computational and Applied Mathematics Pub Date : 2025-04-01 DOI: 10.1016/j.cam.2025.116653

G. Audone, F. Della Santa, E. Perracchione, S. Pieraccini

引用次数: 0