Communications in Computational Physics最新文献_第2页

Unconstrained ETD Methods on the Diffuse-Interface Model with the Peng-Robinson Equation of State 基于彭-罗宾逊状态方程的扩散界面模型的无约束 ETD 方法

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-05-01 DOI: 10.4208/cicp.oa-2023-0256

Menghuo Chen,Yuanqing Wu,Xiaoyu Feng, Shuyu Sun

{"title":"Unconstrained ETD Methods on the Diffuse-Interface Model with the Peng-Robinson Equation of State","authors":"Menghuo Chen,Yuanqing Wu,Xiaoyu Feng, Shuyu Sun","doi":"10.4208/cicp.oa-2023-0256","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0256","url":null,"abstract":"In this study, we apply first-order exponential time differencing (ETD) methods to solve benchmark problems for the diffuse-interface model using the Peng-Robinson equation of state. We demonstrate the unconditional stability of the proposed algorithm within the ETD framework. Additionally, we analyzed the complexity of the algorithm, revealing that computations like matrix multiplications and inversions in each time step exhibit complexity strictly less than $mathcal{O}(n^2),$ where $n$ represents\u0000the number of variables or grid points. The main objective was to develop an algorithm with enhanced performance and robustness. To achieve this, we avoid iterative\u0000solutions (such as matrix inversion) in each time step, as they are sensitive to matrix\u0000properties. Instead, we adopted a hierarchical matrix ($mathcal{H}$-matrix) approximation for\u0000the matrix inverse and matrix exponential used in each time step. By leveraging hierarchical matrices with a rank $k ≪ n,$ we achieve a complexity of $O(kn{rm log}(n))$ for\u0000their product with an $n$-vector, which outperforms the traditional $mathcal{O}(n^2)$ complexity.\u0000Overall, our focus is on creating an unconditionally stable algorithm with improved\u0000computational efficiency and reliability.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":"18 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of a Mixed Finite Element Method for Stochastic Cahn-Hilliard Equation with Multiplicative Noise 带有乘法噪声的随机卡恩-希利亚德方程的混合有限元方法分析

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-05-01 DOI: 10.4208/cicp.oa-2023-0172

Yukun Li,Corey Prachniak, Yi Zhang

{"title":"Analysis of a Mixed Finite Element Method for Stochastic Cahn-Hilliard Equation with Multiplicative Noise","authors":"Yukun Li,Corey Prachniak, Yi Zhang","doi":"10.4208/cicp.oa-2023-0172","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0172","url":null,"abstract":"This paper proposes and analyzes a novel fully discrete finite element scheme\u0000with an interpolation operator for stochastic Cahn-Hilliard equations with functional-type noise. The nonlinear term satisfies a one-sided Lipschitz condition and the diffusion term is globally Lipschitz continuous. The novelties of this paper are threefold.\u0000Firstly, the $L^2$-stability ($L^∞$ in time) and $H^2$-stability ($L^2$ in time) are proved for the\u0000proposed scheme. The idea is to utilize the special structure of the matrix assembled by the nonlinear term. None of these stability results has been proved for the\u0000fully implicit scheme in existing literature due to the difficulty arising from the interaction of the nonlinearity and the multiplicative noise. Secondly, higher moment\u0000stability in $L^2$-norm of the discrete solution is established based on the previous stability results. Thirdly, the Hölder continuity in time for the strong solution is established under the minimum assumption of the strong solution. Based on these findings, the\u0000strong convergence in $H^{−1}$-norm of the discrete solution is discussed. Several numerical experiments including stability and convergence are also presented to validate our\u0000theoretical results.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":"6 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Postprocessing Techniques of High-Order Galerkin Approximations to Nonlinear Second-Order Initial Value Problems with Applications to Wave Equations 非线性二阶初值问题高阶 Galerkin 近似的后处理技术及其在波方程中的应用

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-04-01 DOI: 10.4208/cicp.oa-2023-0232

Mingzhu Zhang, Lijun Yi

{"title":"Postprocessing Techniques of High-Order Galerkin Approximations to Nonlinear Second-Order Initial Value Problems with Applications to Wave Equations","authors":"Mingzhu Zhang, Lijun Yi","doi":"10.4208/cicp.oa-2023-0232","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0232","url":null,"abstract":"The aim of this paper is to propose and analyze two postprocessing techniques for improving the accuracy of the $C^1$- and $C^0$-continuous Galerkin (CG) time\u0000stepping methods for nonlinear second-order initial value problems, respectively. We\u0000first derive several optimal a priori error estimates and nodal superconvergent estimates for the $C^1$- and $C^0$-$CG$ methods. Then we propose two simple but efficient local\u0000postprocessing techniques for the $C^1$- and $C^0$-$CG$ methods, respectively. The key idea\u0000of the postprocessing techniques is to add a certain higher order generalized Jacobi\u0000polynomial of degree $k+1$ to the $C^1$- or $C^0$-$CG$ approximation of degree $k$ on each local\u0000time step. We prove that, for problems with regular solutions, such postprocessing\u0000techniques improve the global convergence rates for the $L^2$-, $H^1$- and $L^∞$-error estimates of the $C^1$- and $C^0$-$CG$ methods with quasi-uniform meshes by one order. As\u0000applications, we apply the superconvergent postprocessing techniques to the $C^1$- and $C^0$-$CG$ time discretization of nonlinear wave equations. Several numerical examples\u0000are presented to verify the theoretical results.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":"31 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Towards the Efficient Calculation of Quantity of Interest from Steady Euler Equations I: A Dual-Consistent DWR-Based $h$-Adaptive Newton-GMG Solver 从稳定欧拉方程高效计算感兴趣的量 I. 基于 $h$ 自适应牛顿-GMG 求解器的双重一致 DWR基于 $h$ 自适应牛顿-GMG 求解器的双一致性 DWR

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-04-01 DOI: 10.4208/cicp.oa-2023-0196

Jingfeng Wang, Guanghui Hu

{"title":"Towards the Efficient Calculation of Quantity of Interest from Steady Euler Equations I: A Dual-Consistent DWR-Based $h$-Adaptive Newton-GMG Solver","authors":"Jingfeng Wang, Guanghui Hu","doi":"10.4208/cicp.oa-2023-0196","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0196","url":null,"abstract":"The dual consistency is an important issue in developing stable DWR error estimation towards the goal-oriented mesh adaptivity. In this paper, such an issue\u0000is studied in depth based on a Newton-GMG framework for the steady Euler equations. Theoretically, the numerical framework is redescribed using the Petrov-Galerkin\u0000scheme, based on which the dual consistency is depicted. It is found that for a problem with general configuration, a boundary modification technique is an effective approach to preserve the dual consistency in our numerical framework. Numerically,\u0000a geometrical multigrid is proposed for solving the dual problem, and a regularization term is designed to guarantee the convergence of the iteration. The following\u0000features of our method can be observed from numerical experiments, i). a stable numerical convergence of the quantity of interest can be obtained smoothly for problems\u0000with different configurations, and ii). towards accurate calculation of quantity of interest, mesh grids can be saved significantly using the proposed dual-consistent DWR\u0000method, compared with the dual-inconsistent one.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":"47 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An Implicit, Asymptotic-Preserving and Energy-Charge-Conserving Method for the Vlasov-Maxwell System Near Quasi-Neutrality 准中性附近弗拉索夫-麦克斯韦系统的隐含、渐近保全和能量电荷保全方法

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-04-01 DOI: 10.4208/cicp.oa-2023-0133

Chuwen Ma, Shi Jin

引用次数: 0

Generalization Error in the Deep Ritz Method with Smooth Activation Functions 具有平滑激活函数的深度里兹方法的泛化误差

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-04-01 DOI: 10.4208/cicp.oa-2023-0253

Janne Siipola

引用次数: 0

A Second Order Numerical Scheme of the Cahn-Hilliard-Navier-Stokes System with Flory-Huggins Potential 含 Flory-Huggins 势的卡恩-希利亚德-纳维尔-斯托克斯系统的二阶数值方案

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-04-01 DOI: 10.4208/cicp.oa-2023-0038

Wenbin Chen,Jianyu Jing,Qianqian Liu,Cheng Wang, Xiaoming Wang

{"title":"A Second Order Numerical Scheme of the Cahn-Hilliard-Navier-Stokes System with Flory-Huggins Potential","authors":"Wenbin Chen,Jianyu Jing,Qianqian Liu,Cheng Wang, Xiaoming Wang","doi":"10.4208/cicp.oa-2023-0038","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0038","url":null,"abstract":"A second order accurate in time, finite difference numerical scheme is proposed and analyzed for the Cahn-Hilliard-Navier-Stokes system, with logarithmic\u0000Flory-Huggins energy potential. In the numerical approximation to the chemical potential, a modified Crank-Nicolson approximation is applied to the singular logarithmic nonlinear term, while the expansive term is updated by an explicit second order\u0000Adams-Bashforth extrapolation, and an alternate temporal stencil is used for the surface diffusion term. Moreover, a nonlinear artificial regularization term is included in\u0000the chemical potential approximation, which ensures the positivity-preserving property for the logarithmic arguments, i.e., the numerical value of the phase variable is\u0000always between −1 and 1 at a point-wise level. Meanwhile, the convective term in the\u0000phase field evolutionary equation is updated in a semi-implicit way, with second order\u0000accurate temporal approximation. The fluid momentum equation is also computed by\u0000a semi-implicit algorithm. The unique solvability and the positivity-preserving property of the second order scheme is proved, accomplished by an iteration process. A\u0000modified total energy stability of the second order scheme is also derived. Some numerical results are presented to demonstrate the accuracy and the robust performance\u0000of the proposed second order scheme.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":"158 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Hybrid Finite Difference Fifth-Order Multi-Resolution WENO Scheme for Hamilton-Jacobi Equations 针对汉密尔顿-雅可比方程的混合有限差分五阶多分辨率 WENO 方案

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-04-01 DOI: 10.4208/cicp.oa-2023-0002

Zhenming Wang,Jun Zhu,Linlin Tian, Ning Zhao

{"title":"Hybrid Finite Difference Fifth-Order Multi-Resolution WENO Scheme for Hamilton-Jacobi Equations","authors":"Zhenming Wang,Jun Zhu,Linlin Tian, Ning Zhao","doi":"10.4208/cicp.oa-2023-0002","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0002","url":null,"abstract":"In this paper, a fifth-order hybrid multi-resolution weighted essentially non-oscillatory (WENO) scheme in the finite difference framework is proposed for solving\u0000one- and two-dimensional Hamilton-Jacobi equations. Firstly, a new discontinuity sensor is designed based on the extreme values of the highest degree polynomial in the\u0000multi-resolution WENO procedures. This hybrid strategy does not contain any human parameters related to specific problems and can identify the troubled grid points\u0000accurately and automatically. Secondly, a hybrid multi-resolution WENO scheme for\u0000Hamilton-Jacobi equations is developed based on the above discontinuity sensor and a\u0000simplified multi-resolution WENO scheme, which yields uniform high-order accuracy\u0000in smooth regions and sharply resolves discontinuities. Compared with the existing\u0000multi-resolution WENO scheme, the method developed in this paper can inherit its\u0000many advantages and is more efficient. Finally, some benchmark numerical experiments are performed to demonstrate the performance of the presented fifth-order hybrid multi-resolution WENO scheme for one- and two-dimensional Hamilton-Jacobi\u0000equations.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":"6 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations 用于多尺度动力学方程的渐近保全神经网络

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-04-01 DOI: 10.4208/cicp.oa-2023-0211

Shi Jin,Zheng Ma, Keke Wu

{"title":"Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations","authors":"Shi Jin,Zheng Ma, Keke Wu","doi":"10.4208/cicp.oa-2023-0211","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0211","url":null,"abstract":"In this paper, we present two novel Asymptotic-Preserving Neural Networks (APNNs) for tackling multiscale time-dependent kinetic problems, encompassing the linear transport equation and Bhatnagar-Gross-Krook (BGK) equation in all\u0000ranges of Knudsen number. Our primary objective is to devise accurate APNN approaches for resolving multiscale kinetic equations, which is also efficient in the small\u0000Knudsen number regime. The first APNN for linear transport equation is based on\u0000even-odd decomposition, which relaxes the stringent conservation prerequisites while\u0000concurrently introducing an auxiliary deep neural network. We conclude that enforcing the initial condition for the linear transport equation with inflow boundary\u0000conditions is crucial for this network. For the Boltzmann-BGK equation, the APNN\u0000incorporates the conservation of mass, momentum, and total energy into the APNN\u0000framework as well as exact boundary conditions. A notable finding of this study is that\u0000approximating the zeroth, first, and second moments—which govern the conservation\u0000of density, momentum, and energy for the Boltzmann-BGK equation, is simpler than\u0000the distribution itself. Another interesting phenomenon observed in the training process is that the convergence of density is swifter than that of momentum and energy.\u0000Finally, we investigate several benchmark problems to demonstrate the efficacy of our\u0000proposed APNN methods.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":"15 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An Efficient High-Order Gas-Kinetic Scheme with Hybrid WENO-AO Method for the Euler and Navier-Stokes Solutions 用混合 WENO-AO 方法解决欧拉和纳维-斯托克斯问题的高效高阶气体动力学方案

IF 3.7 3区物理与天体物理

Communications in Computational Physics Pub Date : 2024-04-01 DOI: 10.4208/cicp.oa-2023-0108

Junlei Mu,Congshan Zhuo,Qingdian Zhang,Sha Liu, Chengwen Zhong

{"title":"An Efficient High-Order Gas-Kinetic Scheme with Hybrid WENO-AO Method for the Euler and Navier-Stokes Solutions","authors":"Junlei Mu,Congshan Zhuo,Qingdian Zhang,Sha Liu, Chengwen Zhong","doi":"10.4208/cicp.oa-2023-0108","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0108","url":null,"abstract":"The high-order gas-kinetic scheme (HGKS) features good robustness, high\u0000efficiency and satisfactory accuracy,the performance of which can be further improved\u0000combined with WENO-AO (WENO with adaptive order) scheme for reconstruction.\u0000To reduce computational costs in the reconstruction procedure, this paper proposes\u0000to combine HGKS with a hybrid WENO-AO scheme. The hybrid WENO-AO scheme\u0000reconstructs target variables using upwind linear approximation directly if all extreme\u0000points of the reconstruction polynomials for these variables are outside the large stencil. Otherwise, the WENO-AO scheme is used. Unlike combining the hybrid WENO\u0000scheme with traditional Riemann solvers, the troubled cell indicator of the hybrid\u0000WENO-AO method is fully utilized in the spatial reconstruction process of HGKS.\u0000During normal and tangential reconstruction, the gas-kinetic scheme flux not only\u0000needs to reconstruct the conservative variables on the left and right interfaces but also\u0000to reconstruct the derivative terms of the conservative variables. By reducing the number of times that the WENO-AO scheme is used, the calculation cost is reduced. The\u0000high-order gas-kinetic scheme with the hybrid WENO-AO method retains original robustness and accuracy of the WENO5-AO GKS, while exhibits higher computational\u0000efficiency.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":"117 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0