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A Structure-Preserving JKO Scheme for the SizeModified Poisson-Nernst-Planck-Cahn-Hilliard Equations 尺寸修正Poisson-Nernst-Planck-Cahn-Hilliard方程的保结构JKO格式
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0078
Jie Ding null, Xiang Ji
{"title":"A Structure-Preserving JKO Scheme for the SizeModified Poisson-Nernst-Planck-Cahn-Hilliard Equations","authors":"Jie Ding null, Xiang Ji","doi":"10.4208/nmtma.oa-2022-0078","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0078","url":null,"abstract":". In this paper, we propose a structure-preserving numerical scheme for the size-modified Poisson-Nernst-Planck-Cahn-Hilliard (SPNPCH) equations derived from the free energy including electrostatic energies, entropies, steric energies, and Cahn-Hilliard mixtures. Based on the Jordan-Kinderlehrer-Otto (JKO) framework and the Benamou-Brenier formula of quadratic Wasserstein distance, the SPNPCH equations are transformed into a constrained optimization problem. By exploiting the convexity of the objective function, we can prove the existence and uniqueness of the numerical solution to the optimization problem. Mass conservation and unconditional energy-dissipation are preserved automatically by this scheme. Furthermore, by making use of the singularity of the entropy term which keeps the concentration from approaching zero, we can ensure the positivity of concentration. To solve the optimization problem, we apply the quasi-Newton method, which can ensure the positivity of concentration in the iterative process. Numerical tests are performed to confirm the anticipated accuracy and the desired physical properties of the developed scheme. Finally, the proposed scheme can also be applied to study the influence of ionic sizes and gradient energy coefficients on ion distribution.","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48956618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection 具有斜率选择的MBE方程的能量稳定滤波后向Euler格式
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0072
Jiexin Wang, Hong-Lin Liao null, Ying Zhao
{"title":"An Energy Stable Filtered Backward Euler Scheme for the MBE Equation with Slope Selection","authors":"Jiexin Wang, Hong-Lin Liao null, Ying Zhao","doi":"10.4208/nmtma.oa-2022-0072","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0072","url":null,"abstract":". As a promising strategy to adjust the order in the variable-order BDF algo-rithm, a time filtered backward Euler scheme is investigated for the molecular beam epitaxial equation with slope selection. The temporal second-order convergence in the L 2 norm is established under a convergence-solvability-stability (CSS)-consistent time-step constraint. The CSS-consistent condition means that the maximum step-size limit required for convergence is of the same order to that for solvability and stability (in certain norms) as the small interface parameter ε → 0 + . Similar to the backward Euler scheme, the time filtered backward Euler scheme preserves some physical properties of the original problem at the discrete levels, including the volume conservation, the energy dissipation law and L 2 norm boundedness. Numerical tests are included to support the theoretical results.","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48666198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field 磁化与磁场平行的铁磁流体模型的混合有限元方法
4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0163
Yongke Wu and Xiaoping Xie
{"title":"Mixed Finite Element Methods for the Ferrofluid Model with Magnetization Paralleled to the Magnetic Field","authors":"Yongke Wu and Xiaoping Xie","doi":"10.4208/nmtma.oa-2022-0163","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0163","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135061153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations 泊松/亥姆霍兹方程的新六阶紧化格式
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0073
K. Pan, K. Fu, Jin Li, Hongling Hu null, Zhilin Li
{"title":"New Sixth-Order Compact Schemes for Poisson/Helmholtz Equations","authors":"K. Pan, K. Fu, Jin Li, Hongling Hu null, Zhilin Li","doi":"10.4208/nmtma.oa-2022-0073","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0073","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47520406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes 矩形网格上二阶超收敛WG有限元的构造
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0082
Xiu Ye null, Shangyou Zhang
{"title":"Constructing Order Two Superconvergent WG Finite Elements on Rectangular Meshes","authors":"Xiu Ye null, Shangyou Zhang","doi":"10.4208/nmtma.oa-2022-0082","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0082","url":null,"abstract":". In this paper, we introduce a stabilizer free weak Galerkin (SFWG) finite element method for second order elliptic problems on rectangular meshes. With a special weak Gradient space, an order two superconvergence for the SFWG finite element solution is obtained, in both L 2 and H 1 norms. A local post-process lifts such a P k weak Galerkin solution to an optimal order P k +2 solution. The numerical results confirm the theory","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48089056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations 非线性时间分数阶Schrödinger方程的线性化变换$L1$ Galerkin fem的无条件收敛性
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0087
Wanqiu Yuan, Dongfang Li null, C. Zhang
{"title":"Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations","authors":"Wanqiu Yuan, Dongfang Li null, C. Zhang","doi":"10.4208/nmtma.oa-2022-0087","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0087","url":null,"abstract":". A linearized transformed L 1 Galerkin finite element method (FEM) is presented for numerically solving the multi-dimensional time fractional Schr¨odinger equations. Unconditionally optimal error estimates of the fully-discrete scheme are proved. Such error estimates are obtained by combining a new discrete fractional Gr¨onwall inequality, the corresponding Sobolev embedding theorems and some inverse inequalities. While the previous unconditional convergence results are usually obtained by using the temporal-spatial error spitting approaches. Numerical examples are presented to confirm the theoretical results","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42925581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 7
New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications 无界区间上新的有理插值基函数及其应用
IF 1.3 4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0109
Dongqin Gu, Zhong-Qing Wang null, Chao Zhang
{"title":"New Rational Interpolation Basis Functions on the Unbounded Intervals and Their Applications","authors":"Dongqin Gu, Zhong-Qing Wang null, Chao Zhang","doi":"10.4208/nmtma.oa-2022-0109","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0109","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49208478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Alternating Direction Method of Multipliers for Inverse Lithography Problem 反光刻问题乘法器的交替方向法
4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0151
Junqing Chen and Haibo Liu
{"title":"An Alternating Direction Method of Multipliers for Inverse Lithography Problem","authors":"Junqing Chen and Haibo Liu","doi":"10.4208/nmtma.oa-2022-0151","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0151","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136177895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Sparse Deep Neural Network for Nonlinear Partial Differential Equations 非线性偏微分方程的稀疏深度神经网络
4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0104
Yuesheng Xu null, Taishan Zeng
{"title":"Sparse Deep Neural Network for Nonlinear Partial Differential Equations","authors":"Yuesheng Xu null, Taishan Zeng","doi":"10.4208/nmtma.oa-2022-0104","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0104","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135006184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
MC-Nonlocal-PINNs: Handling Nonlocal Operators in PINNs Via Monte Carlo Sampling mc -Nonlocal- pinn:通过蒙特卡罗采样处理pinn中的非局部算子
4区 数学
Numerical Mathematics-Theory Methods and Applications Pub Date : 2023-06-01 DOI: 10.4208/nmtma.oa-2022-0201
Xiaodong Feng, Yue Qian and Wanfang Shen
{"title":"MC-Nonlocal-PINNs: Handling Nonlocal Operators in PINNs Via Monte Carlo Sampling","authors":"Xiaodong Feng, Yue Qian and Wanfang Shen","doi":"10.4208/nmtma.oa-2022-0201","DOIUrl":"https://doi.org/10.4208/nmtma.oa-2022-0201","url":null,"abstract":"","PeriodicalId":51146,"journal":{"name":"Numerical Mathematics-Theory Methods and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136170800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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