East Asian Journal on Applied Mathematics最新文献

A Hybrid Neural-Network and MAC Scheme for Stokes Interface Problems 针对斯托克斯接口问题的混合神经网络和 MAC 方案

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-05-01 DOI: 10.4208/eajam.2024-006.060424

Che-Chia Chang,Chen-Yang Dai,Wei-Fan Hu,Te-Sheng Lin, Ming-Chih Lai

{"title":"A Hybrid Neural-Network and MAC Scheme for Stokes Interface Problems","authors":"Che-Chia Chang,Chen-Yang Dai,Wei-Fan Hu,Te-Sheng Lin, Ming-Chih Lai","doi":"10.4208/eajam.2024-006.060424","DOIUrl":"https://doi.org/10.4208/eajam.2024-006.060424","url":null,"abstract":"In this paper, we present a hybrid neural-network and MAC (Marker-And-Cell) scheme for solving Stokes equations with singular forces on an embedded interface in regular domains. As known, the solution variables (the pressure and velocity)\u0000exhibit non-smooth behaviors across the interface so extra discretization efforts must be\u0000paid near the interface in order to have small order of local truncation errors in finite\u0000difference schemes. The present hybrid approach avoids such additional difficulty. It\u0000combines the expressive power of neural networks with the convergence of finite difference schemes to ease the code implementation and to achieve good accuracy at the same\u0000time. The key idea is to decompose the solution into singular and regular parts. The\u0000neural network learning machinery incorporating the given jump conditions finds the\u0000singular part solution, while the standard MAC scheme is used to obtain the regular part\u0000solution with associated boundary conditions. The two- and three-dimensional numerical results show that the present hybrid method converges with second-order accuracy\u0000for the velocity and first-order accuracy for the pressure, and it is comparable with the\u0000traditional immersed interface method in literature.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":"36 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256799","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

A Pre-Training Deep Learning Method for Simulating the Large Bending Deformation of Bilayer Plates 模拟双层板大弯曲变形的预训练深度学习方法

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-05-01 DOI: 10.4208/eajam.2023-325.070124

Xiang Li,Yulei Liao, Pingbing Ming

引用次数: 0

An Adaptive Moving Mesh Method for Simulating Finite-time Blowup Solutions of the Landau-Lifshitz-Gilbert Equation 模拟兰道-利夫希茨-吉尔伯特方程有限时间炸毁解的自适应移动网格法

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-05-01 DOI: 10.4208/eajam.2023-322.250224

Zheyue Fang, Xiaoping Wang

引用次数: 0

Orthogonality Sampling Method for Identifying Small Anomalies in Real-World Microwave Imaging 在真实世界微波成像中识别微小异常的正交采样法

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2022-318.170723

Chi Young Ahn,Seongje Chae,Sangwoo Kang,Kwang-Jae Lee,Won-Kwang Park, Seong-Ho Son

引用次数: 0

Real Reduced Matrix mKdV Integrable Hierarchies Under Two Local Group Reductions 两个局部组还原下的实还原矩阵 mKdV 可积分层次结构

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2022-310.300623

Wen-Xiu Ma

引用次数: 0

Multivariate Feedback Particle Filter Rederived from the Splitting-Up Scheme 从拆分方案再衍生出的多元反馈粒子滤波器

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2022-184.030823

Huimin Miao, Xue Luo

{"title":"Multivariate Feedback Particle Filter Rederived from the Splitting-Up Scheme","authors":"Huimin Miao, Xue Luo","doi":"10.4208/eajam.2022-184.030823","DOIUrl":"https://doi.org/10.4208/eajam.2022-184.030823","url":null,"abstract":"The multivariate feedback particle filter (FPF) is formulated from the viewpoint of splitting-up methods. The essential difference between this formulation and\u0000the formal derivation is that instead of one-time control at a discrete time instant, we\u0000consider the updating stage as a stochastic flow of particles in each time interval. This allows to easily obtain a consistent stochastic flow by comparing the Kolmogorov forward\u0000equation of particles and the updating part of the Kushner’s equation in the splitting-up\u0000method. Moreover, if an optimal stochastic flow exists, the convergence of the splitting-up method can be studied by passing to an FPF with a continuous time. To guarantee the\u0000existence of a stochastic flow, we validate the Poincaré inequality for the alternating distributions, given the time discretization and the observation path, under mild conditions\u0000on the nonlinear filtering system and the initial state. Besides, re-examining the original\u0000derivation of the FPF, we show that the optimal transport map between the prior and\u0000the posterior is an $f$-divergence invariant in the abstract Bayesian inference framework.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":"44 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564659","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

Partitioned Dashnic-Zusmanovich Type Matric with Applications 分区达什尼奇-祖斯玛诺维奇类型矩阵及其应用

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2023-019.100823

Wenlong Zeng, Jianzhou Liu

引用次数: 0

Advection-Pressure Splitting Schemes for the Equations of Blood Flow Conservative and Non-Conservative Forms 血流方程保守和非保守形式的对流-压力分割方案

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2023-045.090523

Eleuterio F. Toro,Annunziato Siviglia,Alessandra Spilimbergo, Lucas O. Müller

{"title":"Advection-Pressure Splitting Schemes for the Equations of Blood Flow Conservative and Non-Conservative Forms","authors":"Eleuterio F. Toro,Annunziato Siviglia,Alessandra Spilimbergo, Lucas O. Müller","doi":"10.4208/eajam.2023-045.090523","DOIUrl":"https://doi.org/10.4208/eajam.2023-045.090523","url":null,"abstract":"We present a class of simple advection-pressure splitting numerical methods\u0000to solve the blood flow equations in compliant arterial vessels. The schemes are inspired\u0000by the TV flux vector splitting approach for conservative systems, proposed by Toro and\u0000Vázquez [30]. But the reformulated TV-type splitting schemes of this paper have a wider\u0000range of applicability, including systems of equations in non-conservative form. The\u0000spatial differential operator is split into advection terms, which may be in conservative form, from pressure terms in conservative or non-conservative form. Additionally,\u0000unlike the original TV scheme, the reformulated splitting of this paper fully preserves\u0000the continuity equation as part of the pressure system. This last feature is consistent\u0000with zero-dimensional models for blood flow that are based on neglecting the inertial\u0000term in the momentum equation. The schemes are also well suited for systems in which\u0000geometric and biomechanical parameters of the problem vary discontinuously. The splitting schemes of this paper are systematically assessed on a carefully designed suite of\u0000test problems and compared with several existing, mainstream methods. Overall, the\u0000proposed numerical methods perform very satisfactorily and suggest themselves as attractive computational tools for modelling the dynamics of bodily fluids under realistic\u0000conditions.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564663","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

On Pricing Options Under Two Stochastic Volatility Processes 论两种随机波动过程下的期权定价

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-04-01 DOI: 10.4208/eajam.2022-356.180923

Wenjia Xie, Zhongyi Huang

引用次数: 0

A Diagonalization-Based Parallel-in-Time Algorithm for Crank-Nicolson’s Discretization of the Viscoelastic Equation 基于对角线化的时间并行算法，用于粘弹性方程的克兰克-尼科尔森离散化

IF 1.2 4区数学

East Asian Journal on Applied Mathematics Pub Date : 2024-01-01 DOI: 10.4208/eajam.2022-304.070323

Fu Li, Yingxiang Xu

{"title":"A Diagonalization-Based Parallel-in-Time Algorithm for Crank-Nicolson’s Discretization of the Viscoelastic Equation","authors":"Fu Li, Yingxiang Xu","doi":"10.4208/eajam.2022-304.070323","DOIUrl":"https://doi.org/10.4208/eajam.2022-304.070323","url":null,"abstract":"In this paper, we extend a diagonalization-based parallel-in-time (PinT) algorithm to the viscoelastic equation. The central difference method is used for spatial discretization, while for temporal discretization, we use the Crank-Nicolson scheme. Then an all-at-once system collecting all the solutions at each time level is formed and solved using a fixed point iteration preconditioned by an $α$-circulant matrix in parallel. Via a rigorous analysis, we find that the spectral radius of the iteration matrix is uniformly bounded by $α/(1 − α),$ independent of the model parameters (the damping coefficient $varepsilon$ and the wave velocity $sqrt{gamma}$) and the discretization parameters (the time step $tau$ and the spatial mesh size $h$). Unlike the classical wave equation with Dirichlet boundary condition where the upper bound $α/(1 − α)$ is very sharp, we find that the occurrence of the damping term $−varepsilon∆y_t,$ as well as the large final time $T,$ leads to even faster convergence of the algorithm, especially when $α$ is not very small. We illustrate our theoretical findings with several numerical examples.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":"215 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139082096","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