Communications in Applied Mathematics and Computational Science最新文献

Application of a fourth-order accurate finite-volume method with adaptive refinement in space and time to multifluid plasma simulations 在多流体等离子体模拟中应用空间和时间自适应细化的四阶精确有限体积法

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2024-08-28 DOI: 10.2140/camcos.2024.19.57

Scott Polak, Xinfeng Gao

引用次数: 0

Bright-dark rogue wave transition in coupled AB system via the physics-informed neural networks method 通过物理信息神经网络方法实现耦合 AB 系统中的明暗流氓波转换

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2024-06-17 DOI: 10.2140/camcos.2024.19.1

Shi-Lin Zhang, Min-Hua Wang, Yin-Chuan Zhao

引用次数: 0

Multiderivative time integration methods preserving nonlinear functionals via relaxation 通过松弛保留非线性函数的多因次时间积分法

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2024-06-17 DOI: 10.2140/camcos.2024.19.27

Hendrik Ranocha, Jochen Schütz

引用次数: 0

A parallel-in-time collocation method using diagonalization: theory and implementation for linear problems 使用对角化的并行实时配准法：线性问题的理论与实现

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2023-12-21 DOI: 10.2140/camcos.2023.18.55

Gayatri Čaklović, Robert Speck, Martin Frank

{"title":"A parallel-in-time collocation method using diagonalization: theory and implementation for linear problems","authors":"Gayatri Čaklović, Robert Speck, Martin Frank","doi":"10.2140/camcos.2023.18.55","DOIUrl":"https://doi.org/10.2140/camcos.2023.18.55","url":null,"abstract":"We present and analyze a parallel implementation of a parallel-in-time collocation method based on <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>α</mi></math>-circulant preconditioned Richardson iterations. While many papers explore this family of single-level, time-parallel “all-at-once” integrators from various perspectives, performance results of actual parallel runs are still scarce. This leaves a critical gap, because the efficiency and applicability of any parallel method heavily rely on the actual parallel performance, with only limited guidance from theoretical considerations. Further, challenges like selecting good parameters, finding suitable communication strategies, and performing a fair comparison to sequential time-stepping methods can be easily missed. In this paper, we first extend the original idea of these fixed point iterative approaches based on <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>α</mi></math>-circulant preconditioners to high-order collocation methods, adding yet another level of parallelization in time “across the method”. We derive an adaptive strategy to select a new <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>α</mi></math>-circulant preconditioner for each iteration during runtime for balancing convergence rates, round-off errors, and inexactness of inner system solves for the individual time-steps. After addressing these more theoretical challenges, we present an open-source space- and time-parallel implementation and evaluate its performance for two different test problems. ","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":"31 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139027434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Hopf bifurcation analysis of a phage therapy model 噬菌体疗法模型的霍普夫分岔分析

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2023-12-21 DOI: 10.2140/camcos.2023.18.87

Ei Ei Kyaw, Hongchan Zheng, Jingjing Wang

引用次数: 0

A source term method for Poisson problems with a discontinuous diffusion coefficient 非连续扩散系数泊松问题的源项方法

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2023-12-21 DOI: 10.2140/camcos.2023.18.153

John D. Towers

引用次数: 0

A numerical study of Landau damping with PETSc-PIC 利用 PETSc-PIC 对兰道阻尼进行数值研究

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2023-12-21 DOI: 10.2140/camcos.2023.18.135

Daniel S. Finn, Matthew G. Knepley, Joseph V. Pusztay, Mark F. Adams

引用次数: 0

A comparative study of iterative Riemann solvers for the shallow water and Euler equations 浅水方程和欧拉方程的黎曼迭代求解器比较研究

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2023-12-21 DOI: 10.2140/camcos.2023.18.107

Carlos Muñoz Moncayo, Manuel Quezada de Luna, David I. Ketcheson

{"title":"A comparative study of iterative Riemann solvers for the shallow water and Euler equations","authors":"Carlos Muñoz Moncayo, Manuel Quezada de Luna, David I. Ketcheson","doi":"10.2140/camcos.2023.18.107","DOIUrl":"https://doi.org/10.2140/camcos.2023.18.107","url":null,"abstract":"We investigate the achievable efficiency of exact solvers for the Riemann problem for two systems of first-order hyperbolic PDEs: the shallow water equations and the Euler equations of compressible gas dynamics. Many approximate solvers have been developed for these systems; exact solution algorithms have received less attention because the computation of the exact solution typically requires an iterative solution of algebraic equations, which can be expensive or unreliable. We investigate a range of iterative algorithms and initial guesses. In addition to existing algorithms, we propose simple new algorithms that are guaranteed to converge and to remain in the range of physically admissible values at all iterations. We apply the existing and new iterative schemes to an ensemble of test Riemann problems. For the shallow water equations, we find that Newton’s method with a simple modification converges quickly and reliably. For the Euler equations we obtain similar results; however, when the required precision is high, a combination of Ostrowski and Newton iterations converges faster. These solvers are slower than standard approximate solvers like Roe and HLLE, but come within a factor of two in speed. We also provide a preliminary comparison of the accuracy of a finite volume discretization using an exact solver versus standard approximate solvers. ","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":"19 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139027095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 connected component labeling algorithm for implicitly defined domains 隐式定义域的连通构件标注算法

3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2023-06-15 DOI: 10.2140/camcos.2023.18.29

Robert I. Saye

引用次数: 0

Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes 领域感知高斯过程的高级平稳和非平稳核设计

IF 2.1 3区数学

Communications in Applied Mathematics and Computational Science Pub Date : 2022-10-07 DOI: 10.2140/camcos.2022.17.131

Marcus M. Noack, James A. Sethian

{"title":"Advanced stationary and nonstationary kernel designs for domain-aware Gaussian processes","authors":"Marcus M. Noack, James A. Sethian","doi":"10.2140/camcos.2022.17.131","DOIUrl":"https://doi.org/10.2140/camcos.2022.17.131","url":null,"abstract":"Gaussian process regression is a widely applied method for function approximation and uncertainty quantification. The technique has recently gained popularity in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, we want to draw attention to nonstationary kernel designs that can be defined in the same framework to yield flexible multitask Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results show that informing a Gaussian process of domain knowledge, combined with additional flexibility and communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation. ","PeriodicalId":49265,"journal":{"name":"Communications in Applied Mathematics and Computational Science","volume":"51 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138524700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 12