arXiv - CS - Numerical Analysis最新文献_第8页

Multisymplecticity in finite element exterior calculus 有限元外部微积分中的多折射性

arXiv - CS - Numerical Analysis Pub Date : 2023-12-06 DOI: arxiv-2312.03657

Ari Stern, Enrico Zampa

引用次数: 0

Energy-consistent integration of mechanical systems based on Livens principle 基于Livens原理的机械系统能量一致性集成

arXiv - CS - Numerical Analysis Pub Date : 2023-12-05 DOI: arxiv-2312.02825

Philipp L. Kinon, Peter Betsch

引用次数: 0

Divergence-Free Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Rotating Shallow Water Magnetohydrodynamics 基于无散度通量全球化的旋转浅水磁流体动力学平衡路径保守中心迎风方案

arXiv - CS - Numerical Analysis Pub Date : 2023-12-05 DOI: arxiv-2312.02881

Alina Chertock, Alexander Kurganov, Michael Redle, Vladimir Zeitlin

{"title":"Divergence-Free Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Rotating Shallow Water Magnetohydrodynamics","authors":"Alina Chertock, Alexander Kurganov, Michael Redle, Vladimir Zeitlin","doi":"arxiv-2312.02881","DOIUrl":"https://doi.org/arxiv-2312.02881","url":null,"abstract":"We develop a new second-order flux globalization based path-conservative\u0000central-upwind (PCCU) scheme for rotating shallow water magnetohydrodynamic\u0000equations. The new scheme is designed not only to maintain the divergence-free\u0000constraint of the magnetic field at the discrete level but also to satisfy the\u0000well-balanced (WB) property by exactly preserving some physically relevant\u0000steady states of the underlying system. The locally divergence-free constraint\u0000of the magnetic field is enforced by following the method recently introduced\u0000in [A. Chertock, A. Kurganov, M. Redle, and K. Wu, ArXiv preprint (2022),\u0000arXiv:2212.02682]: we consider a Godunov-Powell modified version of the studied\u0000system, introduce additional equations by spatially differentiating the\u0000magnetic field equations, and modify the reconstruction procedures for magnetic\u0000field variables. The WB property is ensured by implementing a flux\u0000globalization approach within the PCCU scheme, leading to a method capable of\u0000preserving both still- and moving-water equilibria exactly. In addition to\u0000provably achieving both the WB and divergence-free properties, the new method\u0000is implemented on an unstaggered grid and does not require any (approximate)\u0000Riemann problem solvers. The performance of the proposed method is demonstrated\u0000in several numerical experiments that confirm the lack of spurious\u0000oscillations, robustness, and high resolution of the obtained results.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":" 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Assessing Nonlinear Diffusion Acceleration for Boltzmann Fokker Planck Equation in Slab Geometry 平板几何中Boltzmann - Fokker - Planck方程的非线性扩散加速度评估

arXiv - CS - Numerical Analysis Pub Date : 2023-12-05 DOI: arxiv-2312.02930

Japan K. Patel, Barry D. Ganapol, Martha M. Matuszak

引用次数: 0

Inexact linear solves in the low-rank ADI iteration for large Sylvester equations 大型Sylvester方程的低阶ADI迭代中的不精确线性解

arXiv - CS - Numerical Analysis Pub Date : 2023-12-05 DOI: arxiv-2312.02891

Patrick Kürschner

{"title":"Inexact linear solves in the low-rank ADI iteration for large Sylvester equations","authors":"Patrick Kürschner","doi":"arxiv-2312.02891","DOIUrl":"https://doi.org/arxiv-2312.02891","url":null,"abstract":"We consider the low-rank alternating directions implicit (ADI) iteration for\u0000approximately solving large-scale algebraic Sylvester equations. Inside every\u0000iteration step of this iterative process a pair of linear systems of equations\u0000has to be solved. We investigate the situation when those inner linear systems\u0000are solved inexactly by an iterative methods such as, for example,\u0000preconditioned Krylov subspace methods. The main contribution of this work are\u0000thresholds for the required accuracies regarding the inner linear systems which\u0000dictate when the employed inner Krylov subspace methods can be safely\u0000terminated. The goal is to save computational effort by solving the inner\u0000linear system as inaccurate as possible without endangering the functionality\u0000of the low-rank Sylvester-ADI method. Ideally, the inexact ADI method mimics\u0000the convergence behaviour of the more expensive exact ADI method, where the\u0000linear systems are solved directly. Alongside the theoretical results, also\u0000strategies for an actual practical implementation of the stopping criteria are\u0000developed. Numerical experiments confirm the effectiveness of the proposed\u0000strategies.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":" 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Higher-order FEM and CIP-FEM for Helmholtz equation with high wave number and perfectly matched layer truncation 具有高波数和完全匹配层截断的亥姆霍兹方程的高阶有限元和cip有限元

arXiv - CS - Numerical Analysis Pub Date : 2023-12-05 DOI: arxiv-2312.02476

Yonglin Li, Haijun Wu

{"title":"Higher-order FEM and CIP-FEM for Helmholtz equation with high wave number and perfectly matched layer truncation","authors":"Yonglin Li, Haijun Wu","doi":"arxiv-2312.02476","DOIUrl":"https://doi.org/arxiv-2312.02476","url":null,"abstract":"The high-frequency Helmholtz equation on the entire space is truncated into a\u0000bounded domain using the perfectly matched layer (PML) technique and\u0000subsequently, discretized by the higher-order finite element method (FEM) and\u0000the continuous interior penalty finite element method (CIP-FEM). By formulating\u0000an elliptic problem involving a linear combination of a finite number of\u0000eigenfunctions related to the PML differential operator, a wave-number-explicit\u0000decomposition lemma is proved for the PML problem, which implies that the PML\u0000solution can be decomposed into a non-oscillating elliptic part and an\u0000oscillating but analytic part. The preasymptotic error estimates in the energy\u0000norm for both the $p$-th order CIP-FEM and FEM are proved to be $C_1(kh)^p +\u0000C_2k(kh)^{2p} +C_3 E^{rm PML}$ under the mesh condition that $k^{2p+1}h^{2p}$\u0000is sufficiently small, where $k$ is the wave number, $h$ is the mesh size, and\u0000$E^{rm PML}$ is the PML truncation error which is exponentially small. In\u0000particular, the dependences of coefficients $C_j~(j=1,2)$ on the source $f$ are\u0000improved. Numerical experiments are presented to validate the theoretical\u0000findings, illustrating that the higher-order CIP-FEM can greatly reduce the\u0000pollution errors.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stochastic Optimal Control Matching 随机最优控制匹配

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.02027

Carles Domingo-Enrich, Jiequn Han, Brandon Amos, Joan Bruna, Ricky T. Q. Chen

{"title":"Stochastic Optimal Control Matching","authors":"Carles Domingo-Enrich, Jiequn Han, Brandon Amos, Joan Bruna, Ricky T. Q. Chen","doi":"arxiv-2312.02027","DOIUrl":"https://doi.org/arxiv-2312.02027","url":null,"abstract":"Stochastic optimal control, which has the goal of driving the behavior of\u0000noisy systems, is broadly applicable in science, engineering and artificial\u0000intelligence. Our work introduces Stochastic Optimal Control Matching (SOCM), a\u0000novel Iterative Diffusion Optimization (IDO) technique for stochastic optimal\u0000control that stems from the same philosophy as the conditional score matching\u0000loss for diffusion models. That is, the control is learned via a least squares\u0000problem by trying to fit a matching vector field. The training loss, which is\u0000closely connected to the cross-entropy loss, is optimized with respect to both\u0000the control function and a family of reparameterization matrices which appear\u0000in the matching vector field. The optimization with respect to the\u0000reparameterization matrices aims at minimizing the variance of the matching\u0000vector field. Experimentally, our algorithm achieves lower error than all the\u0000existing IDO techniques for stochastic optimal control for four different\u0000control settings. The key idea underlying SOCM is the path-wise\u0000reparameterization trick, a novel technique that is of independent interest,\u0000e.g., for generative modeling.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":" 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Coverage Explorer: Coverage-guided Test Generation for Cyber Physical Systems 覆盖探索者:网络物理系统的覆盖引导测试生成

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.02313

Sanaz Sheikhi, Stanley Bak

引用次数: 0

Axisymmetric Virtual Elements For Problems of Elasticity and Plasticity 弹性与塑性问题的轴对称虚元

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.01559

Louie L. Yaw

引用次数: 0

Model Reduction on Manifolds: A differential geometric framework 流形的模型约简:一个微分几何框架

arXiv - CS - Numerical Analysis Pub Date : 2023-12-04 DOI: arxiv-2312.01963

Patrick Buchfink, Silke Glas, Bernard Haasdonk, Benjamin Unger

引用次数: 0