arXiv - CS - Numerical Analysis最新文献_第10页

Localization of trace norms in two and three dimensions 二维和三维轨迹规范的定位

arXiv - CS - Numerical Analysis Pub Date : 2023-12-02 DOI: arxiv-2312.01101

Silvia Bertoluzza

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Data-Driven Autoencoder Numerical Solver with Uncertainty Quantification for Fast Physical Simulations 数据驱动自编码器数值解算器与不确定性量化快速物理模拟

arXiv - CS - Numerical Analysis Pub Date : 2023-12-02 DOI: arxiv-2312.01021

Christophe Bonneville, Youngsoo Choi, Debojyoti Ghosh, Jonathan L. Belof

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Asymptotic-preserving gyrokinetic implicit particle-orbit integrator for arbitrary electromagnetic fields 任意电磁场的渐近保持陀螺动力学隐式粒子轨道积分器

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00730

Lee Ricketson, Luis Chacón

{"title":"Asymptotic-preserving gyrokinetic implicit particle-orbit integrator for arbitrary electromagnetic fields","authors":"Lee Ricketson, Luis Chacón","doi":"arxiv-2312.00730","DOIUrl":"https://doi.org/arxiv-2312.00730","url":null,"abstract":"We extend the asymptotic preserving and energy conserving time integrator for\u0000charged-particle motion developed in [Ricketson & Chac'on, JCP, 2020] to\u0000include finite Larmor-radius (FLR) effects in the presence of electric-field\u0000length-scales comparable to the particle gyro-radius (the gyro-kinetic limit).\u0000We introduce two modifications to the earlier scheme. The first is the explicit\u0000gyro-averaging of the electric field at the half time-step, along with an\u0000analogous modification to the current deposition, which we show preserves total\u0000energy conservation in implicit PIC schemes. The number of gyrophase samples is\u0000chosen adaptively, ensuring proper averaging for large timesteps, and the\u0000recovery of full-orbit dynamics in the small time-step limit. The second\u0000modification is an alternating large and small time-step strategy that ensures\u0000the particle trajectory samples gyrophases evenly. We show that this strategy\u0000relaxes the time-step restrictions on the scheme, allowing even larger\u0000speed-ups than previously achievable. We demonstrate the new method with\u0000several single-particle motion tests in a variety of electromagnetic field\u0000configurations featuring gyro-scale variation in the electric field. The\u0000results demonstrate the advertised ability to capture FLR effects accurately\u0000even when significantly stepping over the gyration time-scale.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"40 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503948","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

Low-rank-modified Galerkin methods for the Lyapunov equation Lyapunov方程的低秩修正Galerkin方法

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00463

Kathryn Lund, Davide Palitta

{"title":"Low-rank-modified Galerkin methods for the Lyapunov equation","authors":"Kathryn Lund, Davide Palitta","doi":"arxiv-2312.00463","DOIUrl":"https://doi.org/arxiv-2312.00463","url":null,"abstract":"Of all the possible projection methods for solving large-scale Lyapunov\u0000matrix equations, Galerkin approaches remain much more popular than\u0000Petrov-Galerkin ones. This is mainly due to the different nature of the\u0000projected problems stemming from these two families of methods. While a\u0000Galerkin approach leads to the solution of a low-dimensional matrix equation\u0000per iteration, a matrix least-squares problem needs to be solved per iteration\u0000in a Petrov-Galerkin setting. The significant computational cost of these\u0000least-squares problems has steered researchers towards Galerkin methods in\u0000spite of the appealing minimization properties of Petrov-Galerkin schemes. In\u0000this paper we introduce a framework that allows for modifying the Galerkin\u0000approach by low-rank, additive corrections to the projected matrix equation\u0000problem with the two-fold goal of attaining monotonic convergence rates similar\u0000to those of Petrov-Galerkin schemes while maintaining essentially the same\u0000computational cost of the original Galerkin method. We analyze the\u0000well-posedness of our framework and determine possible scenarios where we\u0000expect the residual norm attained by two low-rank-modified variants to behave\u0000similarly to the one computed by a Petrov-Galerkin technique. A panel of\u0000diverse numerical examples shows the behavior and potential of our new\u0000approach.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":"40 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138503953","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

Neural networks for the approximation of Euler's elastica 欧拉弹性近似的神经网络

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00644

Elena Celledoni, Ergys Çokaj, Andrea Leone, Sigrid Leyendecker, Davide Murari, Brynjulf Owren, Rodrigo T. Sato Martín de Almagro, Martina Stavole

引用次数: 0

The Existence the Solution of Nonlinear Discrete Schemes and Convergence of a Linearized Iterative Method for time-dependent PNP Equations 时变PNP方程的非线性离散格式的存在性、解和线性化迭代法的收敛性

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00291

Yang Liu, Shi Shu, Ying Yang

引用次数: 0

Approximation Bounds for Model Reduction on Polynomially Mapped Manifolds 多项式映射流形模型约简的近似界

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00724

Patrick Buchfink, Silke Glas, Bernard Haasdonk

引用次数: 0

A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains 离散域上求解抛物型偏微分方程的一个框架

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00327

Leticia Mattos Da Silva, Oded Stein, Justin Solomon

引用次数: 0

On the Periodicity of Singular Vectors and the Holomorphic Block-Circulant SVD on the Unit Circumference 单位周长上奇异向量的周期性及全纯块循环奇异向量分解

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00707

Giovanni Barbarino

引用次数: 0

A Probabilistic Neural Twin for Treatment Planning in Peripheral Pulmonary Artery Stenosis 肺动脉周围动脉狭窄治疗计划的概率神经孪生

arXiv - CS - Numerical Analysis Pub Date : 2023-12-01 DOI: arxiv-2312.00854

John D. Lee, Jakob Richter, Martin R. Pfaller, Jason M. Szafron, Karthik Menon, Andrea Zanoni, Michael R. Ma, Jeffrey A. Feinstein, Jacqueline Kreutzer, Alison L. Marsden, Daniele E. Schiavazzi

{"title":"A Probabilistic Neural Twin for Treatment Planning in Peripheral Pulmonary Artery Stenosis","authors":"John D. Lee, Jakob Richter, Martin R. Pfaller, Jason M. Szafron, Karthik Menon, Andrea Zanoni, Michael R. Ma, Jeffrey A. Feinstein, Jacqueline Kreutzer, Alison L. Marsden, Daniele E. Schiavazzi","doi":"arxiv-2312.00854","DOIUrl":"https://doi.org/arxiv-2312.00854","url":null,"abstract":"The substantial computational cost of high-fidelity models in numerical\u0000hemodynamics has, so far, relegated their use mainly to offline treatment\u0000planning. New breakthroughs in data-driven architectures and optimization\u0000techniques for fast surrogate modeling provide an exciting opportunity to\u0000overcome these limitations, enabling the use of such technology for\u0000time-critical decisions. We discuss an application to the repair of multiple\u0000stenosis in peripheral pulmonary artery disease through either transcatheter\u0000pulmonary artery rehabilitation or surgery, where it is of interest to achieve\u0000desired pressures and flows at specific locations in the pulmonary artery tree,\u0000while minimizing the risk for the patient. Since different degrees of success\u0000can be achieved in practice during treatment, we formulate the problem in\u0000probability, and solve it through a sample-based approach. We propose a new\u0000offline-online pipeline for probabilsitic real-time treatment planning which\u0000combines offline assimilation of boundary conditions, model reduction, and\u0000training dataset generation with online estimation of marginal probabilities,\u0000possibly conditioned on the degree of augmentation observed in already repaired\u0000lesions. Moreover, we propose a new approach for the parametrization of\u0000arbitrarily shaped vascular repairs through iterative corrections of a\u0000zero-dimensional approximant. We demonstrate this pipeline for a diseased model\u0000of the pulmonary artery tree available through the Vascular Model Repository.","PeriodicalId":501061,"journal":{"name":"arXiv - CS - Numerical Analysis","volume":" 26","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138494188","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