Greedy trial subspace selection in meshfree time-stepping scheme with applications in coupled bulk-surface pattern formations

IF 5.4 3区 材料科学 Q2 CHEMISTRY, PHYSICAL
Yichen Su, Leevan Ling
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引用次数: 0

Abstract

Combining kernel-based collocation methods with time-stepping methods to solve parabolic partial differential equations can potentially introduce challenges in balancing temporal and spatial discretization errors. Typically, using kernels with high orders of smoothness on some sufficiently dense set of trial centers provides high spatial approximation accuracy that can exceed the accuracy of finite difference methods in time. The paper proposes a greedy approach for selecting trial subspaces in the kernel-based collocation method applied to time-stepping to balance errors in both well-conditioned and ill-conditioned scenarios. The approach involves selecting trial centers using a fast block-greedy algorithm with new stopping criteria that aim to balance temporal and spatial errors. Numerical simulations of coupled bulk-surface pattern formations, a system involving two functions in the domain and two on the boundary, illustrate the effectiveness of the proposed method in reducing trial space dimensions while maintaining accuracy.
无网格时间步进方案中的贪婪试验子空间选择及其在体表耦合模式形成中的应用
将基于核的配准方法与时间步进方法相结合来求解抛物线偏微分方程,可能会在平衡时间和空间离散化误差方面带来挑战。通常情况下,在一些足够密集的试验中心集上使用具有高阶平滑度的核,可以提供很高的空间逼近精度,在时间上可以超过有限差分法的精度。本文提出了一种在基于核的配准方法中选择试验子空间的贪婪方法,该方法应用于时间步进,以平衡有条件和无条件情况下的误差。该方法包括使用快速分块贪婪算法选择试验中心,并采用旨在平衡时间和空间误差的新停止准则。该系统涉及域中的两个函数和边界上的两个函数,对体表耦合模式形成进行的数值模拟说明了所提方法在保持精度的同时减少试验空间维数的有效性。
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来源期刊
ACS Applied Energy Materials
ACS Applied Energy Materials Materials Science-Materials Chemistry
CiteScore
10.30
自引率
6.20%
发文量
1368
期刊介绍: ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.
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