Reduced Basis Approximations of the Solutions to Spectral Fractional Diffusion Problems,arXiv - CS - Numerical Analysis

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Reduced Basis Approximations of the Solutions to Spectral Fractional Diffusion Problems
arXiv - CS - Numerical Analysis Pub Date : 2019-05-05 , DOI: arxiv-1905.01754
Andrea Bonito, Diane Guignard, Ashley R. Zhang

We consider the numerical approximation of the spectral fractional diffusion problem based on the so called Balakrishnan representation. The latter consists of an improper integral approximated via quadratures. At each quadrature point, a reaction-diffusion problem must be approximated and is the method bottle neck. In this work, we propose to reduce the computational cost using a reduced basis strategy allowing for a fast evaluation of the reaction-diffusion problems. The reduced basis does not depend on the fractional power $s$ for $0

中文翻译：

谱分数扩散问题解的简化基近似

我们考虑基于所谓的 Balakrishnan 表示的光谱分数扩散问题的数值近似。后者由通过正交近似的不当积分组成。在每个正交点，必须近似反应扩散问题，这是方法的瓶颈。在这项工作中，我们建议使用简化的基础策略来降低计算成本，从而可以快速评估反应扩散问题。减少的基础不依赖于 $0 的分数幂 $s$

更新日期：2020-01-17

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