A reduced basis method for fractional diffusion operators I

Danczul Tobias; Schoeberl Joachim

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A reduced basis method for fractional diffusion operators I

机译：分数阶扩散算子的约简基方法I

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We propose and analyze new numerical methods to evaluate fractional norms and apply fractional powers of elliptic operators. By means of a reduced basis method, we project to a small dimensional subspace where explicit diagonalization via the eigensystem is feasible. The method relies on several independent evaluations of (I -t(i)(2) Delta)(-1) f, which can be computed in parallel. We prove exponential convergence rates for the optimal choice of sampling points t(i), provided by the so-called Zolotarev points. Numerical experiments confirm the analysis and demonstrate the efficiency of our algorithm.

机译：我们提出并分析了新的数值方法来评估分数范数并应用椭圆算子的分数幂。通过约简基方法，我们投影到一个小维子空间，其中通过特征系统进行显式对角化是可行的。该方法依赖于对（I -t（i）（2） Delta）（-1） f 的多个独立评估，这些评估可以并行计算。我们证明了由所谓的佐洛塔列夫点提供的采样点t（i）的最优选择的指数收敛率。数值实验验证了所作所得的分析，验证了该算法的有效性。

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来源
《Numerische Mathematik》 |2022年第2期|369-404|共36页
作者
Danczul Tobias; Schoeberl Joachim;
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作者单位

TU Wien;

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原文格式 PDF
正文语种英语
中图分类数值分析;
关键词
PRIORI CONVERGENCE THEORY; BASIS APPROXIMATIONS; EXTENSION PROBLEM; LAPLACIAN; EQUATIONS; POWERS;

机译：先验收敛理论;基近似值;扩展问题;拉普拉斯;方程式;权力;

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A reduced basis method for fractional diffusion operators I

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