Eigenvalue Isogeometric Approximations Based on B-splines: Tools and Results

Sven-Erik Ekström and Stefano Serra-Capizzano

July 2018

Abstract:

In such a short note we consider the spectral analysis of large matrices coming from the numerical approximation of the eigenvalue problem
-(a(x)u'(x))'=λ b(x) u(x), x∈ (0,1),
where u(0) and u(1) are given, by using isogeometric methods based on B-splines. We give precise estimates for the extremal eigenvalues and global distributional results. The techniques involve dyadic decomposition arguments, the GLT analysis, and basic extrapolation methods.

Available as PDF (220 kB, no cover)

Download BibTeX entry.