Isogeometric discretizations for the spectrum of the Laplace operator: outlier-free spline bases

Optimal spline subspaces are an elegant and efficient tool to remove spurious outliers in isogeometric Galerkin discretizations for the approximation of the spectrum of the Laplace operator.

For practical purposes, it is valuable to have a basis construction for such spaces with good computational and spectral properties.

We provide a characterization of the bases that enjoy a B-spline-like support structure and whose mass and stiffness matrices are simultaneously diagonalizable.

It turns out that these mass and stiffness matrices admit explicitly known closed-form expressions for their eigenvalues, implying that the considered bases are outlier-free.

A numerical procedure for constructing such bases is also presented.