2020/06/03 by Gabriele Loli, Loli, Gabriele, Giancarlo Sangalli +3
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2006.02313
openalex publication_date 2020/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper deals with the fast solution of linear systems associated with the mass matrix, in the context of isogeometric analysis. We propose a preconditioner that is both efficient and easy to implement, based on a diagonal-scaled Kronecker product of univariate parametric mass matrices. Its application is faster than a matrix-vector product involving the mass matrix itself. We prove that the condition number of the preconditioned matrix converges to 1 as the mesh size is reduced, that is, the preconditioner is asymptotically equivalent to the exact inverse. Moreover, we give numerical evidence of its good behaviour with respect to the spline degree and the (possibly singular) geometry parametrization. We also extend the preconditioner to the multipatch case through an Additive Schwarz method.