Easy and Efficient preconditioning of the Isogeometric Mass Matrix

Abstract

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.

References in corpus (4)

• Isogeometric mortar methods
• Matrix-free weighted quadrature for a computationally efficient isogeometric $k$-method
• Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: explicit time-stepping and efficient mass matrix inversion
• Biorthogonal splines for optimal weak patch-coupling in isogeometric analysis with applications to finite deformation elasticity