  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.
