  Explicit time integration schemes coupled with Galerkin discretizations of
time-dependent partial differential equations require solving a linear system
with the mass matrix at each time step. For applications in structural
dynamics, the solution of the linear system is frequently approximated through
so-called mass lumping, which consists in replacing the mass matrix by some
diagonal approximation. Mass lumping has been widely used in engineering
practice for decades already and has a sound mathematical theory supporting it
for finite element methods using the classical Lagrange basis. However, the
theory for more general basis functions is still missing. Our paper partly
addresses this shortcoming. Some special and practically relevant properties of
lumped mass matrices are proved and we discuss how these properties naturally
extend to banded and Kronecker product matrices whose structure allows to solve
linear systems very efficiently. Our theoretical results are applied to
isogeometric discretizations but are not restricted to them.
