  In this paper, we investigate the use of a mass lumped fully explicit time
stepping scheme for the discretisation of the wave equation with underlying
material parameters that vary at arbitrarily fine scales. We combine the
leapfrog scheme for the temporal discretisation with the multiscale technique
known as Localized Orthogonal Decomposition for the spatial discretisation. To
speed up the method and to make it fully explicit, a special mass lumping
approach is introduced that relies on an appropriate interpolation operator.
This operator is also employed in the construction of the Localized Orthogonal
Decomposition and is a key feature of the approach. We prove that the method
converges with second order in the energy norm, with a leading constant that
does not depend on the scales at which the material parameters vary. We also
illustrate the performance of the mass lumped method in a set of numerical
experiments.
