  We examine and extend Sparse Grids as a discretization method for partial
differential equations (PDEs). Solving a PDE in $D$ dimensions has a cost that
grows as $O(N^D)$ with commonly used methods. Even for moderate $D$ (e.g.
$D=3$), this quickly becomes prohibitively expensive for increasing problem
size $N$. This effect is known as the Curse of Dimensionality. Sparse Grids
offer an alternative discretization method with a much smaller cost of $O(N
\log^{D-1}N)$. In this paper, we introduce the reader to Sparse Grids, and
extend the method via a Discontinuous Galerkin approach. We then solve the
scalar wave equation in up to $6+1$ dimensions, comparing cost and accuracy
between full and sparse grids. Sparse Grids perform far superior, even in three
dimensions. Our code is freely available as open source, and we encourage the
reader to reproduce the results we show.
