  In this paper we present a Graphical Processing Unit accelerated mixed
variational formulation for fast phononic band-structure calculation of
arbitrarily complex unit cells and report speed gains of a hundred fold over
unoptimized serial cpu computations. To the author's knowledge this is the
first application of gpu computing to a non-FE/FDTD bandstructure algorithm.
The formulation is presented in a form which is applicable to 1-, 2-, and 3-D
cases. However, in this paper we concentrate on optimizing the formulation
within the paradigm of gpu computing, presenting results for 2-D unit cells. We
describe the application of the formulation with a long term view towards
highly efficient and massively distributed band-structure algorithms suitable
for tackling optimization and inverse problems. We report that the accurate
band-structure evaluation over the boundary of the Irreducible Brillouin Zone
(IBZ) for the first 18 phononic branches of a complex 2-D unit cell (with 1132
different phases) can be achieved in less than 20 seconds on a regular desktop.
For a simpler unit cell, the first few phononic branches are calculated in less
than 2.5 seconds on the same system. The scheme presented in this paper,
therefore, represents considerable savings in the computational costs of
phononic band-structures.
