  The history of stellar seismology suggests that observation and theory often
take turns advancing our understanding. The recent tripling of the sample of
pulsating white dwarfs generated by the Sloan Digital Sky Survey represents a
giant leap on the observational side. The time is ripe for a comparable advance
on the theoretical side. There are basically two ways we can improve our
theoretical understanding of pulsating stars: we can improve the fundamental
ingredients of the models, or we can explore the existing models in greater
computational detail. For pulsating white dwarfs, much progress has recently
been made on both fronts: models now exist that connect the interior structure
to its complete evolutionary history, while a method of using parallel
computers for global exploration of relatively simple models has also been
developed. Future advances in theoretical white dwarf asteroseismology will
emerge by combining these two approaches, yielding unprecedented insight into
the physics of diffusion, nuclear burning, and mixing.
