  We study numerically the Casimir interaction between dielectrics in both two
and three dimensions. We demonstrate how sparse matrix factorizations enable
one to study torsional interactions in three dimensions. In two dimensions we
study the full cross-over between non-retarded and retarded interactions as a
function of separation. We use constrained factorizations in order to measure
the interaction of a particle with a rough dielectric surface and compare with
a scaling argument.
