Calculation of weak matrix elements in domain-wall QCD with the DBW2 gauge action

We report the details of our ongoing quenched calculations of weak matrix elements using the combination of domain-wall fermions and the DBW2 gauge action on lattices with $a^{-1}\approx 3$ GeV. A strategy to avoid the problem of fixed topological charge is introduced in generating gauge configurations. After studying the basic run parameters and elemental quantities, we present a preliminary result for the kaon B-parameter ($B_K$).