Boundary element methods are being successfully used for modeling parasitic effects in cutting-edge circuit design. The dense system matrix generated therein presents a time and memory bottleneck. Fast iterative solver techniques, developed to address the problem, suffer from convergence issues which become pronounced for large number of right hand sides as is the case for massively coupled systems. In this paper an iteration free solution scheme is presented. The dense matrix is rendered sparse by applying multilevel multipole expansions, and the resultant sparse matrix is solved by a traditional sparse matrix solver. The accuracy and time and memory requirements for the solver are compared against the regular methods. The advantage of the presented method over the corresponding iterative scheme is also demonstrated.