AbstractThe finite-difference schemes give linear relations of the unknowns. Iterative simulations of partial differential equations are seen as iterative processes, and hence, an attempt is made to treat the points to be simulated as vertices of a graph. One way to pass through the vertices once and only once in an iteration is to simulate in a Hamiltonian circuit. Thus, in this paper, Hamiltonian circuited simulations of an elliptic partial differential equation using a spark as a means of providing linear relationship between unknowns are given. The Hamiltonian circuit in use enables the decomposition of the coefficient matrix into two blocks such that the simulated points are decomposed into two disjoint sets. We appreciate that the simulations now are done in parallel involving much reduced simulation points.