Hamiltonian circuited simulations of elliptic partial differential equations using a spark

The finite-difference schemes give linear relations of tile unknowns. Itera tive simulations of partial differential equations are seen as iterative pr ocesses, and hence, all attempt, is made to treat the points to be simulate d as vertices of a graph. One was to pass through tile vertices once and on ly once in an iteration is to simulate in a Hamiltonian circuit. Thus, in t his paper, Hamiltonian circuited simulations of an elliptic partial differe ntial equation using a spark as a, means of providing linear relationship b etween unknowns are given. The Hamiltonian circuit in use enables tile deco mposition of the coefficient matrix into two blocks such that tile stimulat ed points are decomposed into two disjoint sets. We appreciate that the sim ulations now are dome in parallel involving much reduced simulation points. (C) 2001 Elsevier Science Ltd. Ali rights reserved.