Hamiltonian circuited simulations of elliptic partial differential equations using a spark

• Published in: Applied mathematics letters Vol. 14; no. 4; pp. 413 - 418
• Main Authors: Hirowati Shariffudin, R., Abdullah, A.R.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2001; Elsevier
• Subjects: Computational techniques; Elliptic partial differential equations; Exact sciences and technology; Finite-difference methods; Finite-difference sparks; Hamiltonian circuits; Mathematical methods in physics; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; Physics; Sciences and techniques of general use; Elliptic partial differential equations; Finite-difference sparks; Hamiltonian circuits; Iterative method; Elliptic equation; Hamiltonian circuit; Partial differential equation; Finite difference method
• ISSN: 0893-9659; 1873-5452
• DOI: 10.1016/S0893-9659(00)00170-1

The 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.