BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-70-159
       ENTRY:: November 06, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: The use of direct methods for the solution of the discrete
               Poisson equation on non-rectangular regions
        TYPE:: Technical Report
      AUTHOR:: George, John Alan
        DATE:: June 1970
       PAGES:: 26
    ABSTRACT:: Some direct and iterative schemes are presented for solving a
               standard finite-difference scheme for Poisson's equation on a
               two-dimensional bounded region R with Dirichlet conditions
               specified on the boundary $\delta$R. These procedures make
               use of special-purpose direct methods for solving rectangular
               Poisson problems. The region is imbedded in a rectangle and a
               uniform mesh is superimposed on it. The usual five-point
               Poisson difference operator is applied over the whole
               rectangle, yielding a block-tridiagonal system of equations.
               The original problem, however, determines only the elements
               of the right-hand side which correspond to grid points lying
               within $\delta$R; the remaining elements can be treated as
               parameters. The iterative algorithms construct a sequence of
               right-hand sides in such a way that the corresponding
               sequence of solutions on the rectangle converges to the
               solution of the imbedded problem.
       NOTES:: [Adminitrivia V1/Prg/19951106]
         END:: STAN//CS-TR-70-159