Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!swrinde!emory!hubcap!jpd
From: jpd@aplvax.jhuapl.edu (James Darling)
Newsgroups: comp.parallel
Subject: Re: Elliptic Equation Solvers on CM-2 ?
Keywords: Helmholtz equation, FFT, Poisson's equation, Connection Machine
Message-ID: <9180@hubcap.clemson.edu>
Date: 31 May 90 20:13:53 GMT
Sender: fpst@hubcap.clemson.edu
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Approved: parallel@hubcap.clemson.edu

In article <9167@hubcap.clemson.edu> mccalpin@vax1.udel.edu (John D Mccalpin) writes:
>I am looking at porting a finite-difference model to the Connection
>Machine CM-2, but have not yet figured out how to get optimum
>performance out of the implicit equation solver.
>
>Most of the code is very straightforward and the port is essentially
>done, but at every time step I must solve a linear, constant-coefficient
>elliptic equation of the form:
>
>	u   + u   - g^2*u = f(x,y)
>	 xx    yy
>
>Subject to the boundary conditions:
>
>	u = 0 on x=0, x=L, y=0, y=L	(i.e. a square box!)
>


    I am currently working on an iterative algorithm which solves the
nonlinear Poisson equation (for semiconductor modeling purposes):

        u   +  u    +  (e^u + e^-u) = f(x,y)
         xx     yy

using an iterative relaxation technique on the CM.  It provides global 
convergence for an arbituary initial guess.  Two references are:

	"Parallel Algorithm for the Solution of the Nonlinear Poisson 
        Equation and its Implemenation on the MPP", J.P.Darling and 
        I.D.Mayergoyz, Journal of Parallel and Distributed Computing, 
        Vol 8, Num 2, Feburary 1990, pp. 161-168.

        "Solution of the nonlinear Poisson Equation of Semiconductor 
        Device Theory", I.D.Mayergoyz, Journal Applied Physics, 
        59 (1986), 195.

The first paper describes the details of the algorithm implementation  
and the second paper discusses the algorithmic requirements (mainly that 
your equations have diagonal nonlinearity), required for this technique.

Hope this helps.

            Jim Darling
            jpd@aplvax.jhuapl.edu
            jpd@cmsun.umiacs.umd.edu