From bc305167e675a1a4c93fee322673f37409f2d53a Mon Sep 17 00:00:00 2001 From: "W. 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zcHqXh!GnP-Spd1=Lh#1{phpFWG!%*fh6yZ)F$^V(M94~GB%nxHC=?hZpsE7AeFAtJ z#s8wJDE~v3L@@>yTG52)MkM(XmC0lPfde2xNJM$5ojUSTw0Zw&*#GK8=<5FWsqpZi z?NB?iuC6TLB6xcM&>l_P|8f2Q#U*oe_|Z+WH^qH>i#s|<;ob4H9(e()1_S!(=paiV zQ2@3I(80f_R0`N#5Jh?5Ce?-Nj#u0^AZ2&zw+nX{nnB3A+Yy}c~FXC8nAQh@l^Htj%21iTfTk3C?pb&1QWpjks%N?Oc(6~CjLhzje^nuUBAen2sj3a@7W=frjba0 zl>xLRfO7Dw3?U8uO%DM)>2~U&P;lUQ`ZJXNSWVc00I!mS=`Ys8u{D0$-n`g(hfb040>mM04bD4i~XfO7+M;$ za}K1TX!LJ$3gkil))!#o?c8fn6b!RdPa1)uvG~5XOQqNW%rXk_A|tSrkxKv`*w0`9 zAWQ<-ytK1@fDKF}kibAkX#` + +

Assignment #8

+

Due Friday, November 20

+ +

Purpose

+ +

Learn how to solve PDEs using parallel computers.

+ +

Note: Please identify all your work.

+ +

Solving Poisson Equation

+ +

You are to solve Poisson equation in a parallel code. This elliptic +PDE is typicaly used in demonstrating how to numerically solve +PDEs. It has the advantage of being time independent. In 2D, it takes +the form

+ +

\[ + \frac{\partial^2 u(x,y)}{\partial x^2} + + \frac{\partial^2 u(x,y)}{\partial y^2} + = S(x,y) +\]

+ +

where the field $u(x,y)$ is solved for in a domain in $x$ and $y$ +with specified boundary conditions and source term $S(x,y)$.

+ +

Steps

+ +
    +
  • Use finite difference approach on an equally spaced square lattice to solve the PDE.
  • +
  • Start with the serial 2D Poisson solver code + poisson_2d.tar.gz. + Use the physical set-up as in this code, namely use the domain, + the gaussian source, and the Dirichlet boundary conditions as + specified in this code.
  • +
  • Parallelize the code.
  • +
  • Use the parallel Game of Life + (parallel_life_game.c) + and the 1D Poisson equation solver + (poisson_1d.tar.gz) + codes as guides.
  • +
  • Use MPE or a pipe in the Python graphic code + (plot_image.py) + to display the solution.
  • +
  • Compare your solution (map image of $u(x,y)$) to the serial code + solution as a rough check of the code.
  • +
  • Replace the solution back in the Poisson equation as a further + (more precise) check of the solution (as is done in the serial + code).
  • +
  • Make sure your code works for arbitrary lattice size and number + of processors.
  • + -- 2.26.2