From 472d89565bff39e35738244168817ab78afdb8d9 Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Tue, 9 Nov 2010 11:05:31 -0500 Subject: [PATCH] Update assignment 6 for Fall 2010. --- ....itex2MML => index.2009.11.shtml.itex2MML} | 0 assignments/archive/poisson/index.shtml | 30 +++++++++++++++++++ assignments/current/6 | 2 +- .../index.shtml.itex2MML | 14 ++++----- content/poisson/index.shtml.itex2MML | 8 ++--- 5 files changed, 42 insertions(+), 12 deletions(-) rename assignments/archive/poisson/{index.shtml.itex2MML => index.2009.11.shtml.itex2MML} (100%) create mode 100644 assignments/archive/poisson/index.shtml diff --git a/assignments/archive/poisson/index.shtml.itex2MML b/assignments/archive/poisson/index.2009.11.shtml.itex2MML similarity index 100% rename from assignments/archive/poisson/index.shtml.itex2MML rename to assignments/archive/poisson/index.2009.11.shtml.itex2MML diff --git a/assignments/archive/poisson/index.shtml b/assignments/archive/poisson/index.shtml new file mode 100644 index 0000000..1f0b249 --- /dev/null +++ b/assignments/archive/poisson/index.shtml @@ -0,0 +1,30 @@ + + +

Assignment #6

+

Due Friday, November 19

+ +

Purpose

+ +

Learn how to implement Gauss-Siedel in parallel.

+ +

Note: Please identify all your work.

+ +

This assignment consists in building your own parallel code to +generate the solution of Poisson equation. +The Gauss-Siedel +and SOR algorithms are +explained in the course web pages. The steps toward a parallel code +are also explained.

+ +

Start from the code p.c and +implement the parallel version. Pay particular attention to minimize +communications.

+ +
    +
  1. Produce a correct, parallel code.
  2. +
  3. Instrument both the serial and parallel codes for timing.
  4. +
  5. Find the time dependence of both codes on the grid size.
  6. +
  7. How efficient is your parallel version?
  8. +
+ + diff --git a/assignments/current/6 b/assignments/current/6 index 9869977..80c8f41 120000 --- a/assignments/current/6 +++ b/assignments/current/6 @@ -1 +1 @@ -../archive/mandelbrot/ \ No newline at end of file +../archive/poisson \ No newline at end of file diff --git a/content/2D_Domain_Decomposition/index.shtml.itex2MML b/content/2D_Domain_Decomposition/index.shtml.itex2MML index 5094a33..415c185 100644 --- a/content/2D_Domain_Decomposition/index.shtml.itex2MML +++ b/content/2D_Domain_Decomposition/index.shtml.itex2MML @@ -169,13 +169,13 @@ identical. This stems from the handling of the GHOST lines in the parallel implementation.

Consider the update of the field at the location marked 0 below. -The Gauss-Siedel solution calls for an in-place update of the -field via the finite difference formula in a systematic sweep of the -numerical lattice. This is done via the 2D -finite difference formula. The values of the field at the points 2 and -3 have already been updated if the sweep originates from the -upper-left corner of the lattice, while the field at the point 1 and 4 -are yet to be updated.

+The Gauss-Siedel solution calls +for an in-place update of the field via the finite difference +formula in a systematic sweep of the numerical lattice. This is done +via the 2D finite difference formula. The +values of the field at the points 2 and 3 have already been updated if +the sweep originates from the upper-left corner of the lattice, while +the field at the point 1 and 4 are yet to be updated.

diff --git a/content/poisson/index.shtml.itex2MML b/content/poisson/index.shtml.itex2MML index e39fbcc..9e84cb8 100644 --- a/content/poisson/index.shtml.itex2MML +++ b/content/poisson/index.shtml.itex2MML @@ -169,9 +169,9 @@ field $u_{i,j}$ at the interior grid points.

-

The Gauss-Siedel method consists in replacing the new value of the -field within the same "array". This corresponds to the following -form:

+

The Gauss-Siedel method consists in replacing the +new value of the field within the same "array". This corresponds to +the following form:

\[ u_{i,j}^{k+1} = @@ -203,7 +203,7 @@ the regions of high curvature of the field and on the ability of the numerical grid to cover the domain.

The Gauss-Siedel method converges faster than the Jacobi -method. Yet it is a notoriously slow method, often requiring very +method. However, it is a notoriously slow method, often requiring very large number of iterations to achieve convergence. A better rate of convergence is achieved by the Succesive Over Relaxation (SOR) method. In this approach, the old and new fields are mixed via a -- 2.26.2