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TCGMSG Examples
===============
These example programs are realisitic (?) models of actual applications or
algorithms from chemical-physics. They should make cleanly once the Makefile
has been appropriately modified (which is done automatically for all supported
machines). Serial and shared-memory parallel (and possibly CM and Linda)
versions are also available but not included here.
The programs may be run using the csh script demo in this directory The script
takes a single argument which is the name of the desired demo (scf, md, mc,
jacobi, grid). The script uses a template PROCGRP file (template.p) to
generate the actual PROCGRP file used ... its makes a default file if one does
not exist ... look in that for details.
Self Consistent Field (scf)
---------------------------
This SCF code is a cleaned up and much enhanced version of the one in Szabo
and Ostlund. It uses distributed primitive 1s gaussian functions as a basis
(thus emulating use of s,p,... functions) and computes integrals to
essentially full accuracy. It is a direct SCF (integrals are computed each
iteration using the Schwarz inequality for screeing). An atomic denisty is
used for a starting guess. Damping and level shifting are used to aid
convergence.
Rather than complicate the program with code for parsing input the include
file 'cscf.h' and block data file 'blkdata.f' contain all the data and thus
there are three versions, one for each of the available problem sizes. The
three sizes correpsond to 15 basis functions (Be), 30 basis functions (Be2)
and 60 basis functions (tetrahedral Be4).
[In addition to these three cases there are files for 60, 120 and 240
functions, which are not built by default (type 'make extra' for
these). These are 4, 8 and 16 Be atoms, respectively, arranged in a line.]
The O(N**4) step has been parallelized with the assumption that each process
can hold all of the density and fock matrices which is reasonable for up to
O(1000) basis functions on most workstations networks and many MIMD machines
(e.g. iPSC-i860). The work is dynamically load-balanced, with tasks
comprising 10 sets of integrals (ij|**) (see TWOEL() and NXTASK() in scf.f).
The work of O(N**3) has not been parallelized, but has been optimized to use
BLAS and a tweaked Jacobi diagonalizer with dynamic threshold selection.
Molecular Dynamics (md)
-----------------------
This program bounces a few thousand argon atoms around in a box with periodic
boundary conditions. Pairwise interactions (Leonard-Jones) are used with a
simple integration of the Newtonian equations of motion. This program is
derived from the serial code of Deiter Heerman, but many modifications have
been made. Prof. Frank Harris has a related FORTRAN 9X Connection Machine
version.
The O(N) work constructing the forces has been parallelized, as has the
computation of the pair distribution function. The neighbour list is computed
in parallel every 20 steps with a simple static decomposition. This then
drives the parallelization of the forces computation. To make the simulation
bigger increase the value of mm in the parameter statement at the top of md.f
(mm=8 gives 2048 particles, mm=13 gives 8878). Each particle interacts with
about 80 others, and the neighbor list is computed for about 130 neighbors to
allow for movement before it is updated.
Monte Carlo (mc)
----------------
This code evaluates the energy of the simplest explicitly correlated
electronic wavefunction for the He atom ground state using a variational
monte-carlo method without importance sampling. It is completely boringly
parallel and for realistic problem sizes gives completely linear speed-ups for
several hunderd processes. You have to give it the no. of moves to
equilibrate the system for (neq) and the no. of moves to compute averages over
(nstep). Apropriate values for a very short run are 200 and 500 respectively.
Jacobi iterative linear equation solver (jacobi)
------------------------------------------------
Uses a naive jacobi iterative algorithm to solve a linear equation. This
algorithm is not applicable to real linear equations (sic) and neither is it
the most parallel algorithm available. The code as implemented here gets 780+
MFLOP on a 128 node iPSC-i860 ... a paltry 30% efficiency, but it is not hard
to improve upon either.
All the time is spent in a large matrix vector product which is statically
distributed across the processes. You need to give it the matrix dimension
(pick as big as will fit in memory).
Solution of Laplace's equation on a 2-D grid (grid)
---------------------------------------------------
Solve Laplace's eqn. on a 2-D square grid subject to b.c.s on the boundary.
Use 5 point discretization of the operator and a heirarchy of grids with
red/black gauss seidel w-relaxation. This is not the most efficient means of
solving this equation (probably should use a fast-poisson solver) but it
provides a 'real-world' example of spatial decomposition determining the
parallel decomposition. It is also the only example of a full application in
C that is included here.
If the code is compiled with -DPLOT and run with the option '-plot XXX', where
XXX is one of 'value', 'residual' or 'error', then grids are dumped at
intervals to the file 'plot' (in the directory of process zero). This file
may be displayed with the X11-R4/5 program xpix. Xpix is not built
automatically and must be extracted and built from the shar file in this
directory.
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