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