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<html>
<head>
<title>
MD - Molecular Dynamics
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
MD <br> Molecular Dynamics
</h1>
<hr>
<p>
<b>MD</b>
is a C++ program which
carries out a molecular dynamics simulation.
</p>
<p>
The computation involves following the paths of particles which
exert a distance-dependent force on each other. The particles
are not constrained by any walls; if particles meet, they simply
pass through each other.
</p>
</p>
The problem is treated as a coupled set of differential equations.
The system of differential equation is discretized by choosing a
discrete time step. Given the position and velocity of each particle
at one time step, the algorithm estimates these values at the next time step.
</p>
<p>
To compute the next position of each particle requires the evaluation of
the right hand side of its corresponding differential equation. Since each
of these calculations is independent, there is a potential speedup if the
program can take advantage of parallel computing.
</p>
<p>
This version of the program is intended as a starting point;
students are asked to examine the program and add the appropriate
OpenMP directives to run it in parallel.
</p>
<p>
Note that this program exhibits a remarkable speedup if we simply
compile it with the "-O2" optimization option.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>md</b> <i>nd</i> <i>np</i> <i>step_num</i> <i>dt</i>
</blockquote>
where
<ul>
<li>
<i>nd</i> is the spatial dimension (2 or 3);
</li>
<li>
<i>np</i> is the number of particles (500, for instance);
</li>
<li>
<i>step_num</i> is the number of time steps (500, for instance).
</li>
<li>
<i>dt</i> is the time step size (0.1, for instance).
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>MD</b> is available in
<a href = "../../c_src/md/md.html">a C version</a> and
<a href = "../../cpp_src/md/md.html">a C++ version</a> and
<a href = "../../f77_src/md/md.html">a FORTRAN77 version</a> and
<a href = "../../f_src/md/md.html">a FORTRAN90 version</a> and
<a href = "../../m_src/md/md.html">a MATLAB version</a> and
<a href = "../../py_src/md/md.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/fft_serial/fft_serial.html">
FFT_SERIAL</a>,
a C++ program which
demonstrates the computation of a Fast Fourier Transform,
and is intended as a starting point for developing a parallel version
using OpenMP.
<p>
<p>
<a href = "../../cpp_src/heated_plate/heated_plate.html">
HEATED_PLATE</a>,
a C++ program which
solves the steady state heat equation in a 2D
rectangular region, and is intended as
a starting point for implementing an OpenMP parallel version.
</p>
<p>
<a href = "../../cpp_src/md_openmp/md_openmp.html">
MD_OPENMP</a>,
a C++ program which
carries out a molecular dynamics simulation,
using OpenMP for parallel execution.
</p>
<p>
<a href = "../../f_src/md1/md1.html">
MD1</a>,
a FORTRAN90 program which
carries out a molecular dynamics simulation.
</p>
<p>
<a href = "../../f_src/md2/md2.html">
MD2</a>,
a FORTRAN90 program which
carries out a molecular dynamics simulation.
</p>
<p>
<a href = "../../f_src/md3/md3.html">
MD3</a>,
a FORTRAN90 program which
carries out a molecular dynamics simulation.
</p>
<p>
<a href = "../../f_src/md3glue/md3glue.html">
MD3GLUE</a>,
a FORTRAN90 program which
carries out a molecular dynamics simulation.
</p>
<p>
<a href = "../../f77_src/mdbnch/mdbnch.html">
MDBNCH</a>,
a FORTRAN77 program which
is a benchmark molecular simulation calculation.
</p>
<p>
<a href = "../../cpp_src/mxm_serial/mxm_serial.html">
MXM_SERIAL</a>,
a C++ program which
sets up a matrix multiplication problem A=B*C,
intended as a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../cpp_src/openmp/openmp.html">
OPENMP</a>,
C++ programs which
illustrate the use of OpenMP.
<p>
<p>
<a href = "../../cpp_src/poisson_serial/poisson_serial.html">
POISSON_SERIAL</a>,
a C++ program which
computes an approximate solution to the Poisson equation in a rectangle,
and is intended as the starting point for the creation of a parallel version.
</p>
<p>
<a href = "../../cpp_src/prime_serial/prime_serial.html">
PRIME_SERIAL</a>,
a C++ program which
counts the number of primes between 1 and N,
intended as a starting point for the creation of a parallel version.
</p>
<p>
<a href = "../../cpp_src/quad_serial/quad_serial.html">
QUAD_SERIAL</a>,
a C++ program which
approximates an integral using a quadrature rule,
and is intended as a starting point for parallelization exercises.
</p>
<p>
<a href = "../../cpp_src/search_serial/search_serial.html">
SEARCH_SERIAL</a>,
a C++ program which
searches the integers from A to B for a value J such that F(J) = C.
this version of the program is intended as a starting point for
a parallel approach.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Matthew Allen, Dominic Tildesley,<br>
Computer Simulation of Liquids,<br>
Oxford University Press, 1987,<br>
ISBN: 0198556454,<br>
LC: QC145.2.
</li>
<li>
Peter Arbenz, Wesley Petersen,<br>
Introduction to Parallel Computing - A practical guide with examples in C,<br>
Oxford University Press,<br>
ISBN: 0-19-851576-6,<br>
LC: QA76.58.P47.
</li>
<li>
Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan,
Jeff McDonald, Ramesh Menon,<br>
Parallel Programming in OpenMP,<br>
Morgan Kaufmann, 2001,<br>
ISBN: 1-55860-671-8,<br>
LC: QA76.642.P32.
</li>
<li>
Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,<br>
Using OpenMP: Portable Shared Memory Parallel Processing,<br>
MIT Press, 2007,<br>
ISBN13: 978-0262533027,<br>
LC: QA76.642.C49.
</li>
<li>
Furio Ercolessi,<br>
A Molecular Dynamics Primer
</li>
<li>
Philipp Janert,<br>
Gnuplot in Action: Understanding Data with Graphs,<br>
Manning, 2008,<br>
ISBN: 1-933988-39-8.
</li>
<li>
Dennis Rapaport,<br>
An Introduction to Interactive Molecular-Dynamics Simulation,<br>
Computers in Physics,<br>
Volume 11, Number 4, July/August 1997, pages 337-347.
</li>
<li>
Dennis Rapaport,<br>
The Art of Molecular Dynamics Simulation,<br>
Cambridge University Press, 2004,<br>
ISBN: 0521825687.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "md.cpp">md.cpp</a>,
the source code;
</li>
<li>
<a href = "md.sh">md.sh</a>,
BASH commands to compile, link and load the program.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "md_run.sh">md_run.sh</a>,
BASH commands that runs the program.
</li>
<li>
<a href = "md_output.txt">md_output.txt</a>,
the output file;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for MD.
</li>
<li>
<b>COMPUTE</b> computes the forces and energies.
</li>
<li>
<b>CPU_TIME</b> reports the elapsed CPU time.
</li>
<li>
<b>DIST</b> computes the displacement (and its norm) between two particles.
</li>
<li>
<b>INITIALIZE</b> initializes the positions, velocities, and accelerations.
</li>
<li>
<b>R8MAT_UNIFORM_AB</b> returns a scaled pseudorandom R8MAT.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>UPDATE</b> updates positions, velocities and accelerations.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 27 December 2014.
</i>
<!-- John Burkardt -->
</body>
</html>