2006-09-22 00:22:34 +08:00
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<HTML>
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2010-05-07 23:11:21 +08:00
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Page</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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2006-09-22 00:22:34 +08:00
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<HR>
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<H3>min_style command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>min_style style
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</PRE>
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2010-06-04 08:14:14 +08:00
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<UL><LI>style = <I>cg</I> or <I>hftn</I> or <I>sd</I> or <I>downhill</I> or <I>quickmin</I> or <I>fire</I>
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2006-09-22 00:22:34 +08:00
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>min_style cg
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min_style hftn
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min_style fire
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Choose a minimization algorithm to use when a <A HREF = "minimize.html">minimize</A>
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command is performed.
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</P>
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<P>The <I>cg</I>, <I>htfn</I>. and <I>sd</I> styles are traditional minimizers, which
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relax the potential energy of the system to a local minimum. As a
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by-product they also relax the force on each atom towards 0.0. To
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work effectively these minimizers require the negative gradient of the
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energy of the system (the objective function) be equivalent to the
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force on the atoms. None of these styles use the
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<A HREF = "timestep.html">timestep</A> setting.
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</P>
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<P>The <I>downhill</I>, <I>quickmin</I>, and <I>fire</I> styles are damped-dynamics
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minimizers which are less mathematically rigorous, but tend to work
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well in practice. They perform calculations only using the forces on
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atoms which they relax towards 0.0. As a by-product they also
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typically relax the energy towards a local minimum. However, because
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they ignore the energy of the system, they can work with
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non-conservative interactions, e.g. dynamics that includes damping
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terms, or with a coupled system, like for nudged elastic band (NEB)
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calculations, where inter-replica forces are not an analytic
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derivative of an energy objective function. Since they are performing
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a damped form of dynamics, all of these minimizers update atom
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positions based on the <A HREF = "timestep.html">timestep</A> setting.
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</P>
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<P>Style <I>cg</I> is the Polak-Ribiere (PR) version of the conjugate gradient
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(CG) algorithm. At each iteration, the force gradient is combined
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with the previous iteration information to compute a new search
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direction perpendicular (conjugate) to the previous search direction.
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A linesearch is performed along the search direction to determine the
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distance to move atoms. The PR variant affects how the direction is
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chosen and how the CG method is restarted when it ceases to make
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progress. The PR variant is thought to be the most effective CG
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choice.
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</P>
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2009-09-29 22:10:23 +08:00
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<P>Style <I>hftn</I> is a Hessian-free truncated Newton algorithm. At each
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iteration a quadratic model of the energy potential is solved by a
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conjugate gradient inner iteration. The Hessian (second derivatives)
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of the energy is not formed directly, but approximated in each
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conjugate search direction by a finite difference directional
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derivative. When close to an energy minimum, the algorithm behaves
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like a Newton method and exhibits a quadratic convergence rate to high
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accuracy. In many cases the behavior of <I>hftn</I> is similar to <I>cg</I>,
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2009-09-29 22:10:23 +08:00
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but it offers another minimizer alternative if <I>cg</I> seems to perform
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poorly.
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2009-09-29 22:10:23 +08:00
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</P>
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<P>Style <I>sd</I> is a steepest descent algorithm. At each iteration, the
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search direction is set to the downhill direction corresponding to the
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force vector (negative gradient of energy). A linesearch is performed
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along the search direction to determine the distance to move atoms.
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Typically, steepest descent will not converge as quickly as CG, but
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may be more robust in some situations.
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</P>
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<P>Style <I>downhill</I> is a simple damped-dynamics minimizer which is
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conceptually similar to steepest descent. At each iteration, forces
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are computed and the each atom's position is updated by an Euler
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step:
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</P>
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<PRE>Xnew = X + dt*dt * F/m
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</PRE>
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<P>where X is the old position, dt is the timestep, m is the atom mass,
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and F is the force on the atom. This is effectively an Euler time
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integration step with the velocity set to 0.0. The timestep used is
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set by the <A HREF = "timestep.html">timestep</A> command, except that if any forces
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are too large, the timestep is limited so that no atoms displaces more
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than <I>dmax</I>, as set by the <A HREF = "min_modify.html">min_modify</A> command.
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</P>
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<P>Style <I>quickmin</I> is a damped-dynamics minimizer based on the Quickmin
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algorithm of <A HREF = "#Jonsson">(Jonsson)</A> as described in
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<A HREF = "#Sheppard">(Sheppard)</A>. It performs an Euler update of the position
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and velocity each iteration as follows:
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</P>
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<PRE>Xnew = X + dt V
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Vnew = V + dt F/m
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</PRE>
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<P>where V is the velocity of each atom, which is intially set to 0.0 by
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the minimizer. Quickmin also projects the velocity onto the force
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direction (steepest descent) and zeroes the velocity whenever it
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becomes anti-parallel to the force (moving uphill).
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</P>
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<P>Style <I>fire</I> is a damped-dynamics minimizer based on the FIRE
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algorithm <A HREF = "#Bitzek">(Bitzek)</A>. It is an enhancement to the Quickmin
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algorithm which adds an effective intertia term to the equations of
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motion and adapts the timestep and degree of projection of the
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velocity onto the force direction, in an attempt to converge more
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quickly.
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2006-09-22 00:22:34 +08:00
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</P>
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<P><B>Restrictions:</B> none
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "min_modify.html">min_modify</A>, <A HREF = "minimize.html">minimize</A>
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</P>
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<P><B>Default:</B>
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</P>
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<PRE>min_style cg
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</PRE>
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2010-06-04 08:14:14 +08:00
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<HR>
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<A NAME = "Bitzek"></A>
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<P><B>(Bitzek)</B> Bitzek, Koskinen, Gahler, Moseler, Gumbsch,
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Phys Rev Lett, 97, 170201 (2006).
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</P>
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<A NAME = "Sheppard"></A>
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<P><B>(Sheppard)</B> Sheppard, Terrell, Henkelman, J Chem Phys, 128, 134106 (2008).
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</P>
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<A NAME = "Jonsson"></A>
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<P><B>(Jonsson)</B> Jonsson, Mills, Jacobson, Classical and Quantum
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Dynamics in Condensed Phase Simulations, J Chem Phys, 128, 134106 (2008).
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</P>
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2006-09-22 00:22:34 +08:00
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</HTML>
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