src/integrators/DLM.cpp

/*
 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
 *
 * The University of Notre Dame grants you ("Licensee") a
 * non-exclusive, royalty free, license to use, modify and
 * redistribute this software in source and binary code form, provided
 * that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the
 *    distribution.
 *
 * This software is provided "AS IS," without a warranty of any
 * kind. All express or implied conditions, representations and
 * warranties, including any implied warranty of merchantability,
 * fitness for a particular purpose or non-infringement, are hereby
 * excluded.  The University of Notre Dame and its licensors shall not
 * be liable for any damages suffered by licensee as a result of
 * using, modifying or distributing the software or its
 * derivatives. In no event will the University of Notre Dame or its
 * licensors be liable for any lost revenue, profit or data, or for
 * direct, indirect, special, consequential, incidental or punitive
 * damages, however caused and regardless of the theory of liability,
 * arising out of the use of or inability to use software, even if the
 * University of Notre Dame has been advised of the possibility of
 * such damages.
 *
 * SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
 * research, please cite the appropriate papers when you publish your
 * work.  Good starting points are:
 *                                                                      
 * [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).             
 * [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).          
 * [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).          
 * [4]  Vardeman & Gezelter, in progress (2009).                        
 */
 
#include "DLM.hpp"

namespace OpenMD {

  void DLM::doRotate(StuntDouble* sd, Vector3d& ji, RealType dt) {
    RealType dt2 = 0.5 * dt;    
    RealType angle;

    RotMat3x3d A = sd->getA();
    Mat3x3d I = sd->getI();

    // use the angular velocities to propagate the rotation matrix a full time step
    if (sd->isLinear()) {

      int i = sd->linearAxis();
      int j = (i+1)%3;
      int k = (i+2)%3;

      angle = dt2 * ji[j] / I(j, j);
      rotateStep( k, i, angle, ji, A );

      angle = dt * ji[k] / I(k, k);
      rotateStep( i, j, angle, ji, A);

      angle = dt2 * ji[j] / I(j, j);
      rotateStep( k, i, angle, ji, A );

    } else {
      // rotate about the x-axis
      angle = dt2 * ji[0] / I(0, 0);
      rotateStep( 1, 2, angle, ji, A );

      // rotate about the y-axis
      angle = dt2 * ji[1] / I(1, 1);
      rotateStep( 2, 0, angle, ji, A );

      // rotate about the z-axis
      angle = dt * ji[2] / I(2, 2);
      sd->addZangle(angle);
      rotateStep( 0, 1, angle, ji, A);

      // rotate about the y-axis
      angle = dt2 * ji[1] / I(1, 1);
      rotateStep( 2, 0, angle, ji, A );

      // rotate about the x-axis
      angle = dt2 * ji[0] / I(0, 0);
      rotateStep( 1, 2, angle, ji, A );

    }

    sd->setA( A  );
  }


  void DLM::rotateStep(int axes1, int axes2, RealType angle, Vector3d& ji, RotMat3x3d& A) {

    RealType sinAngle;
    RealType cosAngle;
    RealType angleSqr;
    RealType angleSqrOver4;
    RealType top, bottom;

    RotMat3x3d tempA(A);  // initialize the tempA
    Vector3d tempJ(0.0);

    RotMat3x3d rot = RotMat3x3d::identity(); // initalize rot as a unit matrix

    // use a small angle aproximation for sin and cosine
    /*
    angleSqr = angle * angle;
    angleSqrOver4 = angleSqr / 4.0;
    top = 1.0 - angleSqrOver4;
    bottom = 1.0 + angleSqrOver4;

    cosAngle = top / bottom;
    sinAngle = angle / bottom;
    */
    // or don't use the small angle approximation:
    cosAngle = cos(angle);
    sinAngle = sin(angle);

    rot(axes1, axes1) = cosAngle;
    rot(axes2, axes2) = cosAngle;

    rot(axes1, axes2) = sinAngle;
    rot(axes2, axes1) = -sinAngle;

    // rotate the momentum acoording to: ji[] = rot[][] * ji[]
    ji = rot * ji;

    // This code comes from converting an algorithm detailed in 
    // J. Chem. Phys. 107 (15), pp. 5840-5851 by Dullweber, 
    // Leimkuhler and McLachlan (DLM) for use in our code.
    // In Appendix A, the DLM paper has the change to the rotation 
    // matrix as: Q = Q * rot.transpose(), but our rotation matrix 
    // A is actually equivalent to Q.transpose(). This fact can be 
    // seen on page 5849 of the DLM paper where a lab frame 
    // dipole \mu_i(t) is expressed in terms of a body-fixed
    // reference orientation, \bar{\mu_i} and the rotation matrix, Q:
    //  \mu_i(t) = Q * \bar{\mu_i}
    // Our code computes lab frame vectors from body-fixed reference
    // vectors using:
    //   v_{lab} = A.transpose() * v_{body}
    //  (See StuntDouble.hpp for confirmation of this fact).
    //
    // So, using the identity:
    //  (A * B).transpose() = B.transpose() * A.transpose(),  we
    // get the equivalent of Q = Q * rot.transpose() for our code to be:

    A = rot * A;
  
  }


}
Revision:	1697
Committed:	Fri Mar 16 21:17:36 2012 UTC (13 years, 7 months ago) by skuang
File size:	5368 byte(s)
Log Message:	vss-rnemd
#	User	Rev	Content
1	gezelter	507	/*
2	gezelter	246	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3			*
4			* The University of Notre Dame grants you ("Licensee") a
5			* non-exclusive, royalty free, license to use, modify and
6			* redistribute this software in source and binary code form, provided
7			* that the following conditions are met:
8			*
9	gezelter	1390	* 1. Redistributions of source code must retain the above copyright
10	gezelter	246	* notice, this list of conditions and the following disclaimer.
11			*
12	gezelter	1390	* 2. Redistributions in binary form must reproduce the above copyright
13	gezelter	246	* notice, this list of conditions and the following disclaimer in the
14			* documentation and/or other materials provided with the
15			* distribution.
16			*
17			* This software is provided "AS IS," without a warranty of any
18			* kind. All express or implied conditions, representations and
19			* warranties, including any implied warranty of merchantability,
20			* fitness for a particular purpose or non-infringement, are hereby
21			* excluded. The University of Notre Dame and its licensors shall not
22			* be liable for any damages suffered by licensee as a result of
23			* using, modifying or distributing the software or its
24			* derivatives. In no event will the University of Notre Dame or its
25			* licensors be liable for any lost revenue, profit or data, or for
26			* direct, indirect, special, consequential, incidental or punitive
27			* damages, however caused and regardless of the theory of liability,
28			* arising out of the use of or inability to use software, even if the
29			* University of Notre Dame has been advised of the possibility of
30			* such damages.
31	gezelter	1390	*
32			* SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your
33			* research, please cite the appropriate papers when you publish your
34			* work. Good starting points are:
35			*
36			* [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
37			* [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
38			* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).
39			* [4] Vardeman & Gezelter, in progress (2009).
40	gezelter	246	*/
41
42			#include "DLM.hpp"
43
44	gezelter	1390	namespace OpenMD {
45	gezelter	246
46	tim	963	void DLM::doRotate(StuntDouble* sd, Vector3d& ji, RealType dt) {
47			RealType dt2 = 0.5 * dt;
48			RealType angle;
49	gezelter	246
50			RotMat3x3d A = sd->getA();
51			Mat3x3d I = sd->getI();
52
53			// use the angular velocities to propagate the rotation matrix a full time step
54			if (sd->isLinear()) {
55
56	gezelter	507	int i = sd->linearAxis();
57			int j = (i+1)%3;
58			int k = (i+2)%3;
59	gezelter	246
60	gezelter	507	angle = dt2 * ji[j] / I(j, j);
61			rotateStep( k, i, angle, ji, A );
62	gezelter	246
63	gezelter	507	angle = dt * ji[k] / I(k, k);
64			rotateStep( i, j, angle, ji, A);
65	gezelter	246
66	gezelter	507	angle = dt2 * ji[j] / I(j, j);
67			rotateStep( k, i, angle, ji, A );
68	gezelter	246
69			} else {
70	gezelter	507	// rotate about the x-axis
71			angle = dt2 * ji[0] / I(0, 0);
72			rotateStep( 1, 2, angle, ji, A );
73	gezelter	246
74	gezelter	507	// rotate about the y-axis
75			angle = dt2 * ji[1] / I(1, 1);
76			rotateStep( 2, 0, angle, ji, A );
77	gezelter	246
78	gezelter	507	// rotate about the z-axis
79			angle = dt * ji[2] / I(2, 2);
80			sd->addZangle(angle);
81			rotateStep( 0, 1, angle, ji, A);
82	gezelter	246
83	gezelter	507	// rotate about the y-axis
84			angle = dt2 * ji[1] / I(1, 1);
85			rotateStep( 2, 0, angle, ji, A );
86	gezelter	246
87	gezelter	507	// rotate about the x-axis
88			angle = dt2 * ji[0] / I(0, 0);
89			rotateStep( 1, 2, angle, ji, A );
90	gezelter	246
91			}
92
93			sd->setA( A );
94	gezelter	507	}
95	gezelter	246
96
97	tim	963	void DLM::rotateStep(int axes1, int axes2, RealType angle, Vector3d& ji, RotMat3x3d& A) {
98	gezelter	246
99	tim	963	RealType sinAngle;
100			RealType cosAngle;
101			RealType angleSqr;
102			RealType angleSqrOver4;
103			RealType top, bottom;
104	gezelter	246
105			RotMat3x3d tempA(A); // initialize the tempA
106			Vector3d tempJ(0.0);
107
108			RotMat3x3d rot = RotMat3x3d::identity(); // initalize rot as a unit matrix
109
110			// use a small angle aproximation for sin and cosine
111	skuang	1697	/*
112	xsun	1216	angleSqr = angle * angle;
113			angleSqrOver4 = angleSqr / 4.0;
114			top = 1.0 - angleSqrOver4;
115			bottom = 1.0 + angleSqrOver4;
116	gezelter	246
117	xsun	1216	cosAngle = top / bottom;
118			sinAngle = angle / bottom;
119	skuang	1697	*/
120			// or don't use the small angle approximation:
121			cosAngle = cos(angle);
122			sinAngle = sin(angle);
123	xsun	1216
124	gezelter	246	rot(axes1, axes1) = cosAngle;
125			rot(axes2, axes2) = cosAngle;
126
127			rot(axes1, axes2) = sinAngle;
128			rot(axes2, axes1) = -sinAngle;
129
130			// rotate the momentum acoording to: ji[] = rot[][] * ji[]
131			ji = rot * ji;
132
133	xsun	1216	// This code comes from converting an algorithm detailed in
134			// J. Chem. Phys. 107 (15), pp. 5840-5851 by Dullweber,
135			// Leimkuhler and McLachlan (DLM) for use in our code.
136			// In Appendix A, the DLM paper has the change to the rotation
137			// matrix as: Q = Q * rot.transpose(), but our rotation matrix
138			// A is actually equivalent to Q.transpose(). This fact can be
139			// seen on page 5849 of the DLM paper where a lab frame
140			// dipole \mu_i(t) is expressed in terms of a body-fixed
141			// reference orientation, \bar{\mu_i} and the rotation matrix, Q:
142			// \mu_i(t) = Q * \bar{\mu_i}
143			// Our code computes lab frame vectors from body-fixed reference
144			// vectors using:
145			// v_{lab} = A.transpose() * v_{body}
146			// (See StuntDouble.hpp for confirmation of this fact).
147			//
148			// So, using the identity:
149			// (A * B).transpose() = B.transpose() * A.transpose(), we
150			// get the equivalent of Q = Q * rot.transpose() for our code to be:
151
152			A = rot * A;
153	gezelter	246
154	gezelter	507	}
155	gezelter	246
156
157			}