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. Acknowledgement of the program authors must be made in any
 *    publication of scientific results based in part on use of the
 *    program.  An acceptable form of acknowledgement is citation of
 *    the article in which the program was described (Matthew
 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
 *    Parallel Simulation Engine for Molecular Dynamics,"
 *    J. Comput. Chem. 26, pp. 252-271 (2005))
 *
 * 2. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 3. 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.
 */
 
#include "DLM.hpp"

namespace oopse {

  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:	3325
Committed:	Wed Jan 23 21:22:50 2008 UTC (17 years, 3 months ago) by xsun
File size:	5318 byte(s)
Log Message:	Fixed Langevin Dynamics and DLM
#	Content
1	/*
2	* 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	* 1. Acknowledgement of the program authors must be made in any
10	* publication of scientific results based in part on use of the
11	* program. An acceptable form of acknowledgement is citation of
12	* the article in which the program was described (Matthew
13	* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14	* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15	* Parallel Simulation Engine for Molecular Dynamics,"
16	* J. Comput. Chem. 26, pp. 252-271 (2005))
17	*
18	* 2. Redistributions of source code must retain the above copyright
19	* notice, this list of conditions and the following disclaimer.
20	*
21	* 3. Redistributions in binary form must reproduce the above copyright
22	* notice, this list of conditions and the following disclaimer in the
23	* documentation and/or other materials provided with the
24	* distribution.
25	*
26	* This software is provided "AS IS," without a warranty of any
27	* kind. All express or implied conditions, representations and
28	* warranties, including any implied warranty of merchantability,
29	* fitness for a particular purpose or non-infringement, are hereby
30	* excluded. The University of Notre Dame and its licensors shall not
31	* be liable for any damages suffered by licensee as a result of
32	* using, modifying or distributing the software or its
33	* derivatives. In no event will the University of Notre Dame or its
34	* licensors be liable for any lost revenue, profit or data, or for
35	* direct, indirect, special, consequential, incidental or punitive
36	* damages, however caused and regardless of the theory of liability,
37	* arising out of the use of or inability to use software, even if the
38	* University of Notre Dame has been advised of the possibility of
39	* such damages.
40	*/
41
42	#include "DLM.hpp"
43
44	namespace oopse {
45
46	void DLM::doRotate(StuntDouble* sd, Vector3d& ji, RealType dt) {
47	RealType dt2 = 0.5 * dt;
48	RealType angle;
49
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	int i = sd->linearAxis();
57	int j = (i+1)%3;
58	int k = (i+2)%3;
59
60	angle = dt2 * ji[j] / I(j, j);
61	rotateStep( k, i, angle, ji, A );
62
63	angle = dt * ji[k] / I(k, k);
64	rotateStep( i, j, angle, ji, A);
65
66	angle = dt2 * ji[j] / I(j, j);
67	rotateStep( k, i, angle, ji, A );
68
69	} else {
70	// rotate about the x-axis
71	angle = dt2 * ji[0] / I(0, 0);
72	rotateStep( 1, 2, angle, ji, A );
73
74	// rotate about the y-axis
75	angle = dt2 * ji[1] / I(1, 1);
76	rotateStep( 2, 0, angle, ji, A );
77
78	// 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
83	// rotate about the y-axis
84	angle = dt2 * ji[1] / I(1, 1);
85	rotateStep( 2, 0, angle, ji, A );
86
87	// rotate about the x-axis
88	angle = dt2 * ji[0] / I(0, 0);
89	rotateStep( 1, 2, angle, ji, A );
90
91	}
92
93	sd->setA( A );
94	}
95
96
97	void DLM::rotateStep(int axes1, int axes2, RealType angle, Vector3d& ji, RotMat3x3d& A) {
98
99	RealType sinAngle;
100	RealType cosAngle;
101	RealType angleSqr;
102	RealType angleSqrOver4;
103	RealType top, bottom;
104
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
112	angleSqr = angle * angle;
113	angleSqrOver4 = angleSqr / 4.0;
114	top = 1.0 - angleSqrOver4;
115	bottom = 1.0 + angleSqrOver4;
116
117	cosAngle = top / bottom;
118	sinAngle = angle / bottom;
119
120	// or don't use the small angle approximation:
121	//cosAngle = cos(angle);
122	//sinAngle = sin(angle);
123	rot(axes1, axes1) = cosAngle;
124	rot(axes2, axes2) = cosAngle;
125
126	rot(axes1, axes2) = sinAngle;
127	rot(axes2, axes1) = -sinAngle;
128
129	// rotate the momentum acoording to: ji[] = rot[][] * ji[]
130	ji = rot * ji;
131
132
133	// 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
154	}
155
156
157	}