mantaflow  0.10
A framework for fluid simulation
solvana.h
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1 
2 /******************************************************************************
3  *
4  * MantaFlow fluid solver framework
5  * Copyright 2011 Tobias Pfaff, Nils Thuerey
6  *
7  * This program is free software, distributed under the terms of the
8  * GNU General Public License (GPL)
9  * http://www.gnu.org/licenses
10  *
11  * Analytical solutions to some problems
12  * generated using MATLAB symbolic math ccode
13  *
14  ******************************************************************************/
15 
16 #ifndef _SOLVANA_H
17 #define _SOLVANA_H
18 
20 inline void SolveOverconstraint34(float e1x, float e1y, float e1z,
21  float e2x, float e2y, float e2z,
22  float e3x, float e3y, float e3z,
23  float g1, float g2, float g3,
24  float& x1, float& x2, float& x3)
25 {
26  float e1x2 = e1x*e1x, e1y2 = e1y*e1y, e1z2 = e1z*e1z;
27  float e2x2 = e2x*e2x, e2y2 = e2y*e2y, e2z2 = e2z*e2z;
28  float e3x2 = e3x*e3x, e3y2 = e3y*e3y, e3z2 = e3z*e3z;
29  float e1xy = e1x*e1y, e1xz = e1x*e1z, e1yz = e1y*e1z;
30  float e2xy = e2x*e2y, e2xz = e2x*e2z, e2yz = e2y*e2z;
31  float e3xy = e3x*e3y, e3xz = e3x*e3z, e3yz = e3y*e3z;
32  float e12x = e1x*e2x, e12y = e1y*e2y, e12z = e1z*e2z;
33  float e13x = e1x*e3x, e13y = e1y*e3y, e13z = e1z*e3z;
34  float e23x = e2x*e3x, e23y = e2y*e3y, e23z = e2z*e3z;
35  float t1543 = e3y2*e2x2;
36  float t1544 = e3x2*e2y2;
37  float t1545 = e3z2*e2x2;
38  float t1546 = e3x2*e2z2;
39  float t1547 = e3z2*e2y2;
40  float t1548 = e3y2*e2z2;
41  float t1549 = e2y2*e1x2;
42  float t1550 = e2x2*e1y2;
43  float t1551 = e2z2*e1x2;
44  float t1552 = e2x2*e1z2;
45  float t1553 = e2z2*e1y2;
46  float t1554 = e2y2*e1z2;
47  float t1555 = e3y2*e1x2;
48  float t1556 = e3x2*e1y2;
49  float t1557 = e3z2*e1x2;
50  float t1558 = e3x2*e1z2;
51  float t1559 = e3z2*e1y2;
52  float t1560 = e3y2*e1z2;
53  float t1561 = e3z2*e2y2*e1x2;
54  float t1562 = e3y2*e2z2*e1x2;
55  float t1563 = e3z2*e2x2*e1y2;
56  float t1564 = e3x2*e2z2*e1y2;
57  float t1565 = e3y2*e2x2*e1z2;
58  float t1566 = e3x2*e2y2*e1z2;
59  float t1567 = e1xy*e2x*e3y*2.0;
60  float t1568 = e1xy*e2y*e3x*2.0;
61  float t1569 = e1xz*e2x*e3z*2.0;
62  float t1570 = e1xz*e2z*e3x*2.0;
63  float t1571 = e1yz*e2y*e3z*2.0;
64  float t1572 = e1yz*e2z*e3y*2.0;
65  float t1573 = e1x*e2xy*e3y*2.0;
66  float t1574 = e1y*e2xy*e3x*2.0;
67  float t1575 = e1x*e2xz*e3z*2.0;
68  float t1576 = e1z*e2xz*e3x*2.0;
69  float t1577 = e1y*e2yz*e3z*2.0;
70  float t1578 = e1z*e2yz*e3y*2.0;
71  float t1579 = e1x*e2y*e3xy*2.0;
72  float t1580 = e1y*e2x*e3xy*2.0;
73  float t1581 = e1x*e2z*e3xz*2.0;
74  float t1582 = e1z*e2x*e3xz*2.0;
75  float t1583 = e1y*e2z*e3yz*2.0;
76  float t1584 = e1z*e2y*e3yz*2.0;
77  float t1585 = e1xy*e2xz*e3yz*2.0;
78  float t1586 = e1xy*e2yz*e3xz*2.0;
79  float t1587 = e1xz*e2xy*e3yz*2.0;
80  float t1588 = e1xz*e2yz*e3xy*2.0;
81  float t1589 = e1yz*e2xy*e3xz*2.0;
82  float t1590 = e1yz*e2xz*e3xy*2.0;
83  float t1596 = e12x*e3y2*2.0;
84  float t1597 = e13x*e2y2*2.0;
85  float t1598 = e23x*e1y2*2.0;
86  float t1599 = e12x*e3z2*2.0;
87  float t1600 = e13x*e2z2*2.0;
88  float t1601 = e12y*e3x2*2.0;
89  float t1602 = e13y*e2x2*2.0;
90  float t1603 = e23y*e1x2*2.0;
91  float t1604 = e23x*e1z2*2.0;
92  float t1605 = e12y*e3z2*2.0;
93  float t1606 = e13y*e2z2*2.0;
94  float t1607 = e12z*e3x2*2.0;
95  float t1608 = e13z*e2x2*2.0;
96  float t1609 = e23z*e1x2*2.0;
97  float t1610 = e23y*e1z2*2.0;
98  float t1611 = e12z*e3y2*2.0;
99  float t1612 = e13z*e2y2*2.0;
100  float t1613 = e23z*e1y2*2.0;
101  float t1614 = e1xy*e2xy*2.0;
102  float t1615 = e1xz*e2xz*2.0;
103  float t1616 = e1yz*e2yz*2.0;
104  float t1617 = e1xy*e3xy*2.0;
105  float t1618 = e1xz*e3xz*2.0;
106  float t1619 = e1yz*e3yz*2.0;
107  float t1620 = e2xy*e3xy*2.0;
108  float t1621 = e2xz*e3xz*2.0;
109  float t1622 = e2yz*e3yz*2.0;
110  float t1623 = e1xy*e2xy*e3z2*2.0;
111  float t1624 = e1xz*e2xz*e3y2*2.0;
112  float t1625 = e1yz*e2yz*e3x2*2.0;
113  float t1626 = e1xy*e3xy*e2z2*2.0;
114  float t1627 = e1xz*e3xz*e2y2*2.0;
115  float t1628 = e1yz*e3yz*e2x2*2.0;
116  float t1629 = e2xy*e3xy*e1z2*2.0;
117  float t1630 = e2xz*e3xz*e1y2*2.0;
118  float t1631 = e2yz*e3yz*e1x2*2.0;
119  float t1591 = t1550+t1551+t1560+t1543+t1552+t1561+t1570+t1544+t1553+t1562+t1571+t1580+t1545+t1554+t1563+t1572+t1581+t1590+t1546+t1555+t1564+t1573+t1582+t1547+t1556+t1565+t1574+t1583+t1548+t1557+t1566+t1575+t1584+t1549+t1558+t1567+t1576+t1585+t1559+t1568+t1577+t1586+t1569+t1578+t1587-t1596+t1579+t1588-t1597+t1589-t1598-t1599-t1600-t1601-t1610-t1602-t1611-t1620-t1603-t1612-t1621-t1630-t1604-t1613-t1622-t1631-t1605-t1614-t1623-t1606-t1615-t1624-t1607-t1616-t1625-t1608-t1617-t1626-t1609-t1618-t1627-t1619-t1628-t1629;
120  float t1592 = 1.0/t1591;
121  float t1635 = e13x*e2y2;
122  float t1636 = e13x*e2z2;
123  float t1637 = e13y*e2x2;
124  float t1638 = e13y*e2z2;
125  float t1639 = e13z*e2x2;
126  float t1640 = e13z*e2y2;
127  float t1653 = e23x*2.0;
128  float t1654 = e23y*2.0;
129  float t1655 = e23z*2.0;
130  float t1641 = e3x2+e3z2+e3y2+e2y2+t1543+e2z2+t1544+e2x2+t1545+t1546+t1547+t1548-t1620-t1621-t1622-t1653-t1654-t1655;
131  float t1642 = e12x*e3y2;
132  float t1643 = e12x*e3z2;
133  float t1644 = e12y*e3x2;
134  float t1645 = e12y*e3z2;
135  float t1646 = e12z*e3x2;
136  float t1647 = e12z*e3y2;
137  float t1656 = e1x*e2y*e3xy;
138  float t1657 = e1y*e2x*e3xy;
139  float t1658 = e1x*e2z*e3xz;
140  float t1659 = e1z*e2x*e3xz;
141  float t1660 = e1y*e2z*e3yz;
142  float t1661 = e1z*e2y*e3yz;
143  float t1648 = e3x2+e3z2+e3y2-e13x-e13y-e13z+e12x-e23y+e12y+t1642-e23z-t1660+e12z+t1643-t1661+t1644+t1645+t1646+t1647-t1656-t1657-e23x-t1658-t1659;
144  float t1679 = e1x*e2xy*e3y;
145  float t1680 = e1y*e2xy*e3x;
146  float t1681 = e1x*e2xz*e3z;
147  float t1682 = e1z*e2xz*e3x;
148  float t1683 = e1y*e2yz*e3z;
149  float t1684 = e1z*e2yz*e3y;
150  float t1652 = e2y2+e2z2+e2x2+e13x+e13y+e13z+t1640-e12x-e23y-e12y-e23z-e12z+t1635-t1680+t1636-t1681+t1637-t1682+t1638-t1683+t1639-t1684-e23x-t1679;
151  float t1662 = e23x*e1y2;
152  float t1663 = e23y*e1x2;
153  float t1664 = e23x*e1z2;
154  float t1665 = e23z*e1x2;
155  float t1666 = e23y*e1z2;
156  float t1667 = e23z*e1y2;
157  float t1670 = e1xy*e2x*e3y;
158  float t1671 = e1xy*e2y*e3x;
159  float t1672 = e1xz*e2x*e3z;
160  float t1673 = e1xz*e2z*e3x;
161  float t1674 = e1yz*e2y*e3z;
162  float t1675 = e1yz*e2z*e3y;
163  float t1668 = e1x2+e1y2+e1z2-e13x-e13y-e13z-e12x+e23y-e12y+e23z-e12z-t1670+t1662-t1671+t1663-t1672+t1664-t1673+t1665-t1674+t1666-t1675+e23x+t1667;
164  float t1676 = e13x*2.0;
165  float t1677 = e13y*2.0;
166  float t1678 = e13z*2.0;
167  float t1669 = e3x2+e3z2+e3y2+t1560+e1x2+t1555+e1y2+t1556+e1z2+t1557+t1558+t1559-t1617-t1618-t1619-t1676-t1677-t1678;
168  float t1686 = e12x*2.0;
169  float t1687 = e12y*2.0;
170  float t1688 = e12z*2.0;
171  float t1685 = t1550+t1551+e2y2+t1552+e2z2+t1553+e2x2+t1554+e1x2+e1y2+e1z2+t1549-t1614-t1615-t1616-t1686-t1687-t1688;
172  x1 =-g2*(-e1y*t1592*t1641+e2y*t1592*t1648+e3y*t1592*t1652)-g3*(-e1z*t1592*t1641+e2z*t1592*t1648+e3z*t1592*t1652)-g1*(-e1x*t1592*t1641+e2x*t1592*t1648+e3x*t1592*(e2y2+e2z2+e2x2+e13x+e13y+e13z+t1640+t1635+t1636+t1637+t1638+t1639-e12x-e12y-e12z-e23x-e23y-e23z-e1x*e2xy*e3y-e1y*e2xy*e3x-e1x*e2xz*e3z-e1z*e2xz*e3x-e1y*e2yz*e3z-e1z*e2yz*e3y));
173  x2 =-g1*(e1x*t1592*t1648-e2x*t1592*t1669+e3x*t1592*t1668)-g2*(e1y*t1592*t1648-e2y*t1592*t1669+e3y*t1592*t1668)-g3*(e1z*t1592*t1648-e2z*t1592*t1669+e3z*t1592*t1668);
174  x3 =-g1*(e1x*t1592*t1652+e2x*t1592*t1668-e3x*t1592*t1685)-g2*(e1y*t1592*t1652+e2y*t1592*t1668-e3y*t1592*t1685)-g3*(e1z*t1592*t1652+e2z*t1592*t1668-e3z*t1592*t1685);
175 }
176 
177 #endif
178 
SolveOverconstraint34
void SolveOverconstraint34(float e1x, float e1y, float e1z, float e2x, float e2y, float e2z, float e3x, float e3y, float e3z, float g1, float g2, float g3, float &x1, float &x2, float &x3)
solves the equation [e1 e2 e3; 1 1 1]*x = g using least squares
Definition: solvana.h:20
Generated on Tue Sep 19 2017 17:49:04 for mantaflow by   doxygen 1.8.13