forked from Scientific-Computing-Lab/Hydro-PED
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathderivation.f90
194 lines (164 loc) · 5.38 KB
/
derivation.f90
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
! Copyright (c) 2017,
! Eyal Shalev ([email protected])
! Vladimir Lyakhovsky
! All rights reserved to Geological Survey of Israel (GSI)
!
! Redistribution and use in source and binary forms, with or without
! modification, are permitted provided that the following conditions are met:
! * Redistributions of source code must retain the above copyright
! notice, this list of conditions and the following disclaimer.
! * 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.
! * Neither the name of Eyal Shalev or Vladimir Lyakhovsky, nor the
! names of its contributors may be used to endorse or promote products
! derived from this software without specific prior written permission.
!
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
! ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
! WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
! DISCLAIMED. IN NO EVENT SHALL Eyal Shalev & Vladimir Lyakhovsky
! BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
! EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
! PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
! OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
! WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
! OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
! ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
!--------------- derivations of basic functions --------------
! element number num point coordinate inside the element
! dr(k,i); k=node number (1,2,3,4); i=coordinate(x,y,z)
!--------------------------------------------------------
!> @brief Calculates derivations of basic functions
!> @details dr(k,i); k=(1,2,3,4) - node number;
!> i=(1,2,3) stands for (x,y,z)
!> @param[in] n - element number
!> @param[out] dr - derivations of basic functions
subroutine derivation(dr,n)
use sizes
use node_data
use element_data
implicit none
integer::i,n
real(kind=8):: xn(4),yn(4),zn(4)
real(kind=8):: dr(4,3)
real(kind=8):: a,b,c,d,e,vol,v1,v2,v3,v4,onv
! coord 4 element nodes
do i = 1,4
xn(i) = cord(nop(n,i),1)
yn(i) = cord(nop(n,i),2)
zn(i) = cord(nop(n,i),3)
end do
! element volume (G = 6 * volume )
!| 1 x1 y1 z1 |
!| 1 x2 y2 z2 |
!| 1 x3 y3 z3 |
!| 1 x4 y4 z4 |
v1 = xn(2) * (yn(3)*zn(4)-zn(3)*yn(4)) &
- xn(3) * (yn(2)*zn(4)-zn(2)*yn(4)) &
+ xn(4) * (yn(2)*zn(3)-zn(2)*yn(3))
v2 = xn(1) * (yn(3)*zn(4)-zn(3)*yn(4)) &
- xn(3) * (yn(1)*zn(4)-zn(1)*yn(4)) &
+ xn(4) * (yn(1)*zn(3)-zn(1)*yn(3))
v3 = xn(1) * (yn(2)*zn(4)-zn(2)*yn(4)) &
- xn(2) * (yn(1)*zn(4)-zn(1)*yn(4)) &
+ xn(4) * (yn(1)*zn(2)-zn(1)*yn(2))
v4 = xn(1) * (yn(2)*zn(3)-zn(2)*yn(3)) &
- xn(2) * (yn(1)*zn(3)-zn(1)*yn(3)) &
+ xn(3) * (yn(1)*zn(2)-zn(1)*yn(2))
vol = v1 - v2 + v3 - v4
if(vol .ge.0.0_8 )then
! write(6,*)' Negative volume ',-vol/6,' element ', n
! write(6,*)-v1,v2,-v3,v4
! stop
flag(n) = 3
dr = 0.
return
end if
onv= 1.0_8/vol
!A = | 1 y2 z2 |
! | 1 y3 z3 |
! | 1 y4 z4 |
a = yn(3)*zn(4)-zn(3)*yn(4) &
-(yn(2)*zn(4)-zn(2)*yn(4)) &
+ yn(2)*zn(3)-zn(2)*yn(3)
!B = | 1 x2 z2 |
! | 1 x3 z3 |
! | 1 x4 z4 |
b = xn(3)*zn(4)-zn(3)*xn(4) &
-(xn(2)*zn(4)-zn(2)*xn(4)) &
+ xn(2)*zn(3)-zn(2)*xn(3)
!C = | 1 x2 y2 |
! | 1 x3 y3 |
! | 1 x4 y4 |
c = xn(3)*yn(4)-yn(3)*xn(4) &
-(xn(2)*yn(4)-yn(2)*xn(4)) &
+ xn(2)*yn(3)-yn(2)*xn(3)
dr(1,1) = -a * onv
dr(1,2) = b * onv
dr(1,3) = -c * onv
!A = | 1 y1 z1 |
! | 1 y3 z3 |
! | 1 y4 z4 |
a = yn(3)*zn(4)-zn(3)*yn(4) &
-(yn(1)*zn(4)-zn(1)*yn(4)) &
+ yn(1)*zn(3)-zn(1)*yn(3)
!B = | 1 x1 z1 |
! | 1 x3 z3 |
! | 1 x4 z4 |
b = xn(3)*zn(4)-zn(3)*xn(4) &
-(xn(1)*zn(4)-zn(1)*xn(4)) &
+ xn(1)*zn(3)-zn(1)*xn(3)
!C = | 1 x1 y1 |
! | 1 x3 y3 |
! | 1 x4 y4 |
c = xn(3)*yn(4)-yn(3)*xn(4) &
-(xn(1)*yn(4)-yn(1)*xn(4)) &
+ xn(1)*yn(3)-yn(1)*xn(3)
dr(2,1) = a * onv
dr(2,2) = -b * onv
dr(2,3) = c * onv
!A = | 1 y1 z1 |
! | 1 y2 z2 |
! | 1 y4 z4 |
a = yn(2)*zn(4)-zn(2)*yn(4) &
-(yn(1)*zn(4)-zn(1)*yn(4)) &
+ yn(1)*zn(2)-zn(1)*yn(2)
!B = | 1 x1 z1 |
! | 1 x2 z2 |
! | 1 x4 z4 |
b = xn(2)*zn(4)-zn(2)*xn(4) &
-(xn(1)*zn(4)-zn(1)*xn(4)) &
+ xn(1)*zn(2)-zn(1)*xn(2)
!C = | 1 x1 y1 |
! | 1 x2 y2 |
! | 1 x4 y4 |
c = xn(2)*yn(4)-yn(2)*xn(4) &
-(xn(1)*yn(4)-yn(1)*xn(4)) &
+ xn(1)*yn(2)-yn(1)*xn(2)
dr(3,1) = -a * onv
dr(3,2) = b * onv
dr(3,3) = -c * onv
!A = | 1 y1 z1 |
! | 1 y2 z2 |
! | 1 y3 z3 |
a = yn(2)*zn(3)-zn(2)*yn(3) &
-(yn(1)*zn(3)-zn(1)*yn(3)) &
+ yn(1)*zn(2)-zn(1)*yn(2)
!B = | 1 x1 z1 |
! | 1 x2 z2 |
! | 1 x3 z3 |
b = xn(2)*zn(3)-zn(2)*xn(3) &
-(xn(1)*zn(3)-zn(1)*xn(3)) &
+ xn(1)*zn(2)-zn(1)*xn(2)
!C = | 1 x1 y1 |
! | 1 x2 y2 |
! | 1 x3 y3 |
c = xn(2)*yn(3)-yn(2)*xn(3) &
-(xn(1)*yn(3)-yn(1)*xn(3)) &
+ xn(1)*yn(2)-yn(1)*xn(2)
dr(4,1) = a * onv
dr(4,2) = -b * onv
dr(4,3) = c * onv
return
end subroutine derivation