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
|
! cylindrical_cavity This program computes particular solutions to
! the elastic wave equation in cylindrical geometries,
! see: https://bitbucket.org/appelo/pewe
!
! Copyright (C) 2015 Kristoffer Virta & Daniel Appelo
!
!
! This program is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with this program. If not, see <http://www.gnu.org/licenses/>.
!
! Modified by Vanessa Mattesi for inclusion in GetDP:
!
! Exact solution for a cylindrical wall (zero displacement on the
! boundary) and with a shear incident wave for elasticity 2D.
subroutine cylindrical_walls(du,dv,dut,dvt,X,Y,t,omega,lambda,mu,rho,a)
implicit none
double precision :: x,y,du,dv,dvt,dut,t
double precision :: r,theta
double precision :: lambda,mu,rho
double precision :: cp,cs,omega,gamma,eta,a
double precision :: psi_0,f_01,f_02,epsilon_0,epsilon_1,c01,c02
double precision :: epsilon_n
double precision :: f_10,f_11,f_12,f_13,f_14,f_15
double complex :: a_00,a_02,b_01,b_04,m11,m12,m21,m22,ab0(2),q
double complex :: a_10,a_11,a_12,a_13,a_14,a_15
double complex :: b_10,b_11,b_12,b_13,b_14,b_15
double complex :: c11,c12,ab1(2),v,cn1,cn2,abn(2)
double complex :: f_n0,f_n1,f_n2,f_n3,f_n4,f_n5
double complex :: a_n0,a_n1,a_n2,a_n3,a_n4,a_n5
double complex :: b_n0,b_n1,b_n2,b_n3,b_n4,b_n5
integer :: n
double precision , parameter :: pi = acos(-1.d0)
! for GetDP
integer :: ns
double complex, external :: besselh
! Computes displacement field (du(x,y,t),dy(x,y,t))
! of incoming S waves, scattered P waves and scattered S waves at
! time t = 0. Solution at other times are given by
! du(x,y,t) = du(x,y,0)*exp(1i*omega*t),
! dv(x,y,t) = dv(x,y,0)*exp(1i*omega*t).
! Compute radius r and angle theta
r = sqrt(X**2+Y**2)
theta = atan2(Y,X)
! P and S wave speeds
cp = sqrt((lambda+2.d0*mu)/rho)
cs = sqrt(mu/rho)
! To satisfy elastic wave equation
gamma = omega/cp
eta = omega/cs
! Radius of cylinder
!a = 1.d0
! Amplitude of incomming wave
psi_0 = 1.d0
! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Series expansion of solution%%%%%%%%%%%
! disp('COMPUTING COEFICIENTS')
n = 0
f_01= eta*besjn(1,eta*a)
a_00 = -gamma*besselh(1,2,gamma*a)
b_01 = eta*besselh(1,2,eta*a)
epsilon_0 = 1.d0
m11 = a_00
m12 = 0.d0
m21 = 0.d0
m22 = b_01
c01 = 0.d0
c02 = -psi_0*epsilon_0*f_01
AB0(1) = 1.d0/(m11*m22 - m12*m21)*(m22*c01-m12*c02)
AB0(2) = 1.d0/(m11*m22 - m12*m21)*(-m21*c01+m11*c02)
v = AB0(2) * eta*(besselh(1,2,eta*r)) + psi_0*epsilon_0* eta *besjn(1,eta*r)
! for GetDP
ns = max(eta*a+30, 2*eta);
epsilon_1 = 2.d0
! for GetDP: instead of 2:24
do n = 1,1
f_n0 = psi_0*epsilon_1*((0.d0,-1.d0)**n)*(dble(n)/a)*besjn(n,eta*a)
f_n1 = psi_0*epsilon_1*((0.d0,-1.d0)**n)*(eta/2.d0)*(besjn(n-1,eta*a)-besjn(n+1,eta*a))
m11 = (gamma/2.d0)*(besselh(n-1,2,gamma*a)-besselh(n+1,2,gamma*a))
m12 = -(dble(n)/a)*(besselh(int(n),2,eta*a))
m21 = (dble(n)/a)*besselh(int(n),2,gamma*a)
m22 = -(eta/2.d0)*(besselh(n-1,2,eta*a)-besselh(n+1,2,eta*a))
ABn(1) = (1.d0/(m11*m22 - m12*m21))*(m22*f_n0-m12*f_n1)
ABn(2) = (1.d0/(m11*m22 - m12*m21))*(-m21*f_n0+m11*f_n1)
q = q+(-psi_0*epsilon_1*((0.d0,-1.d0)**n)*(dble(n)/r)*besjn(n,eta*r)&
+ ABn(1)*(gamma/2.d0)*(besselh(n-1,2,gamma*r)&
-besselh(n+1,2,gamma*r)) &
- ABn(2)*(dble(n)/r)*besselh(int(n),2,eta*r))*sin(dble(n)*theta)
v = v + (-psi_0*epsilon_1*((0.d0,-1.d0)**n)*(eta/2.d0)*( besjn(n-1,eta*r) &
-besjn(n+1,eta*r)) &
+ ABn(1)*(dble(n)/r)*besselh(int(n),2,gamma*r) &
- ABn(2)*(eta/2.d0)*(besselh(n-1,2,eta*r)&
-besselh(n+1,2,eta*r)))*cos(dble(n)*theta)
end do
!$OMP PARALLEL DO PRIVATE(f_n0,f_n1,a_n0,a_n1,b_n0,b_n1,epsilon_n,m11,m12,m21,m22,cn1,cn2,ABn) REDUCTION(+:q,v)
do n = 2,ns
f_n0 = psi_0*epsilon_1*((0.d0,-1.d0)**n)*(dble(n)/a)*besjn(n,eta*a)
f_n1 = psi_0*epsilon_1*((0.d0,-1.d0)**n)*(eta/2.d0)*(besjn(n-1,eta*a)-besjn(n+1,eta*a))
m11 = (gamma/2.d0)*(besselh(n-1,2,gamma*a)-besselh(n+1,2,gamma*a))
m12 = -(dble(n)/a)*(besselh(int(n),2,eta*a))
m21 = (dble(n)/a)*besselh(int(n),2,gamma*a)
m22 = -(eta/2.d0)*(besselh(n-1,2,eta*a)-besselh(n+1,2,eta*a))
ABn(1) = (1.d0/(m11*m22 - m12*m21))*(m22*f_n0-m12*f_n1)
ABn(2) = (1.d0/(m11*m22 - m12*m21))*(-m21*f_n0+m11*f_n1)
q = q+(-psi_0*epsilon_1*((0.d0,-1.d0)**n)*(dble(n)/r)*besjn(n,eta*r)&
+ ABn(1)*(gamma/2.d0)*(besselh(n-1,2,gamma*r)&
-besselh(n+1,2,gamma*r)) &
- ABn(2)*(dble(n)/r)*besselh(int(n),2,eta*r))*sin(dble(n)*theta)
v = v + (-psi_0*epsilon_1*((0.d0,-1.d0)**n)*(eta/2.d0)*( besjn(n-1,eta*r) &
-besjn(n+1,eta*r)) &
+ ABn(1)*(dble(n)/r)*besselh(int(n),2,gamma*r) &
- ABn(2)*(eta/2.d0)*(besselh(n-1,2,eta*r)&
-besselh(n+1,2,eta*r)))*cos(dble(n)*theta)
end do
!$OMP END PARALLEL DO
! disp('DONE COMPUTING COEFICIENTS')
du = dreal(exp(omega*(0.d0,1.d0)*t)*(cos(theta)*q-sin(theta)*v))
dv = dreal(exp(omega*(0.d0,1.d0)*t)*(sin(theta)*q+cos(theta)*v))
!dut = dreal(omega*(0.d0,1.d0)*exp(omega*(0.d0,1.d0)*t)*(cos(theta)*q-sin(theta)*v))
!dvt = dreal(omega*(0.d0,1.d0)*exp(omega*(0.d0,1.d0)*t)*(sin(theta)*q+cos(theta)*v))
! for GetDP: return imaginary part in dut, dvt
dut = dimag(exp(omega*(0.d0,1.d0)*t)*(cos(theta)*q-sin(theta)*v))
dvt = dimag(exp(omega*(0.d0,1.d0)*t)*(sin(theta)*q+cos(theta)*v))
end subroutine cylindrical_walls
|
