def test_constant():
k=2.718281828459045
#define functions that give costant solution
I=lambda x,y: k
q=lambda x,y: 34 + x
#define some variables
Lx = 10
Ly = 4
T = 3
C = 1.
dt= 0.1
#get constant solution
Nx = int(round(Lx/dt))
Ny = int(round(Ly/dt))
ue =zeros((Nx+1,Ny+1)) +k
u,x,y,t,error=solver(I,None,None,q,0,Lx,Ly,dt,T,C,1,mode='vector')
print 'Test constant solution. Exercise 3.1'
print '||abs(u-ue)||: ', amax(abs(u-ue))
print
assert amax(abs(u-ue))<10**(-16)
def constructed_bugs():
k=2.718281828459045
I=lambda x,y: k
q=lambda x,y: x+y
Lx = 10
Ly = 5
T = 3
C = 1.
dt= 0.5
Nx = int(round(Lx/dt))
Ny = int(round(Ly/dt))
ue =zeros((Nx+1,Ny+1)) +k
u1,x,y,t=solver(I,None,None,q,0,Lx,Ly,dt,T,C,1,mode='scalar',bug='bug1')
u2,x,y,t=solver(I,None,None,q,0,Lx,Ly,dt,T,C,1,mode='scalar',bug='bug2')
u3,x,y,t=solver(I,None,None,q,0,Lx,Ly,dt,T,C,1,mode='scalar',bug='bug3')
u4,x,y,t=solver(I,None,None,q,0,Lx,Ly,dt,T,C,1,mode='scalar',bug='bug4')
u5,x,y,t=solver(I,None,None,q,0,Lx,Ly,dt,T,C,1,mode='scalar',bug='bug5')
print "Test bugs:"
print "bug1 gives error: ",amax(abs(u1-ue))
print "bug2 gives error: ",amax(abs(u2-ue))
print "bug3 gives error: ",amax(abs(u3-ue))
print "bug4 gives error: ",amax(abs(u4-ue))
print "bug5 gives error: ",amax(abs(u5-ue))
print
def test_constant():
k = 2.718281828459045
#define functions that give costant solution
I = lambda x, y: k
q = lambda x, y: 34 + x
#define some variables
Lx = 10
Ly = 4
T = 3
C = 1.
dt = 0.1
#get constant solution
Nx = int(round(Lx / dt))
Ny = int(round(Ly / dt))
ue = zeros((Nx + 1, Ny + 1)) + k
u, x, y, t, error = solver(I,
None,
None,
q,
0,
Lx,
Ly,
dt,
T,
C,
1,
mode='vector')
print 'Test constant solution. Exercise 3.1'
print '||abs(u-ue)||: ', amax(abs(u - ue))
print
assert amax(abs(u - ue)) < 10**(-16)
def test_plug():
#define function that give
q=lambda x,y: 1
#define some variables
Lx = 10
Ly = 3
T = 1
C = 1
dt= 0.1
#get constant solution
Nx = int(round(Lx/dt))
Ny = int(round(Ly/dt))
ue =zeros((Nx+1,Ny+1))
#define initial function
def I(x,y):
if abs(x-Lx/2.)<0.5:
return 2.1
else:
return 0
#solve numerically
u,x,y,t,err = solver(I,None,None,q,0,Lx,Ly,dt,T,C,1,mode='scalar')
#find exact solution at time T
x1 = x+T
x2 = x-T
for i in range(Nx+1):
for j in range(Ny+1):
ue[i,j]=0.5*(I(x1[i],0) + I(x2[i],0))
#calculate error at time t=T
e1 = amax(abs(u-ue))
#Do the exact same for plug wave in y direction:
def I(x,y):
if abs(y-Ly/2.)<0.5:
return 2.1
else:
return 0
#Numerical solution
u,x,y,t,err = solver(I,None,None,q,0,Lx,Ly,dt,T,C,1,mode='scalar')
#find exact solution at time T
y1 = x+T
y2 = x-T
for i in range(Nx+1):
for j in range(Ny+1):
ue[i,j]=0.5*(I(0,y1[j]) + I(0,y2[j]))
#calculate error at time t=T
e2 = amax(abs(u-ue))
print 'Plug error in x ||u(x,y,T)-ue(x,y,T)||: ',e1
print 'Plug error in y ||u(x,y,T)-ue(x,y,T)||: ',e2
print
assert e1<10**(-16) and e2<10**(-16)
def test_plug():
#define function that give
q = lambda x, y: 1
#define some variables
Lx = 10
Ly = 3
T = 1
C = 1
dt = 0.1
#get constant solution
Nx = int(round(Lx / dt))
Ny = int(round(Ly / dt))
ue = zeros((Nx + 1, Ny + 1))
#define initial function
def I(x, y):
if abs(x - Lx / 2.) < 0.5:
return 2.1
else:
return 0
#solve numerically
u, x, y, t, err = solver(I,
None,
None,
q,
0,
Lx,
Ly,
dt,
T,
C,
1,
mode='scalar')
#find exact solution at time T
x1 = x + T
x2 = x - T
for i in range(Nx + 1):
for j in range(Ny + 1):
ue[i, j] = 0.5 * (I(x1[i], 0) + I(x2[i], 0))
#calculate error at time t=T
e1 = amax(abs(u - ue))
#Do the exact same for plug wave in y direction:
def I(x, y):
if abs(y - Ly / 2.) < 0.5:
return 2.1
else:
return 0
#Numerical solution
u, x, y, t, err = solver(I,
None,
None,
q,
0,
Lx,
Ly,
dt,
T,
C,
1,
mode='scalar')
#find exact solution at time T
y1 = x + T
y2 = x - T
for i in range(Nx + 1):
for j in range(Ny + 1):
ue[i, j] = 0.5 * (I(0, y1[j]) + I(0, y2[j]))
#calculate error at time t=T
e2 = amax(abs(u - ue))
print 'Plug error in x ||u(x,y,T)-ue(x,y,T)||: ', e1
print 'Plug error in y ||u(x,y,T)-ue(x,y,T)||: ', e2
print
assert e1 < 10**(-16) and e2 < 10**(-16)
def constructed_bugs():
k = 2.718281828459045
I = lambda x, y: k
q = lambda x, y: x + y
Lx = 10
Ly = 5
T = 3
C = 1.
dt = 0.5
Nx = int(round(Lx / dt))
Ny = int(round(Ly / dt))
ue = zeros((Nx + 1, Ny + 1)) + k
u1, x, y, t = solver(I,
None,
None,
q,
0,
Lx,
Ly,
dt,
T,
C,
1,
mode='scalar',
bug='bug1')
u2, x, y, t = solver(I,
None,
None,
q,
0,
Lx,
Ly,
dt,
T,
C,
1,
mode='scalar',
bug='bug2')
u3, x, y, t = solver(I,
None,
None,
q,
0,
Lx,
Ly,
dt,
T,
C,
1,
mode='scalar',
bug='bug3')
u4, x, y, t = solver(I,
None,
None,
q,
0,
Lx,
Ly,
dt,
T,
C,
1,
mode='scalar',
bug='bug4')
u5, x, y, t = solver(I,
None,
None,
q,
0,
Lx,
Ly,
dt,
T,
C,
1,
mode='scalar',
bug='bug5')
print "Test bugs:"
print "bug1 gives error: ", amax(abs(u1 - ue))
print "bug2 gives error: ", amax(abs(u2 - ue))
print "bug3 gives error: ", amax(abs(u3 - ue))
print "bug4 gives error: ", amax(abs(u4 - ue))
print "bug5 gives error: ", amax(abs(u5 - ue))
print
