def test2D(potential, field):
potAccept2D = np.zeros((NX_2D + 1, NY_2D + 1))
fieldAccept2D = np.zeros((NX_2D + 1, NY_2D + 1, 2))
for i, j in np.ndindex(potAccept2D.shape):
potAccept2D[i, j] = potential(X0_2D + DX_2D * i, Y0_2D + DY_2D * j)
fieldAccept2D[i, j] = field(X0_2D + DX_2D * i, Y0_2D + DY_2D * j)
# Boundary conditions
V0x_2D = dirBC(potAccept2D[0, :])
VNx_2D = dirBC(potAccept2D[NX_2D, :])
V0y_2D = dirBC(potAccept2D[:, 0])
VNy_2D = dirBC(potAccept2D[:, NY_2D])
E0x_2D = neuBC(fieldAccept2D[0, :, 0])
ENx_2D = neuBC(fieldAccept2D[NX_2D, :, 0])
E0y_2D = neuBC(fieldAccept2D[:, 0, 1])
ENy_2D = neuBC(fieldAccept2D[:, NY_2D, 1])
for BC0x_2D in [V0x_2D, E0x_2D]:
for BCNx_2D in [VNx_2D, ENx_2D]:
for BC0y_2D in [V0y_2D, E0y_2D]:
for BCNy_2D in [VNy_2D]: #,ENy_2D]:
for testType in ["direct", "jacobi", "gaussSeidel"]:
for cythonType in [True, False]:
if testType == "direct":
potCalculated2D = esSolve.laplace2D(NX_2D,DX_2D,BC0x_2D,BCNx_2D, \
NY_2D,DY_2D,BC0y_2D,BCNy_2D, \
testType,cythonType)
else:
potCalculated2D = esSolve.laplace2D(NX_2D,DX_2D,BC0x_2D,BCNx_2D, \
NY_2D,DY_2D,BC0y_2D,BCNy_2D, \
testType,relTol,absTol,cythonType)
test(potCalculated2D, potAccept2D)
def test1D(potential, field):
potAccept1D = np.zeros(NX_1D + 1)
fieldAccept1D = np.zeros((NX_1D + 1, 1))
for i in range(NX_1D + 1):
potAccept1D[i] = potential(X0_1D + DX_1D * i)
fieldAccept1D[i] = field(X0_1D + DX_1D * i)
# Boundary conditions
V0_1D = dirBC(potAccept1D[0])
VN_1D = dirBC(potAccept1D[NX_1D])
E0_1D = neuBC(fieldAccept1D[0])
EN_1D = neuBC(fieldAccept1D[NX_1D])
for BC0_1D in [V0_1D, E0_1D]:
for BCN_1D in [VN_1D]: #,EN_1D]:
for testType in ["direct", "jacobi", "gaussSeidel"]:
for cythonType in [True, False]:
if testType == "direct":
potCalculated1D = esSolve.laplace1D(NX_1D,DX_1D,BC0_1D,BCN_1D, \
testType,cythonType)
else:
potCalculated1D = esSolve.laplace1D(NX_1D,DX_1D,BC0_1D,BCN_1D, \
testType,relTol,absTol,cythonType)
test(potCalculated1D, potAccept1D)
def test2D(potential,field):
potAccept2D = np.zeros((NX_2D+1,NY_2D+1))
fieldAccept2D = np.zeros((NX_2D+1,NY_2D+1,2))
for i,j in np.ndindex(potAccept2D.shape):
potAccept2D[i,j] = potential(X0_2D+DX_2D*i,Y0_2D+DY_2D*j)
fieldAccept2D[i,j] = field( X0_2D+DX_2D*i,Y0_2D+DY_2D*j)
# Boundary conditions
V0x_2D = dirBC(potAccept2D[0, : ])
VNx_2D = dirBC(potAccept2D[NX_2D,: ])
V0y_2D = dirBC(potAccept2D[:, 0 ])
VNy_2D = dirBC(potAccept2D[:, NY_2D])
E0x_2D = neuBC(fieldAccept2D[0, :, 0])
ENx_2D = neuBC(fieldAccept2D[NX_2D,:, 0])
E0y_2D = neuBC(fieldAccept2D[:, 0, 1])
ENy_2D = neuBC(fieldAccept2D[:, NY_2D,1])
for BC0x_2D in [V0x_2D,E0x_2D]:
for BCNx_2D in [VNx_2D,ENx_2D]:
for BC0y_2D in [V0y_2D,E0y_2D]:
for BCNy_2D in [VNy_2D]:#,ENy_2D]:
for testType in ["direct","jacobi","gaussSeidel"]:
for cythonType in [True,False]:
if testType == "direct":
potCalculated2D = esSolve.laplace2D(NX_2D,DX_2D,BC0x_2D,BCNx_2D, \
NY_2D,DY_2D,BC0y_2D,BCNy_2D, \
testType,cythonType)
else:
potCalculated2D = esSolve.laplace2D(NX_2D,DX_2D,BC0x_2D,BCNx_2D, \
NY_2D,DY_2D,BC0y_2D,BCNy_2D, \
testType,relTol,absTol,cythonType)
test(potCalculated2D,potAccept2D)
def test1D(potential,field):
potAccept1D = np.zeros(NX_1D+1)
fieldAccept1D = np.zeros((NX_1D+1,1))
for i in range(NX_1D+1):
potAccept1D[i] = potential(X0_1D+DX_1D*i)
fieldAccept1D[i] = field( X0_1D+DX_1D*i)
# Boundary conditions
V0_1D = dirBC(potAccept1D[0 ])
VN_1D = dirBC(potAccept1D[NX_1D])
E0_1D = neuBC(fieldAccept1D[0 ])
EN_1D = neuBC(fieldAccept1D[NX_1D])
for BC0_1D in [V0_1D,E0_1D]:
for BCN_1D in [VN_1D]:#,EN_1D]:
for testType in ["direct","jacobi","gaussSeidel"]:
for cythonType in [True,False]:
if testType == "direct":
potCalculated1D = esSolve.laplace1D(NX_1D,DX_1D,BC0_1D,BCN_1D, \
testType,cythonType)
else:
potCalculated1D = esSolve.laplace1D(NX_1D,DX_1D,BC0_1D,BCN_1D, \
testType,relTol,absTol,cythonType)
test(potCalculated1D,potAccept1D)
def test3D(potential, field):
potAccept3D = np.zeros((NX_3D + 1, NY_3D + 1, NZ_3D + 1))
fieldAccept3D = np.zeros((NX_3D + 1, NY_3D + 1, NZ_3D + 1, 3))
for i, j, k in np.ndindex(potAccept3D.shape):
# consider using np.fromfunction here
potAccept3D[i, j,
k] = potential(X0_3D + DX_3D * i, Y0_3D + DY_3D * j,
Z0_3D + DZ_3D * k)
fieldAccept3D[i, j,
k] = field(X0_3D + DX_3D * i, Y0_3D + DY_3D * j,
Z0_3D + DZ_3D * k)
# Boundary conditions
V0x_3D = dirBC(potAccept3D[0, :, :])
VNx_3D = dirBC(potAccept3D[NX_3D, :, :])
V0y_3D = dirBC(potAccept3D[:, 0, :])
VNy_3D = dirBC(potAccept3D[:, NY_3D, :])
V0z_3D = dirBC(potAccept3D[:, :, 0])
VNz_3D = dirBC(potAccept3D[:, :, NZ_3D])
E0x_3D = neuBC(fieldAccept3D[0, :, :, 0])
ENx_3D = neuBC(fieldAccept3D[NX_3D, :, :, 0])
E0y_3D = neuBC(fieldAccept3D[:, 0, :, 1])
ENy_3D = neuBC(fieldAccept3D[:, NY_3D, :, 1])
E0z_3D = neuBC(fieldAccept3D[:, :, 0, 2])
ENz_3D = neuBC(fieldAccept3D[:, :, NZ_3D, 2])
for BC0x_3D in [V0x_3D, E0x_3D]:
for BCNx_3D in [VNx_3D, ENx_3D]:
for BC0y_3D in [V0y_3D, E0y_3D]:
for BCNy_3D in [VNy_3D, ENy_3D]:
for BC0z_3D in [V0z_3D, E0z_3D]:
for BCNz_3D in [VNz_3D]: #,ENz_3D]:
for testType in [
"direct", "jacobi", "gaussSeidel"
]:
for cythonType in [True, False]:
if testType == "direct":
potCalculated3D = esSolve.laplace3D(NX_3D,DX_3D,BC0x_3D,BCNx_3D, \
NY_3D,DY_3D,BC0y_3D,BCNy_3D, \
NZ_3D,DZ_3D,BC0z_3D,BCNz_3D, \
testType,cythonType)
else:
potCalculated3D = esSolve.laplace3D(NX_3D,DX_3D,BC0x_3D,BCNx_3D, \
NY_3D,DY_3D,BC0y_3D,BCNy_3D, \
NZ_3D,DZ_3D,BC0z_3D,BCNz_3D, \
testType,relTol,absTol,cythonType)
test(potCalculated3D, potAccept3D)
def test3D(potential,field):
potAccept3D = np.zeros((NX_3D+1,NY_3D+1,NZ_3D+1))
fieldAccept3D = np.zeros((NX_3D+1,NY_3D+1,NZ_3D+1,3))
for i,j,k in np.ndindex(potAccept3D.shape):
# consider using np.fromfunction here
potAccept3D[i,j,k] = potential(X0_3D+DX_3D*i,Y0_3D+DY_3D*j,Z0_3D+DZ_3D*k)
fieldAccept3D[i,j,k] = field( X0_3D+DX_3D*i,Y0_3D+DY_3D*j,Z0_3D+DZ_3D*k)
# Boundary conditions
V0x_3D = dirBC(potAccept3D[0, :, : ])
VNx_3D = dirBC(potAccept3D[NX_3D,:, : ])
V0y_3D = dirBC(potAccept3D[:, 0, : ])
VNy_3D = dirBC(potAccept3D[:, NY_3D,: ])
V0z_3D = dirBC(potAccept3D[:, :, 0 ])
VNz_3D = dirBC(potAccept3D[:, :, NZ_3D])
E0x_3D = neuBC(fieldAccept3D[0, :, :, 0])
ENx_3D = neuBC(fieldAccept3D[NX_3D,:, :, 0])
E0y_3D = neuBC(fieldAccept3D[:, 0, :, 1])
ENy_3D = neuBC(fieldAccept3D[:, NY_3D,:, 1])
E0z_3D = neuBC(fieldAccept3D[:, :, 0, 2])
ENz_3D = neuBC(fieldAccept3D[:, :, NZ_3D,2])
for BC0x_3D in [V0x_3D,E0x_3D]:
for BCNx_3D in [VNx_3D,ENx_3D]:
for BC0y_3D in [V0y_3D,E0y_3D]:
for BCNy_3D in [VNy_3D,ENy_3D]:
for BC0z_3D in [V0z_3D,E0z_3D]:
for BCNz_3D in [VNz_3D]:#,ENz_3D]:
for testType in ["direct","jacobi","gaussSeidel"]:
for cythonType in [True,False]:
if testType == "direct":
potCalculated3D = esSolve.laplace3D(NX_3D,DX_3D,BC0x_3D,BCNx_3D, \
NY_3D,DY_3D,BC0y_3D,BCNy_3D, \
NZ_3D,DZ_3D,BC0z_3D,BCNz_3D, \
testType,cythonType)
else:
potCalculated3D = esSolve.laplace3D(NX_3D,DX_3D,BC0x_3D,BCNx_3D, \
NY_3D,DY_3D,BC0y_3D,BCNy_3D, \
NZ_3D,DZ_3D,BC0z_3D,BCNz_3D, \
testType,relTol,absTol,cythonType)
test(potCalculated3D,potAccept3D)
LX = 1.25
LY = 2.3
DX = LX / NX
DY = LY / NY
X0 = 1.0
Y0 = 2.0
amplitude = 2.0
def nonGroundedWall(Yindex):
return amplitude * np.sin(np.pi * Yindex / NY)
# Boundary conditions
V0x = dirBC(np.zeros((NY + 1)))
VNx = dirBC(np.fromfunction(nonGroundedWall, (NY + 1, )))
V0y = dirBC(np.zeros((NX + 1)))
VNy = dirBC(np.zeros((NX + 1)))
start = time.clock()
potential_NoCython = esSolve.laplace2D(NX,
DX,
V0x,
VNx,
NY,
DY,
V0y,
VNy,
"gaussSeidel",
import particleUtils from particle import particle import scipy.constants from dirichlet import dirichlet as dirBC # Grid NX = 20 LX = 1.2 X0 = 1.5 DX = LX / NX # Boundary conditions deltaV_NR = 1.0e-3 # 1.0 mV deltaV_R = 1.0e6 # 1.0 MV V_min = 1.0 V0 = dirBC(V_min) VN_NR = dirBC(V_min + deltaV_NR) VN_R = dirBC(V_min + deltaV_R) # Particle mass = scipy.constants.electron_mass charge = -scipy.constants.elementary_charge X0_particle = X0 V0_particle = 0.0 electron_NR = particle(mass, charge, [X0_particle], [V0_particle]) electron_R_Rpush = particle(mass, charge, [X0_particle], [V0_particle]) electron_R_NRpush = particle(mass, charge, [X0_particle], [V0_particle]) # Time steps T_NR = 0.99 * pow(-2.0 * mass * pow(LX, 2.0) / (charge * deltaV_NR), 0.5)
NX = 25
NY = 30
LX = 1.25
LY = 2.3
DX = LX / NX
DY = LY / NY
X0 = 1.0
Y0 = 2.0
amplitude = 2.0
def nonGroundedWall(Yindex):
return amplitude * np.sin(np.pi * Yindex / NY)
# Boundary conditions
V0x = dirBC(np.zeros((NY+1)))
VNx = dirBC(np.fromfunction(nonGroundedWall, (NY+1,)))
V0y = dirBC(np.zeros((NX+1)))
VNy = dirBC(np.zeros((NX+1)))
start = time.clock()
potential_1 = esSolve.laplace2D(NX,DX,V0x,VNx,NY,DY,V0y,VNy,"gaussSeidel",relTol=0.0,absTol=1.0)
potential_2 = esSolve.laplace2D(NX,DX,V0x,VNx,NY,DY,V0y,VNy,"gaussSeidel",relTol=0.0,absTol=0.5)
potential_3 = esSolve.laplace2D(NX,DX,V0x,VNx,NY,DY,V0y,VNy,"gaussSeidel",relTol=0.0,absTol=1.0e-3)
end = time.clock()
print("That took",round(end-start,1),"seconds.")
import os import sys sys.path.append(os.path.dirname(os.path.realpath(__file__)) + '/../solvers') import matplotlib.pyplot as plt import esSolve from dirichlet import dirichlet as dirBC NX = 100 LX = 1.2 DX = LX / NX V0 = dirBC(1.0) VN = dirBC(2.0) X0 = 1.5 pot1D = esSolve.laplace1D(NX,DX,V0,VN,"gaussSeidel",relTol=0.0,absTol=1.0e-3,useCython=False) # could use X0 here to plot versus position instead of index plt.plot(pot1D) plt.show()
import particleUtils from particle import particle import scipy.constants from dirichlet import dirichlet as dirBC # Grid NX = 20 LX = 1.2 X0 = 1.5 DX = LX / NX # Boundary conditions deltaV_NR = 1.0e-3 # 1.0 mV deltaV_R = 1.0e6 # 1.0 MV V_min = 1.0 V0 = dirBC(V_min) VN_NR = dirBC(V_min + deltaV_NR) VN_R = dirBC(V_min + deltaV_R) # Particle mass = scipy.constants.electron_mass charge = -scipy.constants.elementary_charge X0_particle = X0 V0_particle = 0.0 electron_NR = particle(mass,charge,[X0_particle],[V0_particle]) electron_R_Rpush = particle(mass,charge,[X0_particle],[V0_particle]) electron_R_NRpush = particle(mass,charge,[X0_particle],[V0_particle]) # Time steps T_NR = 0.99*pow(-2.0*mass*pow(LX,2.0)/(charge*deltaV_NR),0.5)
