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 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)
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)
T_R = 0.99 * pow(-2.0 * mass * pow(LX, 2.0) / (charge * deltaV_R), 0.5)
steps = 100
DT_NR = T_NR / steps
DT_R = T_R / steps
# Solve for potential
pot1D_NR = esSolve.laplace1D(NX,
DX,
V0,
VN_NR,
"gaussSeidel",
relTol=0.0,
absTol=1.0e-3 * (deltaV_NR),
useCython=False)
pot1D_R = esSolve.laplace1D(NX,
DX,
V0,
VN_R,
"gaussSeidel",
relTol=0.0,
absTol=1.0e-3 * (deltaV_R),
useCython=False)
# Compute E = - grad V on grid
electricFieldOnGrid_NR = esSolve.potentialToElectricField(pot1D_NR, [DX])
electricFieldOnGrid_R = esSolve.potentialToElectricField(pot1D_R, [DX])
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()
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) T_R = 0.99*pow(-2.0*mass*pow(LX,2.0)/(charge*deltaV_R),0.5) steps = 100 DT_NR = T_NR/steps DT_R = T_R/steps # Solve for potential pot1D_NR = esSolve.laplace1D(NX,DX,V0,VN_NR,"gaussSeidel",relTol=0.0,absTol=1.0e-3*(deltaV_NR),useCython=False) pot1D_R = esSolve.laplace1D(NX,DX,V0,VN_R,"gaussSeidel",relTol=0.0,absTol=1.0e-3*(deltaV_R),useCython=False) # Compute E = - grad V on grid electricFieldOnGrid_NR = esSolve.potentialToElectricField(pot1D_NR,[DX]) electricFieldOnGrid_R = esSolve.potentialToElectricField(pot1D_R,[DX]) positions_NR = [electron_NR.position[0]] velocities_NR = [electron_NR.velocity[0]] positions_R_Rpush = [electron_R_Rpush.position[0]] velocities_R_Rpush = [electron_R_Rpush.velocity[0]] positions_R_NRpush = [electron_R_NRpush.position[0]] velocities_R_NRpush = [electron_R_NRpush.velocity[0]] for step in xrange(steps+1): # Compute E at particle position
