def __init__(self, options=Options(), **kw):
# Define the default options
default_options = Options(
name="Jemmy's Example 1",
numSegments=3,
bifurcationPoints=1,
domainE=Domains(space=[0, 1], time=[0, 1]),
domainLw=Domains(space=[1, 2], time=[0, 1]),
domainUp=Domains(space=[1, 3], time=[0, 1]),
bcDomainE=BoundaryConditions(SealedEnd(), SealedEnd()),
bcDomainLw=BoundaryConditions(SealedEnd(), SealedEnd()),
bcDomainUp=BoundaryConditions(SealedEnd(), SealedEnd()),
solutionE=[],
solutionLw=[],
solutionUp=[],
description="This is the solution for the \
following problem:\
Problem being solved is: [0,3]X[0,1]\
d2u/dx2 = du\dt + u \
BC: du/dx(0,t) = du/dx(2,t) = du/dx(3,t) = 0 \
Initial Conditions:\
u(x,0) = cos(pi*x)\
Solution: u = (e^(-(1 + pi^2)*t)*cos(pi*x)"
)
# Merge the default options and the user generated options
whole_options = default_options << options
super(JemmyEx1, self).__init__(whole_options, **kw)
def __init__(self, options=Options(), **kw):
# Define the default options
default_options = Options(
name="Jemmy's Example 2",
numSegments=3,
bifurcationPoints=1,
segmentsDomain=[
Domains(space=[0, pi / 2], time=[0, 1]),
Domains(space=[pi / 2, pi], time=[0, 1]),
Domains(space=[pi / 2, 3 * (pi / 2)], time=[0, 1])
],
boundaryConditions=[
BoundaryConditions(SealedEnd(), SealedEnd()),
BoundaryConditions(SealedEnd(), SealedEnd()),
BoundaryConditions(SealedEnd(), SealedEnd())
],
description="This is the solution for the \
following problem:\
Problem being solved is: [0,3*pi/2]X[0,1]\
d2u/dx2 = du\dt - 2*u \
BC: du/dx(0,t) = -e^t, du/dx(pi,t) = e^t , du/dx(3*pi/2,t) = 0 \
Initial Conditions:\
u(x,0) = -sin(x)\
Solution: u = (e^-t)*sin(x)")
# Merge the default options and the user generated options
whole_options = default_options << options
super(JemmyEx2, self).__init__(whole_options, **kw)
from Plotting.Simulation import Simulation
from Plotting.IDataPlot import IDataPlot
from numpy import arange
########################################
### Simulation Variable ###
########################################
simDomain = Domains(space=[0, 1], time=[0, 10])
simSteps = Steps(space=0.1, time=0.1)
diffusionValue = 1
reactionValue = 1
kValue = 1
boundaryConditions = BoundaryConditions(KilledEnd(), KilledEnd())
sElements = arange(0, simDomain.space[-1] + simSteps.space,\
simSteps.space)
########################################
### Setting the Simulation ###
########################################
analytical = ValidationWithF(domain=simDomain,steps=simSteps,\
BCs=boundaryConditions,\
kValue = kValue)
font = analytical.createFont()
### Mesh Prep Work ###
########################################
k = 1
coeff_t = 1/k
coeff_dx2 = -1
coeff_v = 1
def f(x,t):
return 4*(math.pi**2)*math.exp(-t)*math.sin(2*math.pi*x)
simModel = CableModel(iApproximation=GalerkinApproximation(),\
font=f,coeff_dx2 = coeff_dx2,coeff_v = coeff_v,
coeff_t=coeff_t,)
segment0 = ISegment('Axon0',BoundaryConditions(KilledEnd(),KilledEnd()),\
simDomain,simSteps,simModel)
#geoMesh = ISegment()
#geoMesh.insert_segments(segment0)
########################################
### Setting the Simulation ###
########################################
#ode_approximation = BackwardEuler(delta_t=delta_t,coeff_t=coeff_t)
#geoMesh.create_region(cable_model)
from NeuroCore.Neuron.Segment.Base import ISegment
from Plotting.IDataPlot import IDataPlot
from Plotting.IDataPlots import IDataPlots
from Plotting.Simulation import Simulation
########################################
### Simulation Variable ###
########################################
simDomain = Domains(space=[0, 12])
simSteps = Steps(space=0.01)
diffusionValue = 100
reactionValue = 10
boundaryConditions = BoundaryConditions(SealedEnd(), SealedEnd())
sElements = numpy.arange(0, simDomain.space[-1] + simSteps.space, \
simSteps.space)
########################################
### Setting the Simulation ###
########################################
analytical = ValidationWithF(domain=simDomain, steps=simSteps, \
BCs=boundaryConditions, \
diffusionValue=diffusionValue, \
reactionValue=reactionValue)
font = analytical.createFont()
simDomain = Domains(space=[0, 1])
simSteps = Steps(space=0.1)
########################################
### Setting the Simulation ###
########################################
def f(x):
return 0
diffusionValue = -0.01
reactionValue = 1
boundaryConditions = BoundaryConditions(Neumann(bcValue=1), Neumann(bcValue=1))
simModel = GeneralModel(iApproximation=GalerkinApproximation(numIntegration=Trapezoidal()),\
font=f,coeff_dx2 = diffusionValue,coeff_v = reactionValue)
segment0 = ISegment('Axon0', boundaryConditions, simDomain, simSteps, simModel)
########################################
### Running the Simulation ###
########################################
sElements = numpy.arange(0, simDomain.space[-1] + simSteps.space,\
simSteps.space)
analytical = analyCableModel(domain=simDomain,steps=simSteps,\
BCs=boundaryConditions,\