def solveFiniteVolume(mesh,
a=1.0,
f=0.0,
fn=0.0,
vel=0.0,
u0=None,
times=None,
uL=None,
relax=1.0,
ws=None,
scheme='CDS',
**kwargs):
"""
"""
# The Workspace is to hold temporary data or preserve matrix rebuild
swatch = pg.core.Stopwatch(True)
sparse = True
workspace = WorkSpace()
if ws:
workspace = ws
a = solver.parseArgToArray(a, [mesh.cellCount(), mesh.boundaryCount()])
f = solver.parseArgToArray(f, mesh.cellCount())
fn = solver.parseArgToArray(fn, mesh.cellCount())
boundsDirichlet = None
boundsNeumann = None
if not hasattr(workspace, 'S'):
if 'uBoundary' in kwargs:
boundsDirichlet = pg.solver.parseArgToBoundaries(
kwargs['uBoundary'], mesh)
if 'duBoundary' in kwargs:
boundsNeumann = pg.solver.parseArgToBoundaries(
kwargs['duBoundary'], mesh)
workspace.S, workspace.rhsBCScales = diffusionConvectionKernel(
mesh=mesh,
a=a,
f=f,
uBoundaries=boundsDirichlet,
duBoundaries=boundsNeumann,
u0=u0,
fn=fn,
vel=vel,
scheme=scheme,
sparse=sparse,
userData=kwargs.pop('userData', None))
print('FVM kernel 1:', swatch.duration(True))
dof = len(workspace.rhsBCScales)
# workspace.uDir = np.zeros(dof)
# if u0 is not None:
# workspace.uDir = np.array(u0)
#
# if len(boundsDirichlet):
# for boundary, val in boundsDirichlet.items():
# workspace.uDir[boundary.leftCell().id()] = val
workspace.ap = np.zeros(dof)
# for nonlinears
if uL is not None:
for i in range(dof):
val = 0.0
if sparse:
val = workspace.S.getVal(i, i) / relax
workspace.S.setVal(i, i, val)
# workspace.S[i, i] /= relax
# workspace.ap[i] = workspace.S[i, i]
else:
val = workspace.S[i, i] / relax
workspace.S[i, i] = val
workspace.ap[i] = val
print('FVM kernel 2:', swatch.duration(True))
# endif: not hasattr(workspace, 'S'):
workspace.rhs = np.zeros(len(workspace.rhsBCScales))
workspace.rhs[0:mesh.cellCount()] = f # * mesh.cellSizes()
# if len(workspace.uDir):
workspace.rhs += workspace.rhsBCScales
# for nonlinear: relax progress with scaled last result
if uL is not None:
workspace.rhs += (1. - relax) * workspace.ap * uL
# print('FVM: Prep:', swatch.duration(True))
if not hasattr(times, '__len__'):
if sparse and not hasattr(workspace, 'solver'):
Sm = pg.matrix.SparseMatrix(workspace.S)
# hold Sm until we have reference counting,
# loosing Sm here will kill LinSolver later
workspace.Sm = Sm
workspace.solver = pg.core.LinSolver(Sm, True)
u = None
if sparse:
u = workspace.solver.solve(workspace.rhs)
else:
u = np.linalg.solve(workspace.S, workspace.rhs)
print('FVM solve:', swatch.duration(True))
return u[0:mesh.cellCount():1]
else:
theta = kwargs.pop('theta', 0.5)
verbose = kwargs.pop('verbose', False)
if sparse:
I = solver.identity(len(workspace.rhs))
else:
I = np.diag(np.ones(len(workspace.rhs)))
print("solve cN")
return solver.crankNicolson(times,
theta,
workspace.S,
I,
f=workspace.rhs,
u0=u0,
verbose=verbose)
def diffusionConvectionKernel(
mesh,
a=None,
b=0.0,
uB=None,
duB=None,
vel=0,
# u0=0,
fn=None,
scheme='CDS',
sparse=False,
time=0.0,
userData=None):
"""
Generate system matrix for diffusion and convection in a velocity field.
Particle concentration u inside a velocity field.
Peclet Number - ratio between convection/diffusion = F/D
F = velocity flow trough volume boundary,
D = diffusion coefficient
Parameters
----------
mesh: :gimliapi:`GIMLI::Mesh`
Mesh represents spatial discretization of the calculation domain
a: value | array | callable(cell, userData)
Diffusion coefficient per cell
b: value | array | callable(cell, userData)
TODO What is b
fn: iterable(cell)
TODO What is fn
vel: ndarray (N,dim) | RMatrix(N,dim)
velocity field [[v_i,]_j,] with i=[1..3] for the mesh dimension
and j = [0 .. N-1] per Cell or per Node so N is either
mesh.cellCount() or mesh.nodeCount()
scheme: str [CDS]
Finite volume scheme
* CDS -- Central Difference Scheme.
maybe irregular for Peclet no. |F/D| > 2
Diffusion dominant. Error of order 2
* UDS -- Upwind Scheme.
Convection dominant. Error of order 1
* HS -- Hybrid Scheme.
Diffusion dominant for Peclet-number |(F/D)| < 2
Convection dominant else.
* PS -- Power Law Scheme.
Identical to HS for Peclet-number |(F/D)| > 10 and near to ES else
Convection dominant.
* ES -- Exponential scheme
Only stationary one-dimensional but exact solution
Returns
-------
S: :gimliapi:`GIMLI::SparseMatrix` | numpy.ndarray(nCells, nCells)
Kernel matrix, depends on vel, a, b, scheme, uB, duB .. if some of this
has been changed you cannot cache these matrix
rhsBoundaryScales: ndarray(nCells)
RHS offset vector
"""
if a is None:
a = pg.Vector(mesh.boundaryCount(), 1.0)
AScheme = None
if scheme == 'CDS':
AScheme = lambda peclet_: 1.0 - 0.5 * abs(peclet_)
elif scheme == 'UDS':
AScheme = lambda peclet_: 1.0
elif scheme == 'HS':
AScheme = lambda peclet_: max(0.0, 1.0 - 0.5 * abs(peclet_))
elif scheme == 'PS':
AScheme = lambda peclet_: max(0.0, (1.0 - 0.1 * abs(peclet_))**5.0)
elif scheme == 'ES':
AScheme = lambda peclet_: (peclet_) / (np.exp(abs(peclet_)) - 1.0) \
if peclet_ != 0.0 else 1
else:
raise BaseException("Scheme unknwon:" + scheme)
useHalfBoundaries = False
dof = mesh.cellCount()
if not uB:
uB = []
if not duB:
duB = []
if useHalfBoundaries:
dof = mesh.cellCount() + len(uB)
S = None
if sparse:
S = pg.matrix.SparseMapMatrix(dof, dof, stype=0) + identity(dof,
scale=b)
else:
S = np.zeros((dof, dof))
rhsBoundaryScales = np.zeros(dof)
# swatch = pg.core.Stopwatch(True)
# we need this to fast identify uBoundary and value by boundary
uBoundaryID = []
uBoundaryVals = [None] * mesh.boundaryCount()
for [b, val] in uB:
if isinstance(b, pg.core.Boundary):
uBoundaryID.append(b.id())
uBoundaryVals[b.id()] = val
elif isinstance(b, pg.core.Node):
for _b in b.boundSet():
if _b.rightCell() is None:
pg.warn(
'Dirichlet for one node considered for the nearest boundary.',
_b.id())
uBoundaryID.append(_b.id())
uBoundaryVals[_b.id()] = val
break
else:
raise BaseException("Please give boundary, value list")
duBoundaryID = []
duBoundaryVals = [None] * mesh.boundaryCount()
for [boundary, val] in duB:
if not isinstance(boundary, pg.core.Boundary):
raise BaseException("Please give boundary, value list")
duBoundaryID.append(boundary.id())
duBoundaryVals[boundary.id()] = val
# iterate over all cells
for cell in mesh.cells():
cID = cell.id()
for bi in range(cell.boundaryCount()):
boundary = pg.core.findBoundary(cell.boundaryNodes(bi))
ncell = boundary.leftCell()
if ncell == cell:
ncell = boundary.rightCell()
v = findVelocity(mesh, vel, boundary, cell, ncell)
# Convection part
F = boundary.norm(cell).dot(v) * boundary.size()
# print(F, boundary.size(), v, vel)
# Diffusion part
D = findDiffusion(mesh, a, boundary, cell, ncell)
# print(F, D, F/D)
# print((1.0 - 0.1 * abs(F/D))**5.0)
if D > 0:
aB = D * AScheme(F / D) + max(-F, 0.0)
else:
aB = max(-F, 0.0)
aB /= cell.size()
# print(cell.center(), boundary.center(), boundary.norm(cell), aB)
if ncell:
# no boundary
if sparse:
S.addVal(cID, ncell.id(), -aB)
S.addVal(cID, cID, +aB)
else:
S[cID, ncell.id()] -= aB
S[cID, cID] += aB
elif not useHalfBoundaries:
if boundary.id() in uBoundaryID:
val = pg.solver.generateBoundaryValue(
boundary,
uBoundaryVals[boundary.id()],
time=time,
userData=userData)
if sparse:
S.addVal(cID, cID, aB)
else:
S[cID, cID] += aB
rhsBoundaryScales[cID] += aB * val
if boundary.id() in duBoundaryID:
# Neumann boundary condition
val = pg.solver.generateBoundaryValue(
boundary,
duBoundaryVals[boundary.id()],
time=time,
userData=userData)
# amount of flow through the boundary .. maybe buggy
# fill be replaced by suitable FE solver
outflow = -val * boundary.size() / cell.size()
if sparse:
S.addVal(cID, cID, outflow)
else:
S[cID, cID] += outflow
if fn is not None:
if sparse:
# * cell.shape().domainSize())
S.addVal(cell.id(), cell.id(), -fn[cell.id()])
else:
# * cell.shape().domainSize()
S[cell.id(), cell.id()] -= fn[cell.id()]
return S, rhsBoundaryScales
def diffusionConvectionKernel(mesh, a=None, b=0.0, f=None,
uB=None, duB=None,
fn=None, vel=0, u0=0,
scheme='CDS', sparse=False, time=0.0,
userData=None):
"""
Peclet Number - ratio between convection/diffusion * Length
Advection .. forced convection
"""
if a is None:
a = pg.RVector(mesh.boundaryCount(), 1.0)
AScheme = None
if scheme == 'CDS':
# CDS - central diff. scheme .. maybe irregular for Peclet no. |F/D|>2
# diffusion dominant
# Error of order 2
AScheme = lambda peclet_: 1.0 - 0.5 * abs(peclet_)
elif scheme == 'UDS':
# UDS - upwind scheme
# Convection dominant
# Error of order 1
AScheme = lambda peclet_: 1.0
elif scheme == 'HS':
# HS - hybrid scheme.
# Diffusion dominant for Peclet-number |(F/D)| < 2
# Convection dominant else
AScheme = lambda peclet_: max(0.0, 1.0 - 0.5 * abs(peclet_))
elif scheme == 'PS':
# PS - power-law scheme.
# Identical to HS for Peclet-number |(F/D)| > 10 and near to ES else
AScheme = lambda peclet_: max(0.0, (1.0 - 0.1 * abs(peclet_))**5.0)
elif scheme == 'ES':
# ES - exponential scheme
# Only stationary one-dimensional but exact solution
AScheme = lambda peclet_: (peclet_) / (np.exp(abs(peclet_)) - 1.0) \
if peclet_ != 0.0 else 1
else:
raise
useHalfBoundaries = False
dof = mesh.cellCount()
if not uB:
uB = []
if not duB:
duB = []
if useHalfBoundaries:
dof = mesh.cellCount() + len(uB)
S = None
if sparse:
S = pg.RSparseMapMatrix(dof, dof, 0) + identity(dof) * b
else:
S = np.zeros((dof, dof))
rhsBoundaryScales = np.zeros(dof)
# swatch = pg.Stopwatch(True)
# we need this to fast identify uBoundary and value by boundary
uBoundaryID = []
uBoundaryVals = [None] * mesh.boundaryCount()
for i, [boundary, val] in enumerate(uB):
if not isinstance(boundary, pg.Boundary):
raise BaseException("Please give boundary, value list")
uBoundaryID.append(boundary.id())
uBoundaryVals[boundary.id()] = val
duBoundaryID = []
duBoundaryVals = [None] * mesh.boundaryCount()
for i, [boundary, val] in enumerate(duB):
if not isinstance(boundary, pg.Boundary):
raise BaseException("Please give boundary, value list")
duBoundaryID.append(boundary.id())
duBoundaryVals[boundary.id()] = val
for cell in mesh.cells():
for bi in range(cell.boundaryCount()):
boundary = pg.findBoundary(cell.boundaryNodes(bi))
ncell = boundary.leftCell()
if ncell == cell:
ncell = boundary.rightCell()
v = findVelocity(mesh, vel, boundary, cell, ncell)
# Convection part
F = boundary.norm(cell).dot(v) * boundary.size()
# Diffusion part
D = findDiffusion(mesh, a, boundary, cell, ncell)
aB = D * AScheme(F / D) + max(-F, 0.0)
aB /= cell.size()
# print(cell.center(), boundary.center(), boundary.norm(cell), aB)
if ncell:
# no boundary
if sparse:
S.addVal(cell.id(), ncell.id(), -aB)
S.addVal(cell.id(), cell.id(), +aB)
else:
S[cell.id(), ncell.id()] -= aB
S[cell.id(), cell.id()] += aB
elif not useHalfBoundaries:
if boundary.id() in uBoundaryID:
val = pg.solver.generateBoundaryValue(boundary,
uBoundaryVals[
boundary.id()],
time=time,
userData=userData)
if sparse:
S.addVal(cell.id(), cell.id(), aB)
else:
S[cell.id(), cell.id()] += aB
rhsBoundaryScales[cell.id()] += aB * val
if boundary.id() in duBoundaryID:
# Neumann boundary condition
val = pg.solver.generateBoundaryValue(
boundary, duBoundaryVals[boundary.id()], time=time,
userData=userData)
if sparse:
# amount of flow through the boundary
S.addVal(cell.id(), cell.id(), val *
boundary.size() / cell.size())
else:
S[cell.id(), cell.id()] += val * \
boundary.size() / cell.size()
if fn is not None:
if sparse:
# * cell.shape().domainSize())
S.addVal(cell.id(), cell.id(), -fn[cell.id()])
else:
# * cell.shape().domainSize()
S[cell.id(), cell.id()] -= fn[cell.id()]
if useHalfBoundaries:
for i, [b, val] in enumerate(duB): # not defined!!!
bIdx = mesh.cellCount() + i
c = b.leftCell()
if not c:
c = b.rightCell()
if c:
n = b.norm(c)
v = findVelocity(mesh, vel, b, c, nc=None)
F = n.dot(v) * b.size()
D = findDiffusion(mesh, a, b, c)
aB = D * AScheme(F / D) + max(-F, 0.0)
if useHalfBoundaries:
if sparse:
S.setVal(c.id(), c.id(), 1.)
S.addVal(c.id(), bIdx, -aB)
else:
S[bIdx, bIdx] = 1.
S[c.id(), bIdx] -= aB
rhsBoundaryScales[bIdx] = aB
return S, rhsBoundaryScales
c = v * dt / (dx*dx) # [(m*m)/s * s/(m*m)] = []
print("Courant-Friedrichs-Lewy condition:", "CLF =", c)
# r needs to be <= 0.5
uE = np.zeros((len(t), len(x)))
uE[0] = u0
uE[0][0] = 0.0
uE[0][-1] = 0.0
uI = np.array(uE)
uFEM = np.array(uE)
#L = np.diag(np.ones(len(x)-1), -1) - 2. * np.diag(np.ones(len(x))) + np.diag(np.ones(len(x)-1), 1)
Lg = solver.triDiagToeplitz(len(x), a=2.0, l=-1.0, r=-1.0,
start=1, end=len(x)-1)
I = solver.identity(len(x))
# L[1,0]=2 # neummann links
# L[-2,-1]=2 # neummann rechts
grid = pg.createGrid(x=x)
uFEM = np.array(uE)
dirichletBC = [[1, 0.0], # top
[2, 0.0]] # bottom
A = solver.createStiffnessMatrix(grid, np.ones(grid.cellCount()))
M = solver.createMassMatrix(grid, np.ones(grid.cellCount()))
for n in range(1, len(t)):
"""
Direct time and space discretization of the second derivatives
# diff in space is 2nd order central
def diffusionConvectionKernel(mesh, a=None, b=0.0,
uB=None, duB=None,
vel=0,
# u0=0,
fn=None,
scheme='CDS', sparse=False, time=0.0,
userData=None):
"""
Generate system matrix for diffusion and convection in a velocity field.
Particle concentration u inside a velocity field.
Peclet Number - ratio between convection/diffusion = F/D
F = velocity flow trough volume boundary,
D = diffusion coefficient
Parameters
----------
mesh : :gimliapi:`GIMLI::Mesh`
Mesh represents spatial discretization of the calculation domain
a : value | array | callable(cell, userData)
Diffusion coefficient per cell
b : value | array | callable(cell, userData)
TODO What is b
fn : iterable(cell)
TODO What is fn
vel : ndarray (N,dim) | RMatrix(N,dim)
velocity field [[v_i,]_j,] with i=[1..3] for the mesh dimension
and j = [0 .. N-1] per Cell or per Node so N is either
mesh.cellCount() or mesh.nodeCount()
scheme : str [CDS]
Finite volume scheme
* CDS -- Central Difference Scheme.
maybe irregular for Peclet no. |F/D| > 2
Diffusion dominant. Error of order 2
* UDS -- Upwind Scheme.
Convection dominant. Error of order 1
* HS -- Hybrid Scheme.
Diffusion dominant for Peclet-number |(F/D)| < 2
Convection dominant else.
* PS -- Power Law Scheme.
Identical to HS for Peclet-number |(F/D)| > 10 and near to ES else
Convection dominant.
* ES -- Exponential scheme
Only stationary one-dimensional but exact solution
Returns
-------
S : :gimliapi:`GIMLI::SparseMatrix` | numpy.ndarray(nCells, nCells)
Kernel matrix, depends on vel, a, b, scheme, uB, duB .. if some of this
has been changed you cannot cache these matrix
rhsBoundaryScales : ndarray(nCells)
RHS offset vector
"""
if a is None:
a = pg.RVector(mesh.boundaryCount(), 1.0)
AScheme = None
if scheme == 'CDS':
AScheme = lambda peclet_: 1.0 - 0.5 * abs(peclet_)
elif scheme == 'UDS':
AScheme = lambda peclet_: 1.0
elif scheme == 'HS':
AScheme = lambda peclet_: max(0.0, 1.0 - 0.5 * abs(peclet_))
elif scheme == 'PS':
AScheme = lambda peclet_: max(0.0, (1.0 - 0.1 * abs(peclet_))**5.0)
elif scheme == 'ES':
AScheme = lambda peclet_: (peclet_) / (np.exp(abs(peclet_)) - 1.0) \
if peclet_ != 0.0 else 1
else:
raise BaseException("Scheme unknwon:" + scheme)
useHalfBoundaries = False
dof = mesh.cellCount()
if not uB:
uB = []
if not duB:
duB = []
if useHalfBoundaries:
dof = mesh.cellCount() + len(uB)
S = None
if sparse:
S = pg.RSparseMapMatrix(dof, dof, stype=0) + identity(dof, scale=b)
else:
S = np.zeros((dof, dof))
rhsBoundaryScales = np.zeros(dof)
# swatch = pg.Stopwatch(True)
# we need this to fast identify uBoundary and value by boundary
uBoundaryID = []
uBoundaryVals = [None] * mesh.boundaryCount()
for [boundary, val] in uB:
if not isinstance(boundary, pg.Boundary):
raise BaseException("Please give boundary, value list")
uBoundaryID.append(boundary.id())
uBoundaryVals[boundary.id()] = val
duBoundaryID = []
duBoundaryVals = [None] * mesh.boundaryCount()
for [boundary, val] in duB:
if not isinstance(boundary, pg.Boundary):
raise BaseException("Please give boundary, value list")
duBoundaryID.append(boundary.id())
duBoundaryVals[boundary.id()] = val
# iterate over all cells
for cell in mesh.cells():
cID = cell.id()
for bi in range(cell.boundaryCount()):
boundary = pg.findBoundary(cell.boundaryNodes(bi))
ncell = boundary.leftCell()
if ncell == cell:
ncell = boundary.rightCell()
v = findVelocity(mesh, vel, boundary, cell, ncell)
# Convection part
F = boundary.norm(cell).dot(v) * boundary.size()
# print(F, boundary.size(), v, vel)
# Diffusion part
D = findDiffusion(mesh, a, boundary, cell, ncell)
# print(F, D, F/D)
# print((1.0 - 0.1 * abs(F/D))**5.0)
aB = D * AScheme(F / D) + max(-F, 0.0)
aB /= cell.size()
# print(cell.center(), boundary.center(), boundary.norm(cell), aB)
if ncell:
# no boundary
if sparse:
S.addVal(cID, ncell.id(), -aB)
S.addVal(cID, cID, +aB)
else:
S[cID, ncell.id()] -= aB
S[cID, cID] += aB
elif not useHalfBoundaries:
if boundary.id() in uBoundaryID:
val = pg.solver.generateBoundaryValue(
boundary,
uBoundaryVals[boundary.id()],
time=time,
userData=userData)
if sparse:
S.addVal(cID, cID, aB)
else:
S[cID, cID] += aB
rhsBoundaryScales[cID] += aB * val
if boundary.id() in duBoundaryID:
# Neumann boundary condition
val = pg.solver.generateBoundaryValue(
boundary,
duBoundaryVals[boundary.id()],
time=time,
userData=userData)
# amount of flow through the boundary
outflow = val * boundary.size() / cell.size()
if sparse:
S.addVal(cID, cID, outflow)
else:
S[cID, cID] += outflow
if fn is not None:
if sparse:
# * cell.shape().domainSize())
S.addVal(cell.id(), cell.id(), -fn[cell.id()])
else:
# * cell.shape().domainSize()
S[cell.id(), cell.id()] -= fn[cell.id()]
return S, rhsBoundaryScales
def solveFiniteVolume(mesh, a=1.0, f=0.0, fn=0.0, vel=0.0, u0=None,
times=None,
uL=None, relax=1.0,
ws=None, scheme='CDS', **kwargs):
"""
"""
# The Workspace is to hold temporary data or preserve matrix rebuild
swatch = pg.Stopwatch(True)
sparse = True
workspace = WorkSpace()
if ws:
workspace = ws
a = solver.parseArgToArray(a, [mesh.cellCount(), mesh.boundaryCount()])
f = solver.parseArgToArray(f, mesh.cellCount())
fn = solver.parseArgToArray(fn, mesh.cellCount())
boundsDirichlet = None
boundsNeumann = None
if not hasattr(workspace, 'S'):
if 'uBoundary' in kwargs:
boundsDirichlet = pg.solver.parseArgToBoundaries(
kwargs['uBoundary'], mesh)
if 'duBoundary' in kwargs:
boundsNeumann = pg.solver.parseArgToBoundaries(
kwargs['duBoundary'], mesh)
workspace.S, workspace.rhsBCScales = diffusionConvectionKernel(
mesh=mesh, a=a, f=f, uBoundaries=boundsDirichlet,
duBoundaries=boundsNeumann, u0=u0, fn=fn, vel=vel,
scheme=scheme, sparse=sparse,
userData=kwargs.pop('userData', None))
print('FVM kernel 1:', swatch.duration(True))
dof = len(workspace.rhsBCScales)
# workspace.uDir = np.zeros(dof)
# if u0 is not None:
# workspace.uDir = np.array(u0)
#
# if len(boundsDirichlet):
# for boundary, val in boundsDirichlet.items():
# workspace.uDir[boundary.leftCell().id()] = val
workspace.ap = np.zeros(dof)
# for nonlinears
if uL is not None:
for i in range(dof):
val = 0.0
if sparse:
val = workspace.S.getVal(i, i) / relax
workspace.S.setVal(i, i, val)
# workspace.S[i, i] /= relax
# workspace.ap[i] = workspace.S[i, i]
else:
val = workspace.S[i, i] / relax
workspace.S[i, i] = val
workspace.ap[i] = val
print('FVM kernel 2:', swatch.duration(True))
# endif: not hasattr(workspace, 'S'):
workspace.rhs = np.zeros(len(workspace.rhsBCScales))
workspace.rhs[0:mesh.cellCount()] = f # * mesh.cellSizes()
# if len(workspace.uDir):
workspace.rhs += workspace.rhsBCScales
# for nonlinear: relax progress with scaled last result
if uL is not None:
workspace.rhs += (1. - relax) * workspace.ap * uL
# print('FVM: Prep:', swatch.duration(True))
if not hasattr(times, '__len__'):
if sparse and not hasattr(workspace, 'solver'):
Sm = pg.RSparseMatrix(workspace.S)
# hold Sm until we have reference counting,
# loosing Sm here will kill LinSolver later
workspace.Sm = Sm
workspace.solver = pg.LinSolver(Sm, True)
u = None
if sparse:
u = workspace.solver.solve(workspace.rhs)
else:
u = np.linalg.solve(workspace.S, workspace.rhs)
print('FVM solve:', swatch.duration(True))
return u[0:mesh.cellCount():1]
else:
theta = kwargs.pop('theta', 0.5)
verbose = kwargs.pop('verbose', False)
if sparse:
I = solver.identity(len(workspace.rhs))
else:
I = np.diag(np.ones(len(workspace.rhs)))
print("solve cN")
return solver.crankNicolson(times, theta, workspace.S, I,
f=workspace.rhs, u0=u0, verbose=verbose)