def elliptic_demo(args):
args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER'])
assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError('Invalid problem number')
args['DIRICHLET-NUMBER'] = int(args['DIRICHLET-NUMBER'])
assert 0 <= args['DIRICHLET-NUMBER'] <= 2, ValueError('Invalid Dirichlet boundary number.')
args['NEUMANN-NUMBER'] = int(args['NEUMANN-NUMBER'])
assert 0 <= args['NEUMANN-NUMBER'] <= 2, ValueError('Invalid Neumann boundary number.')
args['NEUMANN-COUNT'] = int(args['NEUMANN-COUNT'])
assert 0 <= args['NEUMANN-COUNT'] <= 3, ValueError('Invalid Neumann boundary count.')
rhss = [ExpressionFunction('ones(x.shape[:-1]) * 10', 2, ()),
ExpressionFunction('(x[..., 0] - 0.5) ** 2 * 1000', 2, ())]
dirichlets = [ExpressionFunction('zeros(x.shape[:-1])', 2, ()),
ExpressionFunction('ones(x.shape[:-1])', 2, ()),
ExpressionFunction('x[..., 0]', 2, ())]
neumanns = [None,
ConstantFunction(3., dim_domain=2),
ExpressionFunction('50*(0.1 <= x[..., 1]) * (x[..., 1] <= 0.2)'
'+50*(0.8 <= x[..., 1]) * (x[..., 1] <= 0.9)', 2, ())]
domains = [RectDomain(),
RectDomain(right='neumann'),
RectDomain(right='neumann', top='neumann'),
RectDomain(right='neumann', top='neumann', bottom='neumann')]
rhs = rhss[args['PROBLEM-NUMBER']]
dirichlet = dirichlets[args['DIRICHLET-NUMBER']]
neumann = neumanns[args['NEUMANN-NUMBER']]
domain = domains[args['NEUMANN-COUNT']]
for n in [32, 128]:
grid_name = '{1}(({0},{0}))'.format(n, 'RectGrid' if args['--rect'] else 'TriaGrid')
print('Solving on {0}'.format(grid_name))
print('Setup problem ...')
problem = StationaryProblem(
domain=domain,
diffusion=ConstantFunction(1, dim_domain=2),
rhs=rhs,
dirichlet_data=dirichlet,
neumann_data=neumann
)
print('Discretize ...')
if args['--rect']:
grid, bi = discretize_domain_default(problem.domain, diameter=m.sqrt(2) / n, grid_type=RectGrid)
else:
grid, bi = discretize_domain_default(problem.domain, diameter=1. / n, grid_type=TriaGrid)
discretizer = discretize_stationary_fv if args['--fv'] else discretize_stationary_cg
discretization, _ = discretizer(analytical_problem=problem, grid=grid, boundary_info=bi)
print('Solve ...')
U = discretization.solve()
print('Plot ...')
discretization.visualize(U, title=grid_name)
print('')
def elliptic_demo(args):
args['PROBLEM-NUMBER'] = int(args['PROBLEM-NUMBER'])
assert 0 <= args['PROBLEM-NUMBER'] <= 1, ValueError('Invalid problem number')
args['DIRICHLET-NUMBER'] = int(args['DIRICHLET-NUMBER'])
assert 0 <= args['DIRICHLET-NUMBER'] <= 2, ValueError('Invalid Dirichlet boundary number.')
args['NEUMANN-NUMBER'] = int(args['NEUMANN-NUMBER'])
assert 0 <= args['NEUMANN-NUMBER'] <= 2, ValueError('Invalid Neumann boundary number.')
args['NEUMANN-COUNT'] = int(args['NEUMANN-COUNT'])
assert 0 <= args['NEUMANN-COUNT'] <= 3, ValueError('Invalid Neumann boundary count.')
rhss = [GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, 2),
GenericFunction(lambda X: (X[..., 0] - 0.5) ** 2 * 1000, 2)]
dirichlets = [GenericFunction(lambda X: np.zeros(X.shape[:-1]), 2),
GenericFunction(lambda X: np.ones(X.shape[:-1]), 2),
GenericFunction(lambda X: X[..., 0], 2)]
neumanns = [None,
ConstantFunction(3., dim_domain=2),
GenericFunction(lambda X: 50*(0.1 <= X[..., 1]) * (X[..., 1] <= 0.2)
+50*(0.8 <= X[..., 1]) * (X[..., 1] <= 0.9), 2)]
domains = [RectDomain(),
RectDomain(right=BoundaryType('neumann')),
RectDomain(right=BoundaryType('neumann'), top=BoundaryType('neumann')),
RectDomain(right=BoundaryType('neumann'), top=BoundaryType('neumann'), bottom=BoundaryType('neumann'))]
rhs = rhss[args['PROBLEM-NUMBER']]
dirichlet = dirichlets[args['DIRICHLET-NUMBER']]
neumann = neumanns[args['NEUMANN-NUMBER']]
domain = domains[args['NEUMANN-COUNT']]
for n in [32, 128]:
grid_name = '{1}(({0},{0}))'.format(n, 'RectGrid' if args['--rect'] else 'TriaGrid')
print('Solving on {0}'.format(grid_name))
print('Setup problem ...')
problem = EllipticProblem(domain=domain, rhs=rhs, dirichlet_data=dirichlet, neumann_data=neumann)
print('Discretize ...')
if args['--rect']:
grid, bi = discretize_domain_default(problem.domain, diameter=m.sqrt(2) / n, grid_type=RectGrid)
else:
grid, bi = discretize_domain_default(problem.domain, diameter=1. / n, grid_type=TriaGrid)
discretizer = discretize_elliptic_fv if args['--fv'] else discretize_elliptic_cg
discretization, _ = discretizer(analytical_problem=problem, grid=grid, boundary_info=bi)
print('Solve ...')
U = discretization.solve()
print('Plot ...')
discretization.visualize(U, title=grid_name)
print('')
def test_visualize_patch(backend_gridtype):
backend, gridtype = backend_gridtype
domain = LineDomain() if gridtype is OnedGrid else RectDomain()
dim = 1 if gridtype is OnedGrid else 2
rhs = GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim) # NOQA
dirichlet = GenericFunction(lambda X: np.zeros(X.shape[:-1]), dim) # NOQA
diffusion = GenericFunction(lambda X: np.ones(X.shape[:-1]), dim) # NOQA
problem = EllipticProblem(domain=domain, rhs=rhs, dirichlet_data=dirichlet, diffusion_functions=(diffusion,))
grid, bi = discretize_domain_default(problem.domain, grid_type=gridtype)
discretization, data = discretize_elliptic_cg(analytical_problem=problem, grid=grid, boundary_info=bi)
U = discretization.solve()
visualize_patch(data['grid'], U=U, backend=backend)
sleep(2) # so gui has a chance to popup
stop_gui_processes()
def parabolic_demo(args):
args['DIFF'] = float(args['DIFF'])
args['--nt'] = int(args['--nt'])
args['--grid'] = int(args['--grid'])
grid_name = '{1}(({0},{0}))'.format(args['--grid'], 'RectGrid' if args['--rect'] else 'TriaGrid')
print('Solving on {0}'.format(grid_name))
print('Setup problem ...')
domain = RectDomain(top=BoundaryType('neumann'), bottom=BoundaryType('neumann'))
rhs = ConstantFunction(value=0, dim_domain=2)
diffusion_functional = GenericParameterFunctional(mapping=lambda mu: mu['diffusion'],
parameter_type={'diffusion': 0})
neumann = ConstantFunction(value=-1., dim_domain=2)
initial = GenericFunction(lambda X: np.cos(np.pi*X[..., 0])*np.sin(np.pi*X[..., 1]), dim_domain=2)
problem = ParabolicProblem(domain=domain, rhs=rhs, diffusion_functionals=[diffusion_functional],
dirichlet_data=initial, neumann_data=neumann, initial_data=initial)
print('Discretize ...')
if args['--rect']:
grid, bi = discretize_domain_default(problem.domain, diameter=m.sqrt(2) / args['--grid'], grid_type=RectGrid)
else:
grid, bi = discretize_domain_default(problem.domain, diameter=1. / args['--grid'], grid_type=TriaGrid)
discretizer = discretize_parabolic_fv if args['--fv'] else discretize_parabolic_cg
discretization, _ = discretizer(analytical_problem=problem, grid=grid, boundary_info=bi, nt=args['--nt'])
print('The parameter type is {}'.format(discretization.parameter_type))
mu = {'diffusion': args['DIFF']}
print('Solving for diffusion = {} ... '.format(mu['diffusion']))
U = discretization.solve(mu)
print('Plot ...')
discretization.visualize(U, title=grid_name)
print('')
def test_visualize_patch(backend_gridtype):
backend, gridtype = backend_gridtype
domain = LineDomain() if gridtype is OnedGrid else RectDomain()
dim = 1 if gridtype is OnedGrid else 2
rhs = GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim) # NOQA
dirichlet = GenericFunction(lambda X: np.zeros(X.shape[:-1]), dim) # NOQA
diffusion = GenericFunction(lambda X: np.ones(X.shape[:-1]), dim) # NOQA
problem = StationaryProblem(domain=domain, rhs=rhs, dirichlet_data=dirichlet, diffusion=diffusion)
grid, bi = discretize_domain_default(problem.domain, grid_type=gridtype)
discretization, data = discretize_stationary_cg(analytical_problem=problem, grid=grid, boundary_info=bi)
U = discretization.solve()
try:
visualize_patch(data['grid'], U=U, backend=backend)
except PySideMissing as ie:
pytest.xfail("PySide missing")
finally:
stop_gui_processes()
def test_visualize_patch(backend_gridtype):
backend, gridtype = backend_gridtype
domain = LineDomain() if gridtype is OnedGrid else RectDomain()
dim = 1 if gridtype is OnedGrid else 2
rhs = GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim) # NOQA
dirichlet = GenericFunction(lambda X: np.zeros(X.shape[:-1]), dim) # NOQA
diffusion = GenericFunction(lambda X: np.ones(X.shape[:-1]), dim) # NOQA
problem = StationaryProblem(domain=domain, rhs=rhs, dirichlet_data=dirichlet, diffusion=diffusion)
grid, bi = discretize_domain_default(problem.domain, grid_type=gridtype)
d, data = discretize_stationary_cg(analytical_problem=problem, grid=grid, boundary_info=bi)
U = d.solve()
try:
visualize_patch(data['grid'], U=U, backend=backend)
except QtMissing as ie:
pytest.xfail("Qt missing")
finally:
stop_gui_processes()
def test_visualize_patch(backend_gridtype):
backend, gridtype = backend_gridtype
domain = LineDomain() if gridtype is OnedGrid else RectDomain()
dim = 1 if gridtype is OnedGrid else 2
rhs = GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim) # NOQA
dirichlet = GenericFunction(lambda X: np.zeros(X.shape[:-1]), dim) # NOQA
diffusion = GenericFunction(lambda X: np.ones(X.shape[:-1]), dim) # NOQA
problem = EllipticProblem(domain=domain,
rhs=rhs,
dirichlet_data=dirichlet,
diffusion_functions=(diffusion, ))
grid, bi = discretize_domain_default(problem.domain, grid_type=gridtype)
discretization, data = discretize_elliptic_cg(analytical_problem=problem,
grid=grid,
boundary_info=bi)
U = discretization.solve()
visualize_patch(data['grid'], U=U, backend=backend)
sleep(2) # so gui has a chance to popup
for child in multiprocessing.active_children():
child.terminate()