def initialize_direct_space_solver(self, time_level, delta_time, mg_level=None):
if mg_level is None:
mg_level = self._mg_level
assert_is_instance(mg_level, IMultigridLevel, descriptor="Multigrid Level", checking_obj=self)
_stencil = Stencil(self.mg_stencil(delta_time, mg_level.h))
# LOG.debug("Stencil for dt=%f, h=%f: %s" % (delta_time, mg_level.h, _stencil.arr))
time_level = str(time_level)
delta_time = str(delta_time)
if self._direct_solvers.get(time_level) is None:
# LOG.debug("Initializing Solvers for Time Level '%s'" % time_level)
self._direct_solvers[time_level] = {}
# LOG.debug(" Initializing Solver for Time Level '%s' and Delta Node '%s'" % (time_level, delta_time))
# LOG.debug(" shape: %s" % (mg_level.mid.shape))
self._direct_solvers[time_level][delta_time] = {
'mg_level': mg_level,
'stencil': _stencil,
'solver': _stencil.generate_direct_solver(mg_level.mid.shape)
}
from pypint.plugins.multigrid.multigrid_problem import MultigridProblem
from pypint.plugins.multigrid.multigrid_level_provider import MultiGridLevelProvider
from pypint.plugins.multigrid.multigrid_solution import MultiGridSolution
from pypint.plugins.multigrid.level import MultigridLevel1D
from pypint.plugins.multigrid.multigrid_smoother import SplitSmoother, DirectSolverSmoother, WeightedJacobiSmoother
from pypint.utilities import assert_is_callable, assert_is_instance, assert_condition
from pypint.plugins.multigrid.stencil import Stencil
from pypint.plugins.multigrid.interpolation import InterpolationByStencilListIn1D, InterpolationByStencilForLevels, InterpolationByStencilForLevelsClassical
from pypint.plugins.multigrid.restriction import RestrictionStencilPure, RestrictionByStencilForLevels, RestrictionByStencilForLevelsClassical
from operator import iadd,add
import networkx as nx
if __name__ == '__main__':
print("Lets solve, you guessed it, the heat equation")
# heat equation needs a stencil
laplace_stencil = Stencil(np.asarray([1, -2, 1]), None, 2)
# test stencil to some extend
print("===== Stencil tests =====")
print("stencil.b :", laplace_stencil.b)
print("stencil.positions :", laplace_stencil.positions)
for i in laplace_stencil.positions:
print(laplace_stencil.arr[i])
print("stencil.relative_position :", laplace_stencil.relative_positions)
print("stencil.relative_position_woc :", laplace_stencil.relative_positions_woc)
# geometry is a 1 dimensional line
geo = np.asarray([[0, 1]])
print(geo.shape)
# the boundary conditions, in this case dirichlet boundary conditions
boundary_type = ["dirichlet"]*2
"""
def __init__(self, stencil_form, mg_problem, numb_levels=3, coarse_level_shape=(5,)):
pass
if __name__ == '__main__':
# check if level2d is working properly
# but first one has to define a proper level
# and for this one needs a useful stencil
np.set_printoptions(precision=4, edgeitems=4, threshold=10)
print("===== Stencil =====")
laplace_array = np.asarray([[0.0, 1.0, 0.0], [1.0, -4.0, 1.0], [0.0, 1.0, 0.0]])
laplace_stencil = Stencil(np.asarray([[0, 1, 0], [1, -4, 1], [0, 1, 0]]), None, 2)
print("stencil.arr\n", laplace_stencil.arr)
print("stencil.reversed_arr\n", laplace_stencil.reversed_arr)
print("stencil.b \n", laplace_stencil.b)
print("stencil.positions \n", laplace_stencil.positions)
print("stencil.center \n", laplace_stencil.center)
print("===== MgProblem =====")
# define geometry
geo = np.asarray([[0, 1], [0, 1]])
# the boundary conditions, in this case dirichlet boundary conditions
boundary_type = ["dirichlet"]*2
# east_f = lambda x: 2.0
# west_f = lambda x: 8.0
# north_f = lambda x: 1.0
# south_f = lambda x: 4.0
east_f = lambda x: np.sin(x[1]*np.pi)
omega = 1.0
l_plus = np.asarray([0, -2.0/omega, 0])
l_minus = np.asarray([1.0, -2.0*(1.0 - 1.0/omega), 1.0])
top_jacobi_smoother = SplitSmoother(l_plus / top_level.h**2,
l_minus / top_level.h**2,
top_level)
mid_jacobi_smoother = SplitSmoother(l_plus / mid_level.h**2,
l_minus / mid_level.h**2,
mid_level)
low_jacobi_smoother = SplitSmoother(l_plus / low_level.h**2,
l_minus / low_level.h**2,
low_level)
top_stencil = Stencil(laplace_array / top_level.h**2)
mid_stencil = Stencil(laplace_array / mid_level.h**2)
low_stencil = Stencil(laplace_array / low_level.h**2)
print("jacobi minus: %s" % top_stencil.l_minus_jacobi(1.))
print("jacobi plus: %s" % top_stencil.l_plus_jacobi(1.))
low_direct_smoother = DirectSolverSmoother(low_stencil, low_level)
center = np.asarray([0])
# restriction
rst_stencil = Stencil(np.asarray([0.25, 0.5, 0.25]))
rst_top_to_mid = RestrictionByStencilForLevelsClassical(top_level, mid_level, rst_stencil)
rst_mid_to_low = RestrictionByStencilForLevelsClassical(mid_level, low_level, rst_stencil)
# ipl
top_level = MultigridLevel2D((259, 259), mg_problem=mg_problem,
max_borders=borders, role="FL")
mid_level = MultigridLevel2D((129, 129), mg_problem=mg_problem,
max_borders=borders, role="ML")
low_level = MultigridLevel2D((64, 64), mg_problem=mg_problem,
max_borders=borders, role="CL")
mg_problem.fill_rhs(top_level)
top_level.pad()
# define the different stencils
top_stencil = Stencil(laplace_array/top_level.h[0]**2, None, 2)
mid_stencil = Stencil(laplace_array/mid_level.h[0]**2, None, 2)
low_stencil = Stencil(laplace_array/low_level.h[0]**2, None, 2)
top_stencil.modify_rhs(top_level)
omega = 2.0/3.0
l_plus = np.asarray([[0, 0, 0],
[0, -4.0/omega, 0],
[0, 0, 0]])
l_minus = np.asarray([[0, 1.0, 0], [1.0, -4.0*(1.0 - 1.0/omega), 1.0], [0., 1., 0.]])
# define the different smoothers on each level, works just for symmetric grids
top_jacobi_smoother = SplitSmoother(l_plus / top_level.h[0]**2,
l_minus / top_level.h[0]**2,
top_level)
mid_jacobi_smoother = SplitSmoother(l_plus / mid_level.h[0]**2,