def __init__(self,N,Omega):
self.mesh = smartminex_tayhoomesh.getmake_mesh(N)
self.N = N
self.V = VectorFunctionSpace(self.mesh, "CG", 2)
self.Q = FunctionSpace(self.mesh, "CG", 1)
self.velbcs = setget_velbcs_zerosq(self.mesh, self.V)
self.Pdof = 0 #dof removed in the p approximation
self.omega = Omega
self.nu = 0
self.fp = Constant((0))
self.fv = Expression(("40*nu*pow(x[0],2)*pow(x[1],3)*sin(omega*t) - 60*nu*pow(x[0],2)*pow(x[1],2)*sin(omega*t) + 24*nu*pow(x[0],2)*x[1]*pow((x[0] - 1),2)*sin(omega*t) + 20*nu*pow(x[0],2)*x[1]*sin(omega*t) - 12*nu*pow(x[0],2)*pow((x[0] - 1),2)*sin(omega*t) - 32*nu*x[0]*pow(x[1],3)*sin(omega*t) + 48*nu*x[0]*pow(x[1],2)*sin(omega*t) - 16*nu*x[0]*x[1]*sin(omega*t) + 8*nu*pow(x[1],3)*pow((x[0] - 1),2)*sin(omega*t) - 12*nu*pow(x[1],2)*pow((x[0] - 1),2)*sin(omega*t) + 4*nu*x[1]*pow((x[0] - 1),2)*sin(omega*t) - 4*pow(x[0],3)*pow(x[1],2)*pow((x[0] - 1),3)*(2*x[0] - 1)*pow((x[1] - 1),2)*(2*x[1]*(x[1] - 1) + x[1]*(2*x[1] - 1) + (x[1] - 1)*(2*x[1] - 1) - 2*pow((2*x[1] - 1),2))*pow(sin(omega*t),2) - 4*pow(x[0],2)*pow(x[1],3)*pow((x[0] - 1),2)*omega*cos(omega*t) + 6*pow(x[0],2)*pow(x[1],2)*pow((x[0] - 1),2)*omega*cos(omega*t) - 2*pow(x[0],2)*x[1]*pow((x[0] - 1),2)*omega*cos(omega*t) + 2*x[0]*pow(x[1],2)*sin(omega*t) - 2*x[0]*x[1]*sin(omega*t) - pow(x[1],2)*sin(omega*t) + x[1]*sin(omega*t)", "-40*nu*pow(x[0],3)*pow(x[1],2)*sin(omega*t) + 32*nu*pow(x[0],3)*x[1]*sin(omega*t) - 8*nu*pow(x[0],3)*pow((x[1] - 1),2)*sin(omega*t) + 60*nu*pow(x[0],2)*pow(x[1],2)*sin(omega*t) - 48*nu*pow(x[0],2)*x[1]*sin(omega*t) + 12*nu*pow(x[0],2)*pow((x[1] - 1),2)*sin(omega*t) - 24*nu*x[0]*pow(x[1],2)*pow((x[1] - 1),2)*sin(omega*t) - 20*nu*x[0]*pow(x[1],2)*sin(omega*t) + 16*nu*x[0]*x[1]*sin(omega*t) - 4*nu*x[0]*pow((x[1] - 1),2)*sin(omega*t) + 12*nu*pow(x[1],2)*pow((x[1] - 1),2)*sin(omega*t) + 4*pow(x[0],3)*pow(x[1],2)*pow((x[1] - 1),2)*omega*cos(omega*t) - 4*pow(x[0],2)*pow(x[1],3)*pow((x[0] - 1),2)*pow((x[1] - 1),3)*(2*x[1] - 1)*(2*x[0]*(x[0] - 1) + x[0]*(2*x[0] - 1) + (x[0] - 1)*(2*x[0] - 1) - 2*pow((2*x[0] - 1),2))*pow(sin(omega*t),2) - 6*pow(x[0],2)*pow(x[1],2)*pow((x[1] - 1),2)*omega*cos(omega*t) + 2*pow(x[0],2)*x[1]*sin(omega*t) - pow(x[0],2)*sin(omega*t) + 2*x[0]*pow(x[1],2)*pow((x[1] - 1),2)*omega*cos(omega*t) - 2*x[0]*x[1]*sin(omega*t) + x[0]*sin(omega*t)"), t=0, nu=self.nu, omega = self.omega )
self.v = Expression((
"sin(omega*t)*x[0]*x[0]*(1 - x[0])*(1 - x[0])*2*x[1]*(1 - x[1])*(2*x[1] - 1)",
"sin(omega*t)*x[1]*x[1]*(1 - x[1])*(1 - x[1])*2*x[0]*(1 - x[0])*(1 - 2*x[0])"), omega = self.omega, t = 0)
self.vdot = Expression((
"omega*cos(omega*t)*x[0]*x[0]*(1 - x[0])*(1 - x[0])*2*x[1]*(1 - x[1])*(2*x[1] - 1)",
"omega*cos(omega*t)*x[1]*x[1]*(1 - x[1])*(1 - x[1])*2*x[0]*(1 - x[0])*(1 - 2*x[0])"), omega = self.omega, t = 0)
self.p = Expression(("sin(omega*t)*x[0]*(1-x[0])*x[1]*(1-x[1])"), omega = self.omega, t = 0)
bcinds = []
for bc in self.velbcs:
bcdict = bc.get_boundary_values()
bcinds.extend(bcdict.keys())
# indices of the inner velocity nodes
self.invinds = np.setdiff1d(range(self.V.dim()),bcinds)
def test_rearrange_matrices(self):
"""check the algorithm rearranging for B2, solve the
rearranged system and sort back the solution vector
The rearr. is done by swapping columns in the coeff matrix,
thus the resort is done by swapping the entries of the solution
vector"""
from dolfin import *
import test_time_schemes as tts
import dolfin_to_nparrays as dtn
from smamin_utils import col_columns_atend, revert_sort_tob2
import smartminex_tayhoomesh
N = 32
mesh = smartminex_tayhoomesh.getmake_mesh(N)
V = VectorFunctionSpace(mesh, "CG", 2)
Q = FunctionSpace(mesh, "CG", 1)
velbcs = tts.setget_velbcs_zerosq(mesh, V)
bcinds = []
for bc in velbcs:
bcdict = bc.get_boundary_values()
bcinds.extend(bcdict.keys())
# indices of the inner velocity nodes
invinds = np.setdiff1d(range(V.dim()), bcinds)
Ma, Aa, BTa, Ba, MPa = dtn.get_sysNSmats(V, Q)
Mc = Ma[invinds, :][:, invinds]
Ac = Aa[invinds, :][:, invinds]
Bc = Ba[:, invinds]
BTc = BTa[invinds, :]
B2BubInds = smartminex_tayhoomesh.get_B2_bubbleinds(N, V, mesh)
# B2BubInds = np.array([2,4])
# we need the B2Bub indices in the reduced setting vc
# this gives a masked array of boolean type
B2BubBool = np.in1d(np.arange(V.dim())[invinds], B2BubInds)
# B2BubInds = np.arange(len(B2BubIndsBool
Nv = len(invinds)
Np = Q.dim()
dt = 1.0 / N
# the complement of the bubble index in the inner nodes
BubIndC = ~B2BubBool # np.setdiff1d(np.arange(Nv),B2BubBool)
# the bubbles as indices
B2BI = np.arange(len(B2BubBool))[B2BubBool]
# Reorder the matrices for smart min ext
MSme = col_columns_atend(Mc, B2BI)
BSme = col_columns_atend(Bc, B2BI)
B1Sme = BSme[:, : Nv - (Np - 1)]
B2Sme = BSme[:, Nv - (Np - 1) :]
M1Sme = MSme[:, : Nv - (Np - 1)]
M2Sme = MSme[:, Nv - (Np - 1) :]
IterA1 = sps.hstack([sps.hstack([M1Sme, dt * M2Sme]), -dt * BTc[:, 1:]])
IterA2 = sps.hstack([sps.hstack([B1Sme[1:, :], dt * B2Sme[1:, :]]), sps.csr_matrix((Np - 1, (Np - 1)))])
# The rearranged coefficient matrix
IterARa = sps.vstack([IterA1, IterA2])
IterAqq = sps.hstack([Mc, -dt * BTc[:, 1:]])
IterAp = sps.hstack([Bc[1:, :], sps.csr_matrix((Np - 1, Np - 1))])
# The actual coefficient matrix
IterA = sps.vstack([IterAqq, IterAp])
rhs = np.random.random((Nv + Np - 1, 1))
SolActu = sps.linalg.spsolve(IterA, rhs)
SolRa = sps.linalg.spsolve(IterARa, rhs)
# Sort it back
# manually
SortBack = np.zeros((Nv + Np - 1, 1))
# q1
SortBack[BubIndC, 0] = SolRa[: Nv - (Np - 1)]
# tq2
SortBack[B2BI, 0] = dt * SolRa[Nv - (Np - 1) : Nv]
SortBack[Nv:, 0] = SolRa[Nv:]
SolRa = np.atleast_2d(SolRa).T
# and by function
SolRa[Nv - (Np - 1) : Nv, 0] = dt * SolRa[Nv - (Np - 1) : Nv, 0]
SB2 = revert_sort_tob2(SolRa[:Nv,], B2BI)
SB2 = np.vstack([SB2, SolRa[Nv:,]])
# SB2v = np.atleast_2d(SB2)
SolActu = np.atleast_2d(SolActu)
SortBack = np.atleast_2d(SortBack).T
# print SolActu
# print SolRa
# print SortBack
# print SB2
self.assertTrue(np.allclose(SolActu, SortBack, atol=1e-6))
self.assertTrue(np.allclose(SolActu, SB2.T, atol=1e-6))