def h4(grid, Crhs, g1rhs, g2rhs):
# Crhs = plain
#
# g1rhs = zero
#
# g2rhs = zero
#
# build_matrix_fem_2D(grid, Poisson_tri_integrate, TPS_tri_intergrateX, TPS_tri_intergrateY, X, Y)
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
h4 = zeros([len(Nl), 1])
for node in not_slave_node(grid):
# Which row corresponds to the current node?
i = int(node.get_value())
for endpt in connect_iterator(grid, node.get_node_id()):
if grid.get_slave(endpt):
coord = grid.get_coord(endpt)
c = Crhs(coord[0], coord[1])
g1 = g1rhs(coord[0], coord[1])
g2 = g2rhs(coord[0], coord[1])
#print c
#print endpt._id_no
lentry = grid.get_matrix_value(node.get_node_id(), endpt)[0]
g1entry = grid.get_matrix_value(node.get_node_id(), endpt)[2]
g2entry = grid.get_matrix_value(node.get_node_id(), endpt)[3]
#print aentry
h4[i] += c * lentry - g1entry * g1 - g2entry * g2
#h4[i] += c* lentry + g1entry * g1 + g2entry * g2
#print h4
return h4
def h2(grid, g1rhs, wrhs, alpha):
# g1rhs = zero
#
# wrhs =zero
# build_matrix_fem_2D(grid, Poisson_tri_integrate, TPS_tri_intergrateX, TPS_tri_intergrateY, X, Y)
Nl=[]
for node in (not_slave_node(grid)):
Nl.append([node,node.get_node_id()])
Nl=sorted(Nl, key = itemgetter(1))
Nl=[node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
h2= zeros([len(Nl), 1])
for node in not_slave_node(grid):
# Ignore slave (or boundary) nodes
# Which row corresponds to the current node?
i = int(node.get_value())
for endpt in connect_iterator(grid, node.get_node_id()):
if grid.get_slave(endpt):
coord = grid.get_coord(endpt)
#print coord
g1 = g1rhs(coord[0], coord[1])
#print g1
w = wrhs(coord[0], coord[1])
print #w
#print endpt._id_no
lentry = grid.get_matrix_value(node.get_node_id(), endpt)[0]
g1entry = grid.get_matrix_value(node.get_node_id(), endpt)[2]
#print aentry
h2[i] += alpha * g1 * lentry - w * g1entry #G1, G2
#h2[i] += alpha * g1 * lentry +w * g1entry # -G1, -G2
return h2
def h3(grid, g2rhs, wrhs, alpha):
# g2rhs = zero
#
# wrhs = zero
#
# build_matrix_fem_2D(grid, Poisson_tri_integrate, TPS_tri_intergrateX, TPS_tri_intergrateY, X, Y)
#
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
h3 = zeros([len(Nl), 1])
for node in not_slave_node(grid):
# Ignore slave (or boundary) nodes
# Which row corresponds to the current node?
i = int(node.get_value())
for endpt in connect_iterator(grid, node.get_node_id()):
if grid.get_slave(endpt):
coord = grid.get_coord(endpt)
g2 = g2rhs(coord[0], coord[1])
w = wrhs(coord[0], coord[1])
#print c, w
#print endpt._id_no
lentry = grid.get_matrix_value(node.get_node_id(), endpt)[0]
# G2 entries on boundary
g2entry = grid.get_matrix_value(node.get_node_id(), endpt)[3]
#print aentry
h3[i] += alpha * g2 * lentry + w * g2entry
#h3[i] += alpha * g2* lentry - w* g2entry
return h3
def h1(grid, Crhs, wrhs):
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
h1 = zeros((len(Nl), 1))
h = 1 / float(math.sqrt(len(Nl)) + 1)
for node in not_slave_node(grid):
# Ignore slave (or boundary) nodes
# Which row corresponds to the current node?
i = int(node.get_value())
#print node.get_value(), node.get_node_id()._id_no
for endpt in connect_iterator(grid, node.get_node_id()):
#j = int(grid.get_value(endpt))
#print j
if grid.get_slave(endpt):
coord = grid.get_coord(endpt)
c = Crhs(coord[0], coord[1])
w = wrhs(coord[0], coord[1])
#print aentry
lentry = grid.get_matrix_value(node.get_node_id(), endpt)[0]
aentry = grid.get_matrix_value(node.get_node_id(),
endpt)[1] / float(len(Coord))
h1[i] += c * aentry + w * lentry
return h1
def dvector(grid, data):
#build_matrix_fem_2D(grid, Poisson_tri_integrate, TPS_tri_intergrateX, TPS_tri_intergrateY, X, Y)
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
dvector = zeros([len(Nl), 1])
for tri in Interior_triangle_iterator(grid):
if tri[1].get_node_id() < tri[2].get_node_id():
basis1 = set_polynomial_linear_2D(tri[0], tri[2], tri[1])
Idi = int(tri[0].get_value())
for i in range(len(Coord)):
if NIn_triangle(tri[0], tri[1], tri[2], Coord[i]):
dvector[Idi, 0] += basis1.eval(Coord[i][0],
Coord[i][1]) * data[i]
return dvector / float(len(Coord))
def Amatrix(grid):
# node.set_value(Nl.index(node))
#
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
Amatrix = csr_matrix((len(Nl), len(Nl)))
for node in node_iterator(grid):
if not node.get_slave():
idi = int(node.get_value())
#print idi, node.get_coord()
#print node.get_value(), node.get_node_id()._id_no
for endpt in connect_iterator(grid, node.get_node_id()):
idj = int(grid.get_value(endpt))
#print idj, grid.get_coord(endpt)
#print endpt._id_no, grid.get_value(endpt)
aentry = grid.get_matrix_value(node.get_node_id(), endpt)[1]
#print aentry
if not grid.get_slave(endpt):
Amatrix[idi, idj] = aentry
return Amatrix / float(len(Coord))
def Lets_Make_the_Damn_Big_Matrix():
Nl=[]
for node in (not_slave_node(grid)):
Nl.append([node,node.get_node_id()])
Nl=sorted(Nl, key = itemgetter(1))
Nl=[node[0] for node in Nl]
ZeroMatrix = csr_matrix((len(Nl),len(Nl)))
BigMat = bmat([[Amatrix, ZeroMatrix, ZeroMatrix, Lmatrix],\
[ZeroMatrix, alpha*Lmatrix, ZeroMatrix, G1.T],\
[ZeroMatrix, ZeroMatrix, alpha*Lmatrix, G2.T],\
[Lmatrix, G1, G2, ZeroMatrix]])
return BigMat
def Lets_Make_the_Damn_Big_Matrix():
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
BigMat = bmat([[Amatrix, None, None, math.sqrt(alpha)*Lmatrix],\
[None, Lmatrix, None, -G1.T],\
[None, None, Lmatrix, -G2.T],\
[math.sqrt(alpha)*Lmatrix, -G1, -G2, None]])
return BigMat
def h3_bd(grid, g2rhs, wrhs, alpha, Nl): # Nl = 0
#
# for node in node_iterator(grid):
#
# if not node.get_slave():
#
# node.set_value(Nl)
#
# Nl = Nl+1
h3 = np.zeros((len(Nl), ))
for node in not_slave_node(grid):
# Ignore slave (or boundary) nodes
# Which row corresponds to the current node?
i = int(node.get_value())
for endpt in connect_iterator(grid, node.get_node_id()):
if grid.get_slave(endpt):
coord = grid.get_coord(endpt)
g2 = g2rhs(coord[0], coord[1])
w = -alpha * wrhs(coord[0], coord[1])
#print c, w
#print endpt._id_no
lentry = grid.get_matrix_value(node.get_node_id(), endpt)[0]
# G2 entries on boundary
g2entry = grid.get_matrix_value(node.get_node_id(), endpt)[3]
#print aentry
#h3[i] += alpha * g2* lentry - w* g2entry # G1, G2
h3[i] += alpha * g2 * lentry + w * g2entry # -G1, -G2
return h3
def generate_dmatrix():
""" This rountine gernerates dmatrix after deducted boundary conditions
"""
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
dmatrix = zeros([len(Nl), 1])
#print Amatrix
for tri in Interior_triangle_iterator(grid):
if (tri[1].get_node_id() < tri[2].get_node_id()):
#print tri[0]
#print tri[0].get_node_id()._id_no, tri[1].get_node_id()._id_no, tri[2].get_node_id()._id_no
basis1 = set_polynomial_linear_2D(tri[0], tri[2], tri[1])
Idi = int(tri[0].get_value())
for i in range(len(Coord)):
if NIn_triangle(tri[0], tri[1], tri[2], Coord[i]):
#print basis1.eval(Coord[i][0], Coord[i][1]), data[i]
dmatrix[Idi, 0] += basis1.eval(Coord[i][0],
Coord[i][1]) * data[i]
#print dmatrix[Idi,0]
#print dmatrix/float(len(Coord))
return dmatrix / float(len(Coord))
def G2(grid):
#build_matrix_fem_2D(grid, Poisson_tri_integrate, TPS_tri_intergrateX, TPS_tri_intergrateY, X, Y)
Nl=[]
for node in (not_slave_node(grid)):
Nl.append([node,node.get_node_id()])
Nl=sorted(Nl, key = itemgetter(1))
Nl=[node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
G2 = csr_matrix((len(Nl), len(Nl)))
for node in node_iterator(grid):
# Ignore slave (or boundary) nodes
if not node.get_slave():
# Which row corresponds to the current node?
i = int(node.get_value())
for endpt1 in connect_iterator(grid, node.get_node_id()):
# Which column corresponds to the current node?
j = int(grid.get_value(endpt1))
# What is the corresponding matrix value (in the FEM grid)
g2 = grid.get_matrix_value(node.get_node_id(), endpt1)[3]
# We must not include slave nodes in the matrix columns
if not grid.get_slave(endpt1):
G2[i, j] = g2
return G2
def Lmatrix(grid):
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
#
Lmatrix = lil_matrix((len(Nl), len(Nl)))
for node in node_iterator(grid):
# Ignore slave (or boundary) nodes
if not node.get_slave():
# Which row corresponds to the current node?
i = int(node.get_value())
for endpt1 in connect_iterator(grid, node.get_node_id()):
# Which column corresponds to the current node?
j = int(grid.get_value(endpt1))
# What is the corresponding matrix value (in the FEM grid)
lentry = grid.get_matrix_value(node.get_node_id(), endpt1)[0]
# We must not include slave nodes in the matrix columns
if not grid.get_slave(endpt1):
Lmatrix[i, j] = lentry
return Lmatrix
def generate_XGmatrix():
build_equation_linear_2D(grid, TPS_tri_intergrateX, zero)
Nl = []
for node in (not_slave_node(grid)):
#print(i)
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
XGmatrix = zeros([len(Nl), len(Nl)])
for node in node_iterator(grid):
# Ignore slave (or boundary) nodes
if not node.get_slave():
# Which row corresponds to the current node?
i = int(node.get_value())
for endpt1 in connect_iterator(grid, node.get_node_id()):
# Which column corresponds to the current node?
j = int(grid.get_value(endpt1))
# What is the corresponding matrix value (in the FEM grid)
stiffness = grid.get_matrix_value(node.get_node_id(),
endpt1)[0]
# We must not include slave nodes in the matrix columns
if not grid.get_slave(endpt1):
XGmatrix[i, j] = stiffness
return XGmatrix
def h4_bd(grid, Crhs, g1rhs, g2rhs, Nl):
h4 = np.zeros((len(Nl), ))
for node in not_slave_node(grid):
# Which row corresponds to the current node?
i = int(node.get_value())
for endpt in connect_iterator(grid, node.get_node_id()):
if grid.get_slave(endpt):
coord = grid.get_coord(endpt)
c = Crhs(coord[0], coord[1])
g1 = g1rhs(coord[0], coord[1])
g2 = g2rhs(coord[0], coord[1])
#print c
#print endpt._id_no
lentry = grid.get_matrix_value(node.get_node_id(), endpt)[0]
g1entry = grid.get_matrix_value(node.get_node_id(), endpt)[2]
g2entry = grid.get_matrix_value(node.get_node_id(), endpt)[3]
#print aentry
#h4[i] += c* lentry + g1entry * g1 + g2entry * g2 # G1, G2
h4[i] += c * lentry - g1entry * g1 - g2entry * g2 # -G1, -G2
#print h4
return h4
def h1_bd(grid, Crhs, wrhs, alpha, Nl, Coord):
h1 = np.zeros((len(Nl), ))
for node in not_slave_node(grid):
# Ignore slave (or boundary) nodes
# Which row corresponds to the current node?
i = int(node.get_value())
#print node.get_value(), node.get_node_id()._id_no
for endpt in connect_iterator(grid, node.get_node_id()):
#j = int(grid.get_value(endpt))
#print j
if grid.get_slave(endpt):
coord = grid.get_coord(endpt)
c = Crhs(coord[0], coord[1])
w = -alpha * wrhs(coord[0], coord[1])
#print aentry
lentry = grid.get_matrix_value(node.get_node_id(), endpt)[0]
aentry = grid.get_matrix_value(node.get_node_id(),
endpt)[1] / float(len(Coord))
# print node.get_node_id()._id_no, endpt._id_no, aentry, c
h1[i] += c * aentry + w * lentry
return h1
def h2_bd(grid, g1rhs, wrhs, alpha, Nl):
h2 = np.zeros((len(Nl), ))
for node in not_slave_node(grid):
# Ignore slave (or boundary) nodes
# Which row corresponds to the current node?
i = int(node.get_value())
for endpt in connect_iterator(grid, node.get_node_id()):
if grid.get_slave(endpt):
coord = grid.get_coord(endpt)
#print coord
g1 = g1rhs(coord[0], coord[1])
#print g1
w = -alpha * wrhs(coord[0], coord[1])
#print endpt._id_no
lentry = grid.get_matrix_value(node.get_node_id(), endpt)[0]
g1entry = grid.get_matrix_value(node.get_node_id(), endpt)[2]
#print aentry
#h2[i] += alpha * g1 * lentry - w * g1entry #G1, G2
h2[i] += alpha * g1 * lentry + w * g1entry #-G1, -G2
return h2
def Setup_Grid(i):
#from quick_d import dvector
global grid, Coord, Nl, h, Crhs, g1rhs, g2rhs, wrhs, data, intx, inty, nodes, quick_d
x = np.linspace(0, 1.0, 50)
y = np.linspace(0, 1.0, 50)
X, Y = np.meshgrid(x, y)
Z2 = Exy(X, Y)
data = Z2.flatten()
coordx = X.flatten()
coordy = Y.flatten()
Coord = zip(coordx, coordy)
grid = Grid()
n = 2**i + 1
h = 1 / float(n - 1)
intx, inty = np.meshgrid(np.arange(h, 1, h), np.arange(h, 1, h))
x1, y1 = np.meshgrid(np.arange(0, 1 + h, h), np.arange(0, 1 + h, h))
nodes = np.vstack([x1.ravel(), y1.ravel()]).T
true_soln = zero
# Boundares
Crhs = Exy
g1rhs = Xexy
g2rhs = Yexy
wrhs = XYexy
# Build node-eged structure that allows the connection
build_square_grid(n, grid, true_soln)
# Store the matrices values on grid nodes
build_matrix_fem_2D(grid, Poisson_tri_integrate, TPS_tri_intergrateX,
TPS_tri_intergrateY, X, Y)
# Set value for only interior node.
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
#print 'Start sort'
#Sort by node id.
Nl = sorted(Nl, key=itemgetter(1))
#print 'Finish sort'
#print 'START MAKE_LIST'
Nl = [node[0] for node in Nl]
#print 'END MAKE_LIST'
#print 'START SETVALUE'
for node in Nl:
node.set_value(Nl.index(node))
wrhs = XYexy
#
#
#
build_square_grid(n, grid, true_soln)
#
build_matrix_fem_2D(grid, Poisson_tri_integrate, TPS_tri_intergrateX, TPS_tri_intergrateY, X, Y)
Nl=[]
for node in (not_slave_node(grid)):
Nl.append([node,node.get_node_id()])
Nl=sorted(Nl, key = itemgetter(1))
Nl=[node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
#
def generate_Amatrix():
Nl = []
for node in (not_slave_node(grid)):
Nl.append([node, node.get_node_id()])
Nl = sorted(Nl, key=itemgetter(1))
Nl = [node[0] for node in Nl]
for node in Nl:
node.set_value(Nl.index(node))
Amatrix = zeros([len(Nl), len(Nl)])
#plot_fem_grid(grid)
for node in node_iterator(grid):
if not node.get_slave():
print node.get_node_id()._id_no, node.get_value()
for tri in Interior_triangle_iterator(grid):
if (tri[1].get_node_id() < tri[2].get_node_id()):
#print tri[0].get_node_id()._id_no, tri[1].get_node_id()._id_no, tri[2].get_node_id()._id_no
basis1 = set_polynomial_linear_2D(tri[0], tri[2], tri[1])
basis2 = set_polynomial_linear_2D(tri[1], tri[2], tri[0])
basis3 = set_polynomial_linear_2D(tri[2], tri[1], tri[0])
for i in Coord:
if NIn_triangle(tri[0], tri[1], tri[2], i):
#print In_triangle(tri[0] , tri[1], tri[2], i)
#print tri[0].get_node_id()._id_no, tri[1].get_node_id()._id_no, tri[2].get_node_id()._id_no, i,\
#tri[0].get_coord(), tri[1].get_coord(), tri[2].get_coord()
Idi = int(tri[0].get_value())
Amatrix[Idi, Idi] += basis1.eval(i[0], i[1]) * basis1.eval(
i[0], i[1])
if not tri[1].get_slave():
#print tri[1].get_node_id()._id_no, tri[1].get_value()
#print tri[1].get_value()
Idj = int(tri[1].get_value())
Amatrix[Idi,
Idj] += basis1.eval(i[0], i[1]) * basis2.eval(
i[0], i[1])
if not tri[2].get_slave():
#print tri[2].get_node_id()._id_no
Idk = int(tri[2].get_value())
Amatrix[Idi,
Idk] += basis1.eval(i[0], i[1]) * basis3.eval(
i[0], i[1])
# Remove the data once it's been used
#Coord.remove(i)
#
return Amatrix / float(len(Coord))