def loadP2(p, t, n, f):
#Compute the matrix with node-edge indices
emi = msh.edgeIndex(p, t)[1]
# Sum up the matrix element mass weighted with the T matrices (the conecction)
return sum(
map(
lambda K: (TP2(t, emi, K).transpose().dot(
elemLoadP2(np.array([p[i - 1] for i in t[K]]), n, f))),
range(0, len(t))))
def massP2(p,t): #Compute the matrix with node-edge indices emi=msh.edgeIndex(p,t)[1] # Sum up the matrix element mass weighted with the T matrices (the conecction) # in lil_matrix format massm=sum(map(lambda K:(TP2(t,emi,K).transpose() .dot(elemMassP2(np.array([p[i-1] for i in t[K]])))) .dot(TP2(t,emi,K).toarray()),range(0,len(t)))) return sparse.lil_matrix(massm)
def massP2(p, t):
#Compute the matrix with node-edge indices
emi = msh.edgeIndex(p, t)[1]
# Sum up the matrix element mass weighted with the T matrices (the conecction)
# in lil_matrix format
massm = sum(
map(
lambda K: (TP2(t, emi, K).transpose().dot(
elemMassP2(np.array([p[i - 1] for i in t[K]])))).dot(
TP2(t, emi, K).toarray()), range(0, len(t))))
return sparse.lil_matrix(massm)
# determine actual max. mesh width mmw[j] = msh.max_mesh_width(p,t); # LINEAR FINITE ELEMENTS # Compute the discretized system: A_lin = FEM.stiffness(p, t); # stiffness-matrix M_lin = FEM.mass(p, t); # mass-matrix F_lin = FEM.load(p, t, 3, f); # load-vector # Solve the discretized system (A + M)u = F: A_lin = A_lin.tocsr(); # conversion from lil to csr format M_lin = M_lin.tocsr(); u_lin = spsolve(A_lin + M_lin, F_lin); eIndex = msh.edgeIndex(p,t) N = p.shape[0]; # Computing the discretized system: A = FEM.stiffnessP2(p,t,eIndex) M = FEM.massP2(p,t,eIndex) F = FEM.loadP2(p,t,eIndex,f,3) # Solving the discretized system (A + M)u = F: A = A.tocsr(); M = M.tocsr(); u = spsolve(A + M, F); # print np.shape(u), 'N= ', N #u = u[0:N]; # Exact solution of the problem:
def loadP2(p,t,n,f): #Compute the matrix with node-edge indices emi=msh.edgeIndex(p,t)[1] # Sum up the matrix element mass weighted with the T matrices (the conecction) return sum(map(lambda K:(TP2(t,emi,K).transpose() .dot(elemLoadP2(np.array([p[i-1] for i in t[K]]),n,f))),range(0,len(t))))