def runTest(self):
# solve Poisson by standard P1 method
# and P1(dg) interior penalty method.
#
# this will test interior facet assembly and normal
# vectors.
from spfem.mesh import MeshTri
from spfem.asm import AssemblerElement
from spfem.element import ElementTriP1, ElementTriDG
from spfem.utils import direct
import numpy as np
m = MeshTri()
m.refine(3)
e = ElementTriDG(ElementTriP1())
e1 = ElementTriP1()
a = AssemblerElement(m, e)
a1 = AssemblerElement(m, e1)
b1 = AssemblerElement(m, e1, e)
A = a.iasm(lambda du, dv: du[0]*dv[0] + du[1]*dv[1])
M = a.iasm(lambda u, v: u*v)
b = a.iasm(lambda v, x: np.sin(2.0*np.pi*x[0])*v)
B1 = a.fasm(lambda u1,u2,v1,v2,h: 1/h*(u1-u2)*(v1-v2), interior=True)
B2 = a.fasm(lambda u,v,h: 1/h*u*v)
B=B1+B2
C1 = a.fasm(lambda du1,du2,v1,v2,n: 0.5*(du1[0]*n[0]*v1 - du2[0]*n[0]*v2
+ du1[1]*n[1]*v1 - du2[1]*n[1]*v2), interior=True)
C2 = a.fasm(lambda du,v,n: (du[0]*n[0]+du[1]*n[1])*v)
C=C1+C2
D = C+C.T
eps = 1e-3
eta = 1e5
x = direct(A + eta*B - 0*D, b)
K = a1.iasm(lambda du, dv: du[0]*dv[0] + du[1]*dv[1])
f = a1.iasm(lambda v, x: np.sin(2.0*np.pi*x[0])*v)
y = direct(K, f, I=m.interior_nodes())
P = b1.iasm(lambda u,v: u*v)
self.assertAlmostEqual(np.linalg.norm(x-direct(M,P*y)),0,places=4)
def C2(T):
trT = T[0, 0] + T[1, 1]
return np.array([[2. * mu2 * T[0, 0] + lam2 * trT, 2. * mu2 * T[0, 1]],
[2. * mu2 * T[1, 0], 2. * mu2 * T[1, 1] + lam2 * trT]])
def dudv1(du, dv):
return ddot(C1(Eps(du)), Eps(dv))
def dudv2(du, dv):
return ddot(C2(Eps(du)), Eps(dv))
K1 = a1.iasm(dudv1)
K2 = a2.iasm(dudv2)
B1low = m1.nodes_satisfying(lambda x, y: y == -1.0)
B1up = m1.nodes_satisfying(lambda x, y: (y == 0.0) * (x <= scale) *
(x >= -scale))
B2up = m2.nodes_satisfying(lambda x, y: y == 1.0)
B2low = m2.nodes_satisfying(lambda x, y: y == 0.0)
def glue_dofs(Ax, Ay, bx, by, ix, iy, Ix, Iy):
import scipy.sparse as spsp
indices1 = np.arange(Ax.shape[0])
indices2 = np.arange(Ay.shape[0])
trT=T[0,0]+T[1,1]
return np.array([[2.*mu1*T[0,0]+lam1*trT,2.*mu1*T[0,1]],
[2.*mu1*T[1,0],2.*mu1*T[1,1]+lam1*trT]])
def C2(T):
trT=T[0,0]+T[1,1]
return np.array([[2.*mu2*T[0,0]+lam2*trT,2.*mu2*T[0,1]],
[2.*mu2*T[1,0],2.*mu2*T[1,1]+lam2*trT]])
def dudv1(du,dv):
return ddot(C1(Eps(du)),Eps(dv))
def dudv2(du,dv):
return ddot(C2(Eps(du)),Eps(dv))
K1=a1.iasm(dudv1)
K2=a2.iasm(dudv2)
B1low=m1.nodes_satisfying(lambda x,y:y==-1.0)
B1up=m1.nodes_satisfying(lambda x,y:(y==0.0)*(x<=scale)*(x>=-scale))
B2up=m2.nodes_satisfying(lambda x,y:y==1.0)
B2low=m2.nodes_satisfying(lambda x,y:y==0.0)
def glue_dofs(Ax,Ay,bx,by,ix,iy,Ix,Iy):
import scipy.sparse as spsp
indices1=np.arange(Ax.shape[0])
indices2=np.arange(Ay.shape[0])
ix1=np.setdiff1d(indices1,ix)
ix2=ix
