def example():
mesh = MeshLine()
mesh.refine(2)
print(mesh.boundary_nodes())
print(mesh.interior_nodes())
# u = np.array([1, 5, 3, 2, 4]) # 在网格节点上的函数值，有顺序
# mesh.plot(u)
# plt.show()
mapping = mesh.mapping() # 对一维没什么内容，重点看二维，三维
tri = MeshTri(initmesh="reftri")
tri.refine(1)
tri.draw()
mapping = tri.mapping() # CONTINUE
pass
def TriP2Test():
"""Test triangular h-refinement.
Also test facet assembly."""
def U(x):
return 1+x[0]-x[0]**2*x[1]**2
def dUdx(x):
return 1-2*x[0]*x[1]**2
def dUdy(x):
return -2*x[0]**2*x[1]
def dudv(du,dv):
return du[0]*dv[0]+du[1]*dv[1]
def uv(u,v):
return u*v
def F(x,y):
return 2*x**2+2*y**2
def fv(v,x):
return F(x[0],x[1])*v
def G(x,y):
return (x==1)*(3-3*y**2)+\
(x==0)*(0)+\
(y==1)*(1+x-3*x**2)+\
(y==0)*(1+x)
def gv(v,x):
return G(x[0],x[1])*v
dexact={}
dexact[0]=dUdx
dexact[1]=dUdy
mesh=MeshTri()
mesh.draw()
mesh.refine(1)
mesh.draw()
hs=np.array([])
H1errs=np.array([])
L2errs=np.array([])
for itr in range(2):
mesh.refine()
a=AssemblerElement(mesh,ElementTriP2())
A=a.iasm(dudv)
f=a.iasm(fv)
B=a.fasm(uv)
g=a.fasm(gv)
u=np.zeros(a.dofnum_u.N)
u=spsolve(A+B,f+g)
hs=np.append(hs,mesh.param())
L2errs=np.append(L2errs,a.L2error(u,U))
H1errs=np.append(H1errs,a.H1error(u,dexact))
# https://docs.scipy.org/doc/numpy-1.15.0/reference/generated/numpy.polyfit.html
pfit=np.polyfit(np.log10(hs),np.log10(H1errs),1)
assert (pfit[0] >= 0.95*2)
