import numpy,sympy,time,sys
from ..FEM2D import *
from .common import *
class TestMass:
def __init__(self, cu,cv):
x, y = sympy.symbols('x y')
self.cu=cu
self.cv=cv
self.u=sympy.Lambda((x,y),cu)
self.v=sympy.Lambda((x,y),cv)
self.fu=eval("lambda x,y: "+cu)
self.fv=eval("lambda x,y: "+cv)
if self.u.is_polynomial(x,y):
D=sympy.polys.Poly(cu,x,y).as_dict()
self.du=max(numpy.sum(list(D.keys()),axis=1))
else:
self.du=-1
if self.v.is_polynomial(x,y):
D=sympy.polys.Poly(cv,x,y).as_dict()
self.dv=max(numpy.sum(list(D.keys()),axis=1))
else:
self.dv=-1
self.I=sympy.integrate(sympy.integrate(self.u(x,y)*self.v(x,y),(x,0,1)),(y,0,1))
[docs]def validMass2DP1(**kwargs):
""" Validation of Mass Matrix for P1-Lagrange finite elements in 2D
"""
Plot=kwargs.get('plot',True)
Verbose=kwargs.get('verbose',True)
print('*********************************************')
print('* 2D Mass Assembling P1 validations *')
print('*********************************************')
Th=SquareMesh(10)
LF=[['x+2*y','3*x+y+1'],
['x**2+2*y*x+y','3*x*y+y**2+1'],
['x**3+2*y**2*x+y**2+x','2*x*y+y**3+x*y']]
if Verbose:
print('-----------------------------------------')
print(' Test 1: Matrices errors and CPU times ')
print('-----------------------------------------')
T=numpy.zeros(3)
E=numpy.zeros(2)
tstart=time.time()
Mbase=MassAssembling2DP1base(Th.nq,Th.nme,Th.me,Th.areas)
T[0]=time.time()-tstart
if Verbose:
print(" Matrix size : (%d,%d)" % Mbase.shape)
tstart=time.time()
MOptV1=MassAssembling2DP1OptV1(Th.nq,Th.nme,Th.me,Th.areas)
T[1]=time.time()-tstart
E[0]=NormInf(Mbase-MOptV1)
if Verbose:
print(" Error P1base vs OptV1 : %e" % E[0])
tstart=time.time()
MOptV2=MassAssembling2DP1OptV2(Th.nq,Th.nme,Th.me,Th.areas)
T[2]=time.time()-tstart
E[1]=NormInf(Mbase-MOptV2)
if Verbose:
print(" Error P1base vs OptV2 : %e" % E[1])
print(" CPU times base (ref) : %3.4f (s)" % T[0])
print(" CPU times OptV1 : %3.4f (s) - Speed Up X%3.3f" % (T[1],T[0]/T[1]))
print(" CPU times OptV2 : %3.4f (s) - Speed Up X%3.3f" % (T[2],T[0]/T[2]))
if checkTest1(E)==1:
sys.exit()
if Verbose:
print('-----------------------------------------------------')
print(' Test 2: Validations by integration on [0,1]x[0,1] ')
print('-----------------------------------------------------')
deg=numpy.zeros(len(LF))
E=numpy.zeros(len(LF))
for i in range(len(LF)):
test=TestMass(LF[i][0],LF[i][1])
deg[i]=test.du+test.dv
U=test.fu(Th.q[:,0],Th.q[:,1])
V=test.fv(Th.q[:,0],Th.q[:,1])
Ifem=numpy.dot(Mbase*U,V)
E[i]=numpy.abs(Ifem-test.I)
#print("Test %d: u(x,y)=%s, v(x,y)=%s" %(i,test.cu,test.cv))
#print(" -> error : %e\n" % abs(Ifem-test.I))
if Verbose:
print(" function %d : u(x,y)=%s, v(x,y)=%s,\n -> Mass error=%e" % (i,test.cu,test.cv,E[i]) );
if checkTest2(deg,E)==1:
sys.exit()
if Verbose:
print('--------------------------------')
print(' Test 3: Validations by order ')
print('--------------------------------')
LN=range(10,110,10)
n=len(LN)
h=numpy.zeros(n)
Error=numpy.zeros(n)
k=len(LF)-1
test=TestMass(LF[k][0],LF[k][1])
if Verbose:
print("Functions %d: u(x,y)=%s, v(x,y)=%s" %(k,test.cu,test.cv))
for i in range(n):
Th=SquareMesh(LN[i])
tstart=time.time()
M=MassAssembling2DP1OptV2(Th.nq,Th.nme,Th.me,Th.areas)
TT=time.time()-tstart
U=test.fu(Th.q[:,0],Th.q[:,1])
V=test.fv(Th.q[:,0],Th.q[:,1])
Ifem=numpy.dot(M*U,V)
h[i]=GetMaxLengthEdges(Th.q,Th.me)
Error[i]=numpy.abs(Ifem-test.I)
if Verbose:
print(" Matrix size : (%d,%d)" % M.shape)
print(" MassAssemblingP1OptV2 CPU times : %3.3f(s)" % TT)
print(" Error : %e" % Error[i]);
#print(" N=%d, nq=%d, h=%.5e, Error=%.5e" % (LN[i],Th.nq,h[i],Error[i]))
if checkTest3(h,Error)==1:
sys.exit()
if Plot:
PlotTest3(h,Error,'Test 3 : Mass Matrix (2D/P1)')