Source code for pyOptFEM.valid2D.validMass2DP1

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)')