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##############################################################################
#
# Copyright (c) 2003-2018 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
#
##############################################################################
from __future__ import print_function, division
__copyright__="""Copyright (c) 2003-2018 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"
"""
Generic base class for PDE solving tests
"""
from esys.escript import Data, Function, Lsup, Solution, Tensor4, Vector, \
grad, inner, kronecker, matrixmult, whereZero, hasFeature
from esys.escript.linearPDEs import LinearPDE, SolverOptions
import esys.escriptcore.utestselect as unittest
import numpy
HAVE_DIRECT_PASO = hasFeature('paso') and (hasFeature('umfpack') or hasFeature("mkl") or hasFeature("mumps"))
HAVE_MUMPS = hasFeature("mumps")
HAVE_TRILINOS = hasFeature('trilinos')
HAVE_SOLVER = HAVE_DIRECT_PASO or HAVE_TRILINOS
HAVE_SOLVER_COMPLEX = HAVE_TRILINOS or HAVE_MUMPS
class SolveTestCaseTemplate(unittest.TestCase):
"""
this is the template class for testing solvers:
"""
REL_TOL = 1.e-6
SOLVER_VERBOSE = False
SOLVER_TOL = 1.e-8
# the following members must be set by the test methods in subclasses
domain = None
package = None
method = None
preconditioner = SolverOptions.NO_PRECONDITIONER
def getPDE(self, system, iscomplex=False):
dim = self.domain.getDim()
if system:
pde=LinearPDE(self.domain, numEquations=dim, isComplex=iscomplex)
else:
pde=LinearPDE(self.domain, numEquations=1, isComplex=iscomplex)
self.setCoefficients(pde, system)
so = pde.getSolverOptions()
so.setPackage(self.package)
so.setSolverMethod(self.method)
so.setPreconditioner(self.preconditioner)
so.setTolerance(self.SOLVER_TOL)
so.setVerbosity(self.SOLVER_VERBOSE)
pde.setSolverOptions(so)
return pde, self.getSolution(system), self.getGrad(system)
class SolveTestCaseOrder1(SolveTestCaseTemplate):
"""
this is the class for testing solvers for order 1 meshes:
"""
def getGrad(self, system):
"""returns exact gradient"""
dim = self.domain.getDim()
if system:
g_ex = Data(0., (dim,dim), Solution(self.domain))
if dim == 2:
g_ex[0,0] = 2.
g_ex[0,1] = 3.
g_ex[1,0] = 3.
g_ex[1,1] = 2.
else:
g_ex[0,0] = 2.
g_ex[0,1] = 3.
g_ex[0,2] = 4.
g_ex[1,0] = 4.
g_ex[1,1] = 1.
g_ex[1,2] = -2.
g_ex[2,0] = 8.
g_ex[2,1] = 4.
g_ex[2,2] = 5.
else:
g_ex = Data(0., (dim,), Solution(self.domain))
if dim == 2:
g_ex[0] = 2.
g_ex[1] = 3.
else:
g_ex[0] = 2.
g_ex[1] = 3.
g_ex[2] = 4.
return g_ex
def getSolution(self, system):
"""returns exact solution"""
dim = self.domain.getDim()
x = Solution(self.domain).getX()
if system:
u_ex = Vector(0., Solution(self.domain))
if dim == 2:
u_ex[0] = 1.+2.*x[0]+3.*x[1]
u_ex[1] = -1.+3.*x[0]+2.*x[1]
else:
u_ex[0] = 1.+2.*x[0]+3.*x[1]+4.*x[2]
u_ex[1] = -1.+4.*x[0]+1.*x[1]-2.*x[2]
u_ex[2] = 5.+8.*x[0]+4.*x[1]+5.*x[2]
else:
if dim == 2:
u_ex = 1.+2.*x[0]+3.*x[1]
else:
u_ex = 1.+2.*x[0]+3.*x[1]+4.*x[2]
return u_ex
def setCoefficients(self, pde, system):
"""sets PDE coefficients"""
FAC_DIAG = self.FAC_DIAG
FAC_OFFDIAG =self.FAC_OFFDIAG
x = Solution(self.domain).getX()
mask = whereZero(x[0])
dim = self.domain.getDim()
u_ex = self.getSolution(system)
g_ex = self.getGrad(system)
if system:
A = Tensor4(0., Function(self.domain))
for i in range(dim):
A[i,:,i,:] = kronecker(dim)
Y = Vector(0., Function(self.domain))
if dim == 2:
Y[0] = u_ex[0]*FAC_DIAG+u_ex[1]*FAC_OFFDIAG
Y[1] = u_ex[1]*FAC_DIAG+u_ex[0]*FAC_OFFDIAG
else:
Y[0] = u_ex[0]*FAC_DIAG+u_ex[2]*FAC_OFFDIAG+u_ex[1]*FAC_OFFDIAG
Y[1] = u_ex[1]*FAC_DIAG+u_ex[0]*FAC_OFFDIAG+u_ex[2]*FAC_OFFDIAG
Y[2] = u_ex[2]*FAC_DIAG+u_ex[1]*FAC_OFFDIAG+u_ex[0]*FAC_OFFDIAG
pde.setValue(r=u_ex, q=mask*numpy.ones(dim,),
A=A,
D=kronecker(dim)*(FAC_DIAG-FAC_OFFDIAG)+numpy.ones((dim,dim))*FAC_OFFDIAG,
Y=Y,
y=matrixmult(g_ex,self.domain.getNormal()))
else:
pde.setValue(r=u_ex, q=mask, A=kronecker(dim),
y=inner(g_ex, self.domain.getNormal()))
class SolveTestCaseOrder2(SolveTestCaseTemplate):
"""
this is the class for testing solvers for order 2 meshes:
"""
def getGrad(self, system):
"""returns exact gradient"""
dim = self.domain.getDim()
x = Solution(self.domain).getX()
if system:
g_ex = Data(0., (dim,dim), Solution(self.domain))
if dim == 2:
g_ex[0,0] = 2.+8.*x[0]+ 5.*x[1]
g_ex[0,1] = 3.+5.*x[0]+12.*x[1]
g_ex[1,0] = 4.+2.*x[0]+ 6.*x[1]
g_ex[1,1] = 2.+6.*x[0]+ 8.*x[1]
else:
g_ex[0,0] = 2.+6.*x[1]+8.*x[2]+18.*x[0]
g_ex[0,1] = 3.+6.*x[0]+7.*x[2]+20.*x[1]
g_ex[0,2] = 4.+7.*x[1]+8.*x[0]+22.*x[2]
g_ex[1,0] = 4.+3.*x[1]-8.*x[2]- 4.*x[0]
g_ex[1,1] = 1.+3.*x[0]+2.*x[2]+14.*x[1]
g_ex[1,2] = -6.+2.*x[1]-8.*x[0]+10.*x[2]
g_ex[2,0] = 7.-6.*x[1]+2.*x[2]+ 4.*x[0]
g_ex[2,1] = 9.-6.*x[0]+8.*x[2]+16.*x[1]
g_ex[2,2] = 2.+8.*x[1]+2.*x[0]+ 2.*x[2]
else:
g_ex = Data(0., (dim,), Solution(self.domain))
if dim == 2:
g_ex[0] = 2.+8.*x[0]+5.*x[1]
g_ex[1] = 3.+5.*x[0]+12.*x[1]
else:
g_ex[0] = 2.+6.*x[1]+8.*x[2]+18.*x[0]
g_ex[1] = 3.+6.*x[0]+7.*x[2]+20.*x[1]
g_ex[2] = 4.+7.*x[1]+8.*x[0]+22.*x[2]
return g_ex
def getSolution(self, system):
"""returns exact solution"""
dim = self.domain.getDim()
x = Solution(self.domain).getX()
if system:
u_ex = Vector(0., Solution(self.domain))
if dim == 2:
u_ex[0] = 1.+2.*x[0]+3.*x[1]+4.*x[0]**2+5.*x[1]*x[0]+6.*x[1]**2
u_ex[1] = -1.+4.*x[0]+2.*x[1]+1.*x[0]**2+6.*x[1]*x[0]+4.*x[1]**2
else:
u_ex[0] = 1.+2.*x[0]+3.*x[1]+4.*x[2]+\
6.*x[0]*x[1]+7.*x[1]*x[2]+8.*x[2]*x[0]+\
9.*x[0]**2+10.*x[1]**2+11.*x[2]**2
u_ex[1] = 2.+4.*x[0]+1.*x[1]-6.*x[2]+\
3.*x[0]*x[1]+2.*x[1]*x[2]-8.*x[2]*x[0]-\
2.*x[0]**2+7.*x[1]**2+5.*x[2]**2
u_ex[2] = -2.+7.*x[0]+9.*x[1]+2*x[2]-\
6.*x[0]*x[1]+8.*x[1]*x[2]+2.*x[2]*x[0]+\
2.*x[0]**2+8.*x[1]**2+1.*x[2]**2
else:
if dim == 2:
u_ex = 1.+2.*x[0]+3.*x[1]+4.*x[0]**2+5.*x[1]*x[0]+6.*x[1]**2
else:
u_ex = 1.+2.*x[0]+3.*x[1]+4.*x[2]+\
6.*x[0]*x[1]+7.*x[1]*x[2]+8.*x[2]*x[0]+\
9.*x[0]**2+10.*x[1]**2+11.*x[2]**2
return u_ex
def setCoefficients(self, pde, system):
"""sets PDE coefficients"""
FAC_DIAG = self.FAC_DIAG
FAC_OFFDIAG =self.FAC_OFFDIAG
x = Solution(self.domain).getX()
mask = whereZero(x[0])
dim = self.domain.getDim()
u_ex = self.getSolution(system)
g_ex = self.getGrad(system)
if system:
A = Tensor4(0., Function(self.domain))
for i in range(dim):
A[i,:,i,:] = kronecker(dim)
Y = Vector(0., Function(self.domain))
if dim == 2:
Y[0] = u_ex[0]*FAC_DIAG+u_ex[1]*FAC_OFFDIAG-20
Y[1] = u_ex[1]*FAC_DIAG+u_ex[0]*FAC_OFFDIAG-10
else:
Y[0] = u_ex[0]*FAC_DIAG+u_ex[2]*FAC_OFFDIAG+u_ex[1]*FAC_OFFDIAG-60
Y[1] = u_ex[1]*FAC_DIAG+u_ex[0]*FAC_OFFDIAG+u_ex[2]*FAC_OFFDIAG-20
Y[2] = u_ex[2]*FAC_DIAG+u_ex[1]*FAC_OFFDIAG+u_ex[0]*FAC_OFFDIAG-22
pde.setValue(r=u_ex, q=mask*numpy.ones(dim,),
A=A,
D=kronecker(dim)*(FAC_DIAG-FAC_OFFDIAG)+numpy.ones((dim,dim))*FAC_OFFDIAG,
Y=Y,
y=matrixmult(g_ex,self.domain.getNormal()))
else:
pde.setValue(r=u_ex, q=mask, A=kronecker(dim),
y=inner(g_ex, self.domain.getNormal()))
if dim == 2:
pde.setValue(Y=-20.)
else:
pde.setValue(Y=-60.)
class SimpleSolveTestCase(SolveTestCaseOrder1):
"""
testing the real PDEs
"""
FAC_DIAG = 1.
FAC_OFFDIAG = -0.4
def test_single(self):
pde, u_ex, g_ex = self.getPDE(False)
g=grad(u_ex)
self.assertLess(Lsup(g_ex-g), self.REL_TOL*Lsup(g_ex))
u = pde.getSolution()
self.assertFalse(u.isComplex())
self.assertEqual(u.getShape(), ( ))
error = Lsup(u-u_ex)
self.assertLess(error, self.REL_TOL*Lsup(u_ex), "solution error %s is too big."%error)
@unittest.skipIf(not HAVE_SOLVER, "No solver available")
def test_system(self):
pde, u_ex, g_ex = self.getPDE(True)
g = grad(u_ex)
self.assertLess(Lsup(g_ex-g), self.REL_TOL*Lsup(g_ex))
u = pde.getSolution()
self.assertFalse(u.isComplex())
self.assertEqual(u.getShape(), (pde.getDim(), ))
error = Lsup(u-u_ex)
self.assertLess(error, self.REL_TOL*Lsup(u_ex), "solution error %s is too big."%error)
class SimpleSolveTestCaseOrder2(SolveTestCaseOrder2):
"""
testing the real PDEs
"""
FAC_DIAG = 1.
FAC_OFFDIAG = -0.4
def test_single(self):
pde, u_ex, g_ex = self.getPDE(False)
g=grad(u_ex)
self.assertLess(Lsup(g_ex-g), self.REL_TOL*Lsup(g_ex))
u = pde.getSolution()
self.assertFalse(u.isComplex())
self.assertEqual(u.getShape(), ( ))
error = Lsup(u-u_ex)
self.assertLess(error, self.REL_TOL*Lsup(u_ex), "solution error %s is too big."%error)
@unittest.skipIf(not HAVE_SOLVER, "No solver available")
def test_system(self):
pde, u_ex, g_ex = self.getPDE(True)
g = grad(u_ex)
self.assertLess(Lsup(g_ex-g), self.REL_TOL*Lsup(g_ex))
u = pde.getSolution()
error = Lsup(u-u_ex)
self.assertFalse(u.isComplex())
self.assertEqual(u.getShape(), (pde.getDim(), ))
self.assertLess(error, self.REL_TOL*Lsup(u_ex), "solution error %s is too big."%error)
class ComplexSolveTestCase(SolveTestCaseOrder1):
"""
testing the complex PDEs
"""
FAC_DIAG = 1.+0.2j
FAC_OFFDIAG = -0.4
@unittest.skipIf(not HAVE_SOLVER_COMPLEX, "No solver available")
def test_singlecomplex(self):
pde, u_ex, g_ex = self.getPDE(False, iscomplex=True)
g=grad(u_ex)
self.assertLess(Lsup(g_ex-g), self.REL_TOL*Lsup(g_ex))
u = pde.getSolution()
error = Lsup(u-u_ex)
self.assertTrue(u.isComplex())
self.assertEqual(u.getShape(), ())
self.assertLess(error, self.REL_TOL*Lsup(u_ex), "solution error %s is too big."%error)
@unittest.skipIf(not HAVE_SOLVER_COMPLEX, "No solver available")
def test_systemcomplex(self):
pde, u_ex, g_ex = self.getPDE(True, iscomplex=True)
g = grad(u_ex)
self.assertLess(Lsup(g_ex-g), self.REL_TOL*Lsup(g_ex))
u = pde.getSolution()
error = Lsup(u-u_ex)
self.assertTrue(u.isComplex())
self.assertEqual(u.getShape(), (pde.getDim(),))
self.assertLess(error, self.REL_TOL*Lsup(u_ex), "solution error %s is too big."%error)
class ComplexSolveTestCaseOrder2(SolveTestCaseOrder2):
"""
testing the complex PDEs for order 2 meshes
"""
FAC_DIAG = 1.+0.2j
FAC_OFFDIAG = -0.4
@unittest.skipIf(not HAVE_SOLVER_COMPLEX, "No solver available")
def test_singlecomplex(self):
pde, u_ex, g_ex = self.getPDE(False, iscomplex=True)
g=grad(u_ex)
self.assertLess(Lsup(g_ex-g), self.REL_TOL*Lsup(g_ex))
u = pde.getSolution()
self.assertTrue(u.isComplex())
self.assertEqual(u.getShape(), ( ))
error = Lsup(u-u_ex)
self.assertLess(error, self.REL_TOL*Lsup(u_ex), "solution error %s is too big."%error)
@unittest.skipIf(not HAVE_SOLVER_COMPLEX, "No solver available")
def test_systemcomplex(self):
pde, u_ex, g_ex = self.getPDE(True, iscomplex=True)
g = grad(u_ex)
self.assertLess(Lsup(g_ex-g), self.REL_TOL*Lsup(g_ex))
u = pde.getSolution()
error = Lsup(u-u_ex)
self.assertTrue(u.isComplex())
self.assertEqual(u.getShape(), (pde.getDim(), ))
self.assertLess(error, self.REL_TOL*Lsup(u_ex), "solution error %s is too big."%error)
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