class SlippingFault(SaddlePointProblem):
"""
simple example of saddle point problem
"""
def __init__(self, domain):
super(SlippingFault, self).__init__(self)
self.domain = domain
self.__pde_u = LinearPDE(domain,
numEquations=self.domain.getDim(),
numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
def initialize(self,
density=1.,
lmbd=1.,
mu=1.,
traction=Data(),
fixed_u_mask=Data(),
slip=0.):
d = self.domain.getDim()
self.slip = slip
A = self.__pde_u.createCoefficientOfGeneralPDE("A")
for i in range(self.domain.getDim()):
for j in range(self.domain.getDim()):
A[i, j, j, i] += mu
A[i, j, i, j] += mu
A[i, i, j, j] += lmbd
self.__pde_u.setValue(A=A,
q=fixed_u_mask,
Y=-kronecker(Function(self.domain))[d - 1] * g *
density,
y=traction)
def inner(self, p0, p1):
return integrate(inner(p0, p1), FunctionOnContactZero(self.domain))
def solve_f(self, u, p, tol=1.e-8):
self.__pde_u.setTolerance(tol)
self.__pde_u.setValue(y_contact=-p)
# print "p:",inf(p),sup(p)
# print "u:",inf(u),sup(u)
self.__pde_u.setValue(y_contact=-p)
return self.__pde_u.getSolution()
def solve_g(self, u, tol=1.e-8):
dp = Vector(0., FunctionOnContactZero(self.domain))
h = FunctionOnContactZero(self.domain).getSize()
# print jump(u)-self.slip
dp[0] = (self.slip[0] - jump(u[0])) * lam_mu / h
dp[1] = (self.slip[1] - jump(u[1])) * lam_mu / h
dp[2] = (self.slip[2] - jump(u[2])) * lam_mu / h
return dp
class StokesProblem(SaddlePointProblem):
"""
simple example of saddle point problem
"""
def __init__(self, domain, debug=False):
super(StokesProblem, self).__init__(self, debug)
self.domain = domain
self.__pde_u = LinearPDE(domain,
numEquations=self.domain.getDim(),
numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
self.__pde_p = LinearPDE(domain)
self.__pde_p.setReducedOrderOn()
self.__pde_p.setSymmetryOn()
def initialize(self, f=Data(), fixed_u_mask=Data(), eta=1):
self.eta = eta
A = self.__pde_u.createCoefficientOfGeneralPDE("A")
for i in range(self.domain.getDim()):
for j in range(self.domain.getDim()):
A[i, j, j, i] += self.eta
A[i, j, i, j] += self.eta
self.__pde_p.setValue(D=1 / self.eta)
self.__pde_u.setValue(A=A, q=fixed_u_mask, Y=f)
def inner(self, p0, p1):
return integrate(p0 * p1, Function(self.__pde_p.getDomain()))
def solve_f(self, u, p, tol=1.e-8):
self.__pde_u.setTolerance(tol)
g = grad(u)
self.__pde_u.setValue(X=self.eta * symmetric(g) +
p * kronecker(self.__pde_u.getDomain()))
return self.__pde_u.getSolution()
def solve_g(self, u, tol=1.e-8):
self.__pde_p.setTolerance(tol)
self.__pde_p.setValue(X=-u)
dp = self.__pde_p.getSolution()
return dp
class SlippingFault(SaddlePointProblem):
"""
simple example of saddle point problem
"""
def __init__(self,domain):
super(SlippingFault, self).__init__(self)
self.domain=domain
self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
def initialize(self,density=1.,lmbd=1., mu=1., traction=Data(),fixed_u_mask=Data(), slip=0.):
d=self.domain.getDim()
self.slip=slip
A =self.__pde_u.createCoefficientOfGeneralPDE("A")
for i in range(self.domain.getDim()):
for j in range(self.domain.getDim()):
A[i,j,j,i] += mu
A[i,j,i,j] += mu
A[i,i,j,j] += lmbd
self.__pde_u.setValue(A=A,q=fixed_u_mask,Y=-kronecker(Function(self.domain))[d-1]*g*density,y=traction)
def inner(self,p0,p1):
return integrate(inner(p0,p1),FunctionOnContactZero(self.domain))
def solve_f(self,u,p,tol=1.e-8):
self.__pde_u.setTolerance(tol)
self.__pde_u.setValue(y_contact=-p)
# print "p:",inf(p),sup(p)
# print "u:",inf(u),sup(u)
self.__pde_u.setValue(y_contact=-p)
return self.__pde_u.getSolution()
def solve_g(self,u,tol=1.e-8):
dp=Vector(0.,FunctionOnContactZero(self.domain))
h=FunctionOnContactZero(self.domain).getSize()
# print jump(u)-self.slip
dp[0]=(self.slip[0]-jump(u[0]))*lam_mu/h
dp[1]=(self.slip[1]-jump(u[1]))*lam_mu/h
dp[2]=(self.slip[2]-jump(u[2]))*lam_mu/h
return dp
class StokesProblem(SaddlePointProblem):
"""
simple example of saddle point problem
"""
def __init__(self,domain,debug=False):
super(StokesProblem, self).__init__(self,debug)
self.domain=domain
self.__pde_u=LinearPDE(domain,numEquations=self.domain.getDim(),numSolutions=self.domain.getDim())
self.__pde_u.setSymmetryOn()
self.__pde_p=LinearPDE(domain)
self.__pde_p.setReducedOrderOn()
self.__pde_p.setSymmetryOn()
def initialize(self,f=Data(),fixed_u_mask=Data(),eta=1):
self.eta=eta
A =self.__pde_u.createCoefficientOfGeneralPDE("A")
for i in range(self.domain.getDim()):
for j in range(self.domain.getDim()):
A[i,j,j,i] += self.eta
A[i,j,i,j] += self.eta
self.__pde_p.setValue(D=1/self.eta)
self.__pde_u.setValue(A=A,q=fixed_u_mask,Y=f)
def inner(self,p0,p1):
return integrate(p0*p1,Function(self.__pde_p.getDomain()))
def solve_f(self,u,p,tol=1.e-8):
self.__pde_u.setTolerance(tol)
g=grad(u)
self.__pde_u.setValue(X=self.eta*symmetric(g)+p*kronecker(self.__pde_u.getDomain()))
return self.__pde_u.getSolution()
def solve_g(self,u,tol=1.e-8):
self.__pde_p.setTolerance(tol)
self.__pde_p.setValue(X=-u)
dp=self.__pde_p.getSolution()
return dp
