Home       Trees       Indices       Help   
Package esys :: Package escript :: Module flows :: Class StokesProblemCartesian
[hide private]
[frames] | no frames]

Class StokesProblemCartesian

                            object --+    
                                     |    
pdetools.HomogeneousSaddlePointProblem --+
                                         |
                                        StokesProblemCartesian
Known Subclasses:

solves

-(eta*(u_{i,j}+u_{j,i}))_j + p_i = f_i-stress_{ij,j}
u_{i,i}=0

u=0 where fixed_u_mask>0 eta*(u_{i,j}+u_{j,i})*n_j-p*n_i=surface_stress +stress_{ij}n_j

if surface_stress is not given 0 is assumed.

typical usage:

sp=StokesProblemCartesian(domain) sp.setTolerance() sp.initialize(...) v,p=sp.solve(v0,p0) sp.setStokesEquation(...) # new values for some parameters v1,p1=sp.solve(v,p)
Instance Methods [hide private]
float
Bv(self, v, tol)
returns inner product of element p and div(v)
 
__init__(self, domain, **kwargs)
initialize the Stokes Problem
 
getDV(self, p, v, tol)
return the value for v for a given p
SolverOptions
getSolverOptionsDiv(self)
returns the solver options for solving the equation to project the divergence of the velocity onto the function space of presure.
 
getSolverOptionsPressure(self)
returns the solver options used solve the equation for pressure.
SolverOptions
getSolverOptionsVelocity(self)
returns the solver options used solve the equation for velocity.
 
initialize(self, f=<esys.escript.escriptcpp.Data object at 0x1944520>, fixed_u_mask=<esys.escript.escriptcpp.Data object at 0x1944578>, eta=1, surface_stress=<esys.escript.escriptcpp.Data object at 0x19445d0>, stress=<esys.escript.escriptcpp.Data object at 0x1944628>, restoration_factor=0)
assigns values to the model parameters
float
inner_p(self, p0, p1)
Returns inner product of p0 and p1
float
inner_pBv(self, p, Bv)
returns inner product of element p and Bv=-div(v)
equal to the type of p
norm_Bv(self, Bv)
Returns Bv (overwrite).
non-negative float
norm_v(self, v)
returns the norm of v
 
setSolverOptionsDiv(self, options=None)
set the solver options for solving the equation to project the divergence of the velocity onto the function space of presure.
 
setSolverOptionsPressure(self, options=None)
set the solver options for solving the equation for pressure.
 
setSolverOptionsVelocity(self, options=None)
set the solver options for solving the equation for velocity.
 
setStokesEquation(self, f=None, fixed_u_mask=None, eta=None, surface_stress=None, stress=None, restoration_factor=None)
assigns new values to the model parameters.
 
solve_AinvBt(self, p, tol)
Solves Av=B^*p with accuracy tol
equal to the type of p
solve_prec(self, Bv, tol)
applies preconditioner for for BA^{-1}B^* to Bv with accuracy self.getSubProblemTolerance()
 
updateStokesEquation(self, v, p)
updates the Stokes equation to consider dependencies from v and p :note: This method can be overwritten by a subclass.

Inherited from pdetools.HomogeneousSaddlePointProblem: getAbsoluteTolerance, getTolerance, norm_p, resetControlParameters, setAbsoluteTolerance, setControlParameter, setTolerance, solve

Inherited from pdetools.HomogeneousSaddlePointProblem (private): _solve

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

Bv(self, v, tol)

 
returns inner product of element p and div(v)
Parameters:
  • v - a residual
Returns: float
inner product of element p and div(v)
Overrides: pdetools.HomogeneousSaddlePointProblem.Bv

__init__(self, domain, **kwargs)
(Constructor)

 

initialize the Stokes Problem

The approximation spaces used for velocity (=Solution(domain)) and pressure (=ReducedSolution(domain)) must be LBB complient, for instance using quadratic and linear approximation on the same element or using linear approximation with macro elements for the pressure.

Parameters:
  • domain (Domain) - domain of the problem.
Overrides: object.__init__

getDV(self, p, v, tol)

 
return the value for v for a given p
Parameters:
  • p - a pressure
  • v - a initial guess for the value v to return.
Returns:
dv given as Adv=(f-Av-B^*p)
Overrides: pdetools.HomogeneousSaddlePointProblem.getDV

getSolverOptionsPressure(self)

 
returns the solver options used solve the equation for pressure. :rtype: SolverOptions

initialize(self, f=<esys.escript.escriptcpp.Data object at 0x1944520>, fixed_u_mask=<esys.escript.escriptcpp.Data object at 0x1944578>, eta=1, surface_stress=<esys.escript.escriptcpp.Data object at 0x19445d0>, stress=<esys.escript.escriptcpp.Data object at 0x1944628>, restoration_factor=0)

 
assigns values to the model parameters
Parameters:

inner_p(self, p0, p1)

 
Returns inner product of p0 and p1
Parameters:
  • p0 - a pressure
  • p1 - a pressure
Returns: float
inner product of p0 and p1
Overrides: pdetools.HomogeneousSaddlePointProblem.inner_p

inner_pBv(self, p, Bv)

 
returns inner product of element p and Bv=-div(v)
Parameters:
  • p - a pressure increment
  • Bv - a residual
Returns: float
inner product of element p and Bv=-div(v)
Overrides: pdetools.HomogeneousSaddlePointProblem.inner_pBv

norm_Bv(self, Bv)

 
Returns Bv (overwrite).
Returns: equal to the type of p
Overrides: pdetools.HomogeneousSaddlePointProblem.norm_Bv

Note: boundary conditions on p should be zero!

norm_v(self, v)

 
returns the norm of v
Parameters:
  • v - a velovity
Returns: non-negative float
norm of v
Overrides: pdetools.HomogeneousSaddlePointProblem.norm_v

setSolverOptionsDiv(self, options=None)

 
set the solver options for solving the equation to project the divergence of the velocity onto the function space of presure.
Parameters:

setSolverOptionsPressure(self, options=None)

 
set the solver options for solving the equation for pressure. :param options: new solver options :type options: SolverOptions

setSolverOptionsVelocity(self, options=None)

 
set the solver options for solving the equation for velocity.
Parameters:

setStokesEquation(self, f=None, fixed_u_mask=None, eta=None, surface_stress=None, stress=None, restoration_factor=None)

 
assigns new values to the model parameters.
Parameters:

solve_AinvBt(self, p, tol)

 
Solves Av=B^*p with accuracy tol
Parameters:
  • p - a pressure increment
Returns:
the solution of Av=B^*p
Overrides: pdetools.HomogeneousSaddlePointProblem.solve_AinvBt

Note: boundary conditions on v should be zero!

solve_prec(self, Bv, tol)

 
applies preconditioner for for BA^{-1}B^* to Bv with accuracy self.getSubProblemTolerance()
Parameters:
  • Bv - velocity increment
Returns: equal to the type of p
p=P(Bv) where P^{-1} is an approximation of BA^{-1}B^ * )
Overrides: pdetools.HomogeneousSaddlePointProblem.solve_prec

Note: boundary conditions on p are zero.

updateStokesEquation(self, v, p)

 
updates the Stokes equation to consider dependencies from v and p :note: This method can be overwritten by a subclass. Use setStokesEquation to set new values to model parameters.

   Home       Trees       Indices       Help   
Generated by Epydoc 3.0.1 on Sat May 26 00:38:43 2012 http://epydoc.sourceforge.net