Package esys :: Package escript :: Module linearPDEs :: Class LameEquation
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Class LameEquation

   object --+        
            |        
LinearProblem --+    
                |    
        LinearPDE --+
                    |
                   LameEquation

Class to define a Lame equation problem. This problem is defined as:

-grad(μ*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(λ*grad(u[k])[k])[j] = F_i -grad(σ[ij])[j]

with natural boundary conditions:

n[j]*(μ*(grad(u[i])[j]+grad(u[j])[i]) + λ*grad(u[k])[k]) = f_i +n[j]*σ[ij]

and constraints:

u[i]=r[i] where q[i]>0

Instance Methods [hide private]
 
__init__(self, domain, debug=False)
Initializes a new Lame equation.
Data
getCoefficient(self, name)
Returns the value of the coefficient name of the general PDE.
 
setValues(self, **coefficients)
Sets new values to coefficients.

Inherited from LinearPDE: __str__, checkSymmetry, createOperator, getFlux, getRequiredOperatorType, getResidual, getSolution, getSystem, insertConstraint, setValue

Inherited from LinearProblem: alteredCoefficient, checkReciprocalSymmetry, checkSymmetricTensor, createCoefficient, createRightHandSide, createSolution, getCurrentOperator, getCurrentRightHandSide, getCurrentSolution, getDim, getDomain, getDomainStatus, getFunctionSpaceForCoefficient, getFunctionSpaceForEquation, getFunctionSpaceForSolution, getNumEquations, getNumSolutions, getOperator, getOperatorType, getRightHandSide, getShapeOfCoefficient, getSolverOptions, getSystemStatus, hasCoefficient, initializeSystem, introduceCoefficients, invalidateOperator, invalidateRightHandSide, invalidateSolution, invalidateSystem, isOperatorValid, isRightHandSideValid, isSolutionValid, isSymmetric, isSystemValid, isUsingLumping, reduceEquationOrder, reduceSolutionOrder, resetAllCoefficients, resetOperator, resetRightHandSide, resetSolution, setDebug, setDebugOff, setDebugOn, setReducedOrderForEquationOff, setReducedOrderForEquationOn, setReducedOrderForEquationTo, setReducedOrderForSolutionOff, setReducedOrderForSolutionOn, setReducedOrderForSolutionTo, setReducedOrderOff, setReducedOrderOn, setReducedOrderTo, setSolution, setSolverOptions, setSymmetry, setSymmetryOff, setSymmetryOn, setSystemStatus, trace, validOperator, validRightHandSide, validSolution

Inherited from object: __delattr__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, domain, debug=False)
(Constructor)

 

Initializes a new Lame equation.

Parameters:
  • domain (Domain) - domain of the PDE
  • debug - if True debug information is printed
Overrides: object.__init__

getCoefficient(self, name)

 

Returns the value of the coefficient name of the general PDE.

Parameters:
  • name (string) - name of the coefficient requested
Returns: Data
the value of the coefficient name
Raises:
Overrides: LinearProblem.getCoefficient

setValues(self, **coefficients)

 

Sets new values to coefficients.

Parameters:
  • coefficients - new values assigned to coefficients
  • lame_mu (any type that can be cast to a Scalar object on Function) - value for coefficient μ
  • lame_lambda (any type that can be cast to a Scalar object on Function) - value for coefficient λ
  • F (any type that can be cast to a Vector object on Function) - value for internal force F
  • sigma (any type that can be cast to a Tensor object on Function) - value for initial stress σ
  • f (any type that can be cast to a Vector object on FunctionOnBoundary) - value for external force f
  • r (any type that can be cast to a Vector object on Solution or ReducedSolution depending on whether reduced order is used for the representation of the equation) - prescribed values r for the solution in constraints
  • q (any type that can be cast to a Vector object on Solution or ReducedSolution depending on whether reduced order is used for the representation of the equation) - mask for the location of constraints
Raises: