esys.escript.linearPDEs.LameEquation

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

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Type LameEquation

object --+    
         |    
 LinearPDE --+
             |
            LameEquation

Class to define a Lame equation problem:

-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 conditons:

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

Method Summary
	`__init__(self, domain, debug)`
`Data`	`getCoefficientOfGeneralPDE(self, name)` return the value of the coefficient name of the general PDE
	`setValues(self, **coefficients)` sets new values to coefficients
Inherited from LinearPDE
`str`	`__str__(self)` returns string representation of the PDE
	`alteredCoefficient(self, name)` announce that coefficient name has been changed
`Data`	`applyOperator(self, u)` applies the operator of the PDE to a given u or the solution of PDE if u is not present.
`Data`	`checkSymmetry(self, verbose)` test the PDE for symmetry.
`Data`	`copyConstraint(self, u)` copies the constraint into u and returns u.
`Data`	`createCoefficient(self, name)` create a `Data` object corresponding to coefficient name
`Data`	`createCoefficientOfGeneralPDE(self, name)` returns a new instance of a coefficient for coefficient name of the general PDE
`Data`	`getCoefficient(self, name)` returns the value of the coefficient name
`int`	`getDim(self)` returns the spatial dimension of the PDE
`Domain`	`getDomain(self)` returns the domain of the PDE
`Data`	`getFlux(self, u)` returns the flux J for a given u
`FunctionSpace`	`getFunctionSpaceForCoefficient(self, name)` return the `FunctionSpace` to be used for coefficient name
`FunctionSpace`	`getFunctionSpaceForCoefficientOfGeneralPDE(self, name)` return the `FunctionSpace` to be used for coefficient name of the general PDE
`FunctionSpace`	`getFunctionSpaceForEquation(self)` returns the `FunctionSpace` used to discretize the equation
`FunctionSpace`	`getFunctionSpaceForSolution(self)` returns the `FunctionSpace` used to represent the solution
`int`	`getNumEquations(self)` returns the number of equations
`int`	`getNumSolutions(self)` returns the number of unknowns
`Operator`	`getOperator(self)` provides access to the operator of the PDE
`Data`	`getResidual(self, u)` return the residual of u or the current solution if u is not present.
`Data`	`getRightHandSide(self)` provides access to the right hand side of the PDE
`tuple` of `int`	`getShapeOfCoefficient(self, name)` return the shape of the coefficient name
`tuple` of `int`	`getShapeOfCoefficientOfGeneralPDE(self, name)` return the shape of the coefficient name of the general PDE
`Data`	`getSolution(self, **options)` returns the solution of the PDE.
`int`	`getSolverMethod(self)` returns the solver method
`string`	`getSolverMethodName(self)` returns the name of the solver currently used
`int`	`getSolverPackage(self)` returns the package of the solver
`tuple` of `Operator,` and `Data`.	`getSystem(self)` return the operator and right hand side of the PDE
`float`	`getTolerance(self)` returns the tolerance set for the solution
`bool`	`hasCoefficient(self, name)` return True if name is the name of a coefficient
`bool`	`hasCoefficientOfGeneralPDE(self, name)` checks if name is a the name of a coefficient of the general PDE.
`bool`	`isSymmetric(self)` checks if symmetry is indicated.
`bool`	`isUsingLumping(self)` checks if matrix lumping is used a solver method
`bool`	`reduceEquationOrder(self)` return status for order reduction for equation
`bool`	`reduceSolutionOrder(self)` return status for order reduction for the solution
	`resetCoefficients(self)` resets all coefficients to there default values.
	`setDebugOff(self)` switches off debugging
	`setDebugOn(self)` switches on debugging
	`setReducedOrderForEquationOff(self)` switches off reduced order for equation representation
	`setReducedOrderForEquationOn(self)` switches on reduced order for equation representation
	`setReducedOrderForEquationTo(self, flag)` sets order for test functions according to flag
	`setReducedOrderForSolutionOff(self)` switches off reduced order for solution representation
	`setReducedOrderForSolutionOn(self)` switches on reduced order for solution representation
	`setReducedOrderForSolutionTo(self, flag)` sets order for test functions according to flag
	`setReducedOrderOff(self)` switches off reduced order for solution and equation representation
	`setReducedOrderOn(self)` switches on reduced order for solution and equation representation
	`setReducedOrderTo(self, flag)` sets order reduction for both solution and equation representation according to flag.
	`setSolverMethod(self, solver, preconditioner)` sets a new solver
	`setSolverPackage(self, package)` sets a new solver package
	`setSymmetryOff(self)` removes the symmetry flag.
	`setSymmetryOn(self)` sets the symmetry flag.
	`setSymmetryTo(self, flag)` sets the symmetry flag to flag
	`setTolerance(self, tol)` resets the tolerance for the solver method to tol where for an appropriate norm \|.\|
	`setValue(self, **coefficients)` sets new values to coefficients
	`trace(self, text)` print the text message if debugging is swiched on.
Inherited from object
	`__delattr__(...)` x.__delattr__('name') <==> del x.name
	`__getattribute__(...)` x.__getattribute__('name') <==> x.name
	`__hash__(x)` x.__hash__() <==> hash(x)
	`__new__(T, S, ...)` T.__new__(S, ...) -> a new object with type S, a subtype of T
	`__reduce__(...)` helper for pickle
	`__reduce_ex__(...)` helper for pickle
	`__repr__(x)` x.__repr__() <==> repr(x)
	`__setattr__(...)` x.__setattr__('name', value) <==> x.name = value

Class Variable Summary
Inherited from LinearPDE
`int`	`AMG`: algebraic multi grid
`int`	`BICGSTAB`: The stabilized BiConjugate Gradient method.
`int`	`CGS`: The conjugate gardient square method
`int`	`CHOLEVSKY`: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
`int`	`CR`: The conjugate residual method
`int`	`DEFAULT`: The default method used to solve the system of linear equations
`int`	`DIRECT`: The direct solver based on LDU factorization
`int`	`GMRES`: The Gram-Schmidt minimum residual method
`int`	`ILU0`: The incomplete LU factorization preconditioner with no fill in
`int`	`ILUT`: The incomplete LU factorization preconditioner with will in
`int`	`ITERATIVE`: The default iterative solver
`int`	`JACOBI`: The Jacobi preconditioner
`int`	`LUMPING`: Matrix lumping.
`int`	`MINIMUM_FILL_IN`: Reorder matrix to reduce fill-in during factorization
`int`	`MKL`: Intel's MKL solver library
`int`	`NESTED_DISSECTION`: Reorder matrix to improve load balancing during factorization
`int`	`NO_REORDERING`: No matrix reordering allowed
`int`	`PASO`: PASO solver package
`int`	`PCG`: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
`int`	`PRES20`: Special GMRES with restart after 20 steps and truncation after 5 residuals
`int`	`RILU`: recursive ILU
`int`	`SCSL`: SGI SCSL solver library
`float`	`SMALL_TOLERANCE` = 1e-13
`int`	`SSOR`: The symmetric overrealaxtion method
`int`	`UMFPACK`: the UMFPACK library

Method Details

getCoefficientOfGeneralPDE(self, name)

return the value of the coefficient name of the general PDE

Parameters:: name - name of the coefficient requested.
(type=string)

Returns:: the value of the coefficient name
(type=Data)

Raises:: IllegalCoefficient - if name is not one of coefficients "A", B, C, D, X, Y, d, y, d_contact, y_contact, r or q.

Overrides:: esys.escript.linearPDEs.LinearPDE.getCoefficientOfGeneralPDE

Note: This method is called by the assembling routine to map the Possion equation onto the general PDE.

setValues(self, **coefficients)

sets new values to coefficients

Parameters:: coefficients - new values assigned to coefficients

Keyword Parameters:: lame_mu - value for coefficient μ
(type=any type that can be casted to Scalar object on Function.); lame_lambda - value for coefficient λ
(type=any type that can be casted to Scalar object on Function.); F - value for internal force F
(type=any type that can be casted to Vector object on Function); sigma - value for initial stress σ
(type=any type that can be casted to Tensor object on Function); f - value for extrenal force f
(type=any type that can be casted to Vector object on FunctionOnBoundary); r - prescribed values r for the solution in constraints.
(type=any type that can be casted to Vector object on Solution or ReducedSolution depending of reduced order is used for the representation of the equation.); q - mask for location of constraints
(type=any type that can be casted to Vector object on Solution or ReducedSolution depending of reduced order is used for the representation of the equation.)

Raises:: IllegalCoefficient - if an unknown coefficient keyword is used.

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