FEMDocumentation`
FEMDocumentation`

InitializeBoundaryConditions

InitializeBoundaryConditions[vd,sd,{{bc11,},{bc21,},}]

initializes the system of boundary conditions beqni in accordance with variable data vd and solution data sd to generate a BoundaryConditionData object.

Details and OptionsDetails
  • The boundary conditions bcij can either be DirichletCondition or NeumannValue.
  • The i^(th) set of boundary conditions bcij is associated with the i^(th) equation from:
  • sum_(j=1)^idel .(-c_(1j)del u_j+alpha_(1j)u_j-gamma_(1))+beta_(1j)del u_j+a_(1j)u_j-f_1=0 ; ... ; sum_(j=1)^idel .(-c_(ij)del u_j+alpha_(ij)u_j-gamma_(i))+beta_(ij)del u_j+a_(ij)u_j-f_i=0 ; ...
  • The boundary conditions can be functions of space and time.
  • Variable data vd and solution data sd are corresponding lists of variables and values. Templates for vd and sd may be generated using NDSolve`VariableData and NDSolve`SolutionData, and components may be set using NDSolve`SetSolutionDataComponent.
  • InitializeBoundaryConditions verifies and optimizes the boundary conditions in accordance with variable data vd and solution data sd.
  • The "Space" component of vd and sd should be set to the spatial variables and the spatial mesh represented as a NumericalRegion object, respectively.
  • The "DependentVariables" component of vd should be set to the list of unknown function names without arguments.
  • For time-dependent problems, the "Time" component of vd and sd should be set to the temporal variable and the initial time, respectively.
  • For parametric problems, the "Parameters" component of vd and sd should be set to the parametric variables and the initial parametric values, respectively.
  • The following options can be given:
  • "BoundaryTolerance"Automatictolerance for boundary condition predicate
    "ScaleFactor"Automaticscaling factor for transient handling of Dirichlet boundary conditions
  • Examples

    open allclose all

    Basic Examples  (1)

    Load the finite element package:

    In[1]:=
    Click for copyable input

    Set up a NumericalRegion:

    In[2]:=
    Click for copyable input
    Out[2]=

    Set up variable and solution data:

    In[3]:=
    Click for copyable input

    Initialize a boundary condition:

    In[4]:=
    Click for copyable input
    Out[4]=

    Scope  (2)

    See Also

    DirichletCondition  NeumannValue  BoundaryConditionData  InitializePDEMethodData  InitializePDEMethodData  DiscretizeBoundaryConditions  DeployBoundaryConditions  ToNumericalRegion  ToElementMesh

    Tutorials