NDSolve`FEM`
NDSolve`FEM`

DeployBoundaryConditions

DeployBoundaryConditions[{l,s},dbc]

modifies the vector l and the matrix s such that the discretized boundary conditions dbc take effect.

DeployBoundaryConditions[{l,s,d},dbc]

additionally modifies the matrix d.

DeployBoundaryConditions[{l,s,d,m},dbc]

additionally modifies the matrix m.

Details and Options

  • DeployBoundaryConditions by default does not evaluate its first argument. The first argument should explicitly be a list with elements l, s, d, and m that are explicitly symbols that have assigned values corresponding to vectors and matrices. The values are modified in place according to the discretized boundary conditions so that on return from DeployBoundaryConditions, the symbols will evaluate to the new values.
  • The vector l and the matrices s, d, and m are system matrices and can be obtained from a DiscretizePDE object through the string property "All".
  • The DiscretizedBoundaryConditionData object dbc is generated by DiscretizeBoundaryConditions.
  • DeployBoundaryConditions has the following options:
  • "ConstraintMethod"Automaticwhich method to use to realize the constraints
  • The default constraint method keeps the dimensions of the vectors and matrices the same and modifies the values in them to enforce the constraints.

Examples

Basic Examples  (1)

Load the finite element package:

Set up a NumericalRegion:

Set up variable and solution data:

Initialize the coefficients and boundary conditions:

Initialize the method data:

Discretize the PDE and the boundary conditions:

Extract the system matrices:

Deploy the boundary conditions:

Solve the resulting system of equations:

Wolfram Research (2014), DeployBoundaryConditions, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/DeployBoundaryConditions.html.

Text

Wolfram Research (2014), DeployBoundaryConditions, Wolfram Language function, https://reference.wolfram.com/language/FEMDocumentation/ref/DeployBoundaryConditions.html.

CMS

Wolfram Language. 2014. "DeployBoundaryConditions." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/FEMDocumentation/ref/DeployBoundaryConditions.html.

APA

Wolfram Language. (2014). DeployBoundaryConditions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/FEMDocumentation/ref/DeployBoundaryConditions.html

BibTeX

@misc{reference.wolfram_2024_deployboundaryconditions, author="Wolfram Research", title="{DeployBoundaryConditions}", year="2014", howpublished="\url{https://reference.wolfram.com/language/FEMDocumentation/ref/DeployBoundaryConditions.html}", note=[Accessed: 05-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_deployboundaryconditions, organization={Wolfram Research}, title={DeployBoundaryConditions}, year={2014}, url={https://reference.wolfram.com/language/FEMDocumentation/ref/DeployBoundaryConditions.html}, note=[Accessed: 05-November-2024 ]}