PoissonPDEComponent

PoissonPDEComponent[vars,pars]

yields a Poisson PDE term with model variables vars and model parameters pars.

Details

  • PoissonPDEComponent returns a sum of differential operators to be used as a part of partial differential equations:
  • PoissonPDEComponent can be used to model Poisson equations with dependent variable , independent variables and time variable .
  • Stationary model variables vars are vars={u[x1,,xn],{x1,,xn}}.
  • Time-dependent model variables vars are vars={u[t,x1,,xn],t,{x1,,xn}}.
  • The PoissonPDEComponent is based on a diffusion and source term:
  • The Poisson PDE term is realized as a DiffusionPDETerm with 1 as a diffusion coefficient and a SourcePDETerm with coefficient resulting in .
  • The following model parameters pars can be given:
  • parameterdefaultsymbol
    "PoissonSourceTerm"1
  • The source term coefficient is a scalar.
  • The source term coefficient can depend on time, space, parameters and the dependent variables.
  • If the PoissonPDEComponent depends on parameters that are specified in the association pars as ,keypi,pivi,], the parameters are replaced with .

Examples

Basic Examples  (4)

Define a Poisson PDE component:

Define a Poisson PDE component with a symbolic coefficient:

Find the eigenvalues of a Poisson PDE component:

Solve a Poisson equation:

Visualize the result:

Wolfram Research (2020), PoissonPDEComponent, Wolfram Language function, https://reference.wolfram.com/language/ref/PoissonPDEComponent.html.

Text

Wolfram Research (2020), PoissonPDEComponent, Wolfram Language function, https://reference.wolfram.com/language/ref/PoissonPDEComponent.html.

BibTeX

@misc{reference.wolfram_2020_poissonpdecomponent, author="Wolfram Research", title="{PoissonPDEComponent}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/PoissonPDEComponent.html}", note=[Accessed: 17-April-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_poissonpdecomponent, organization={Wolfram Research}, title={PoissonPDEComponent}, year={2020}, url={https://reference.wolfram.com/language/ref/PoissonPDEComponent.html}, note=[Accessed: 17-April-2021 ]}

CMS

Wolfram Language. 2020. "PoissonPDEComponent." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PoissonPDEComponent.html.

APA

Wolfram Language. (2020). PoissonPDEComponent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PoissonPDEComponent.html