LaplacianPDETerm

LaplacianPDETerm[vars]

represents a Laplacian term with model variables vars.

Details

  • The Laplacian term is a differential operator term used to describe many physical phenomena, such as potentials, heat transfer, acoustics, structural mechanics and fluid dynamics.
  • LaplacianPDETerm returns a differential operators term to be used as a part of partial differential equations:
  • LaplacianPDETerm can be used to model Laplacian 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],{x1,…,xn}} or vars={u[t,x1,…,xn],t,{x1,…,xn}}.
  • The Laplacian is realized as a DiffusionPDETerm with –1 as a diffusion coefficient resulting in .
  • The diffusion coefficient –1 affects the meaning of NeumannValue.

Examples

open allclose all

Basic Examples  (2)

Define a stationary Laplacian term:

Find eigenvalues of a Laplacian term:

Scope  (2)

Set up a time-dependent Laplacian:

Find eigenvalues and vectors of a Laplacian term in a 3D shell:

Visualize the result:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_laplacianpdeterm, author="Wolfram Research", title="{LaplacianPDETerm}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/LaplacianPDETerm.html}", note=[Accessed: 18-October-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_laplacianpdeterm, organization={Wolfram Research}, title={LaplacianPDETerm}, year={2020}, url={https://reference.wolfram.com/language/ref/LaplacianPDETerm.html}, note=[Accessed: 18-October-2021 ]}

CMS

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

APA

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