# HelmholtzPDEComponent HelmholtzPDEComponent[vars,pars]

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

# Details  • HelmholtzPDEComponent returns a sum of differential operators to be used as a part of partial differential equations:
• • HelmholtzPDEComponent can be used to model Helmholtz 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 HelmholtzPDEComponent is based on a diffusion and reaction term:
• • The Helmholtz PDE term is realized as a DiffusionPDETerm with 1 as diffusion coefficient and a ReactionPDETerm with coefficient , resulting in .
• The following model parameters pars can be given:
•  parameter default symbol "HelmholtzEigenvalue" 1 "RegionSymmetry" None • The reaction term coefficient is a scalar.
• The reaction term coefficient can depend on time, space, parameters and the dependent variables.
• If the HelmholtzPDEComponent depends on parameters that are specified in the association pars as ,keypi,pivi,], the parameters are replaced with .
• A possible choice for the parameter "RegionSymmetry" is "Axisymmetric".
• "Axisymmetric" region symmetry represents a truncated cylindrical coordinate system where the cylindrical coordinates are reduced by removing the angle variable as follows:
•  dimension reduction equation 1D  2D  • The diffusion coefficient 1 affects the meaning of NeumannValue.
• If the HelmholtzPDEComponent depends on parameters that are specified in the association pars as ,keypi,pivi,, the parameters are replaced with .

# Examples

open allclose all

## Basic Examples(4)

Define a Helmholtz equation:

Activate the equation:

Define a Helmholtz equation with a symbolic coefficient:

Define a Helmholtz equation with an eigenvalue of 2:

Confirm the first eigenvalue of a Helmholtz PDE term specified to have an eigenvalue of 2:

## Scope(1)

Define a 2D axisymmetric Helmholtz equation:

Activate the equation: