Helmholtz Equation

Module for defining the Helmholtz equation.

class HelmholtzEquation(k, forcing_term)

Bases: Equation

Implementation of the Helmholtz equation, defined as follows:

\[\Delta u + k u - f = 0\]

Here, \(k\) is the squared wavenumber, while \(f\) is the forcing term.

Example:

>>> from pina.equation import HelmholtzEquation
>>> eq = HelmholtzEquation(k=1.0, forcing_term=lambda x: x**2)
>>> # Use within a Condition:
>>> # condition = Condition(domain=domain, equation=eq)

Initialization of the HelmholtzEquation class.

Parameters:

• k (float | int) – The squared wavenumber.

• forcing_term (Callable) – The forcing field function, taking as input the points on which evaluation is required.