Equation Factory#

class FixedValue(value, components=None)[source]#

Bases: Equation

Equation to enforce a fixed value. Can be used to enforce Dirichlet Boundary conditions.

Initialization of the FixedValue class.

Parameters:

  • value (float) – The fixed value to be enforced.

  • components (list[str]) – The name of the output variables for which the fixed value condition is applied. It should be a subset of the output labels. If None, all output variables are considered. Default is None.

class FixedGradient(value, components=None, d=None)[source]#

Bases: Equation

Equation to enforce a fixed gradient for a specific condition.

Initialization of the FixedGradient class.

Parameters:

  • value (float) – The fixed value to be enforced to the gradient.

  • components (list[str]) – The name of the output variables for which the fixed gradient condition is applied. It should be a subset of the output labels. If None, all output variables are considered. Default is None.

  • d (list[str]) – The name of the input variables on which the gradient is computed. It should be a subset of the input labels. If None, all the input variables are considered. Default is None.

class FixedFlux(value, components=None, d=None)[source]#

Bases: Equation

Equation to enforce a fixed flux, or divergence, for a specific condition.

Initialization of the FixedFlux class.

Parameters:

  • value (float) – The fixed value to be enforced to the flux.

  • components (list[str]) – The name of the output variables for which the fixed flux condition is applied. It should be a subset of the output labels. If None, all output variables are considered. Default is None.

  • d (list[str]) – The name of the input variables on which the flux is computed. It should be a subset of the input labels. If None, all the input variables are considered. Default is None.

class FixedLaplacian(value, components=None, d=None)[source]#

Bases: Equation

Equation to enforce a fixed laplacian for a specific condition.

Initialization of the FixedLaplacian class.

Parameters:

  • value (float) – The fixed value to be enforced to the laplacian.

  • components (list[str]) – The name of the output variables for which the fixed laplace condition is applied. It should be a subset of the output labels. If None, all output variables are considered. Default is None.

  • d (list[str]) – The name of the input variables on which the laplacian is computed. It should be a subset of the input labels. If None, all the input variables are considered. Default is None.

class Laplace(components=None, d=None)[source]#

Bases: FixedLaplacian

Equation to enforce a null laplacian for a specific condition. The equation is defined as follows:

\[\delta u = 0\]

Initialization of the Laplace class.

Parameters:

  • components (list[str]) – The name of the output variables for which the null laplace condition is applied. It should be a subset of the output labels. If None, all output variables are considered. Default is None.

  • d (list[str]) – The name of the input variables on which the laplacian is computed. It should be a subset of the input labels. If None, all the input variables are considered. Default is None.

class Advection(c)[source]#

Bases: Equation

Implementation of the N-dimensional advection equation with constant velocity parameter. The equation is defined as follows:

\[\frac{\partial u}{\partial t} + c \cdot \nabla u = 0\]

Here, \(c\) is the advection velocity parameter.

Initialization of the Advection class.

Parameters:

c (float | int | List[float] | List[int]) – The advection velocity. If a scalar is provided, the same velocity is applied to all spatial dimensions. If a list is provided, it must contain one value per spatial dimension.

Raises:

ValueError – If c is an empty list.

class AllenCahn(alpha, beta)[source]#

Bases: Equation

Implementation of the N-dimensional Allen-Cahn equation, defined as follows:

\[\frac{\partial u}{\partial t} - \alpha \Delta u + \beta(u^3 - u) = 0\]

Here, \(\alpha\) and \(\beta\) are parameters of the equation.

Initialization of the AllenCahn class.

Parameters:

  • alpha (float | int) – The diffusion coefficient.

  • beta (float | int) – The reaction coefficient.

class DiffusionReaction(alpha, forcing_term)[source]#

Bases: Equation

Implementation of the N-dimensional Diffusion-Reaction equation, defined as follows:

\[\frac{\partial u}{\partial t} - \alpha \Delta u - f = 0\]

Here, \(\alpha\) is a parameter of the equation, while \(f\) is the reaction term.

Initialization of the DiffusionReaction class.

Parameters:

  • alpha (float | int) – The diffusion coefficient.

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

class Helmholtz(k, forcing_term)[source]#

Bases: Equation

Implementation of the Helmholtz equation, defined as follows:

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

Here, \(k\) is a parameter of the equation, while \(f\) is the forcing term.

Initialization of the Helmholtz class.

Parameters:

  • k (float | int) – The parameter of the equation.

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

class Poisson(forcing_term)[source]#

Bases: Equation

Implementation of the Poisson equation, defined as follows:

\[\Delta u - f = 0\]

Here, \(f\) is the forcing term.

Initialization of the Poisson class.

Parameters:

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