scimba_torch.physical_models.kinetic_pde.abstract_kinetic_pde

Abstract models for kinetic and collisional EDPs.

Classes

CollisionalKineticPDE(space[, field, linear])	Base class for collisional kinetic PDEs.
KineticPDE(space[, field, linear])	Base class for representing elliptic Partial Differential Equations (PDEs).

class KineticPDE(space, field=None, linear=False, **kwargs)

Bases: ABC

Base class for representing elliptic Partial Differential Equations (PDEs).

Parameters:

• space (AbstractApproxSpace) – Approximation space used for the PDE

• field (EllipticPDE | TemporalPDE | None) – Associated field

• linear (bool) – Indicates if the PDE is linear

• **kwargs – Additional keyword arguments

time_operator(w, t, x, mu)

Compute the time derivative of the tensor w with respect to the tensor t.

Parameters:

• w (MultiLabelTensor) – Input tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Time derivative tensor

Raises:

NotImplementedError – If not implemented in subclass.

abstract rhs(w, t, x, v, mu)

Compute the right-hand side (RHS) of the PDE.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

RHS tensor

abstract space_operator(w, t, x, v, mu)

Apply the PDE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Operator tensor

abstract bc_rhs(w, t, x, v, n, mu)

Compute the boundary condition RHS.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• n (LabelTensor) – Normal vector tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Boundary condition RHS tensor

abstract bc_operator(w, t, x, v, n, mu)

Apply the boundary condition operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• n (LabelTensor) – Normal vector tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Boundary condition operator tensor

abstract initial_condition(x, v, mu)

Compute the initial condition.

Parameters:

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Initial condition tensor

class CollisionalKineticPDE(space, field=None, linear=False, **kwargs)

Bases: KineticPDE

Base class for collisional kinetic PDEs.

Parameters:

• space (AbstractApproxSpace) – Approximation space used for the PDE

• field (EllipticPDE | TemporalPDE | None) – Associated field

• linear (bool) – Indicates if the PDE is linear

• **kwargs – Additional keyword arguments

abstract rhs(w, t, x, v, mu)

Compute the right-hand side (RHS) of the PDE.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

RHS tensor

abstract space_operator(w, t, x, v, mu)

Apply the PDE operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Operator tensor

abstract bc_rhs(w, t, x, v, n, mu)

Compute the boundary condition RHS.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• n (LabelTensor) – Normal vector tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Boundary condition RHS tensor

abstract bc_operator(w, t, x, v, n, mu)

Apply the boundary condition operator.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• n (LabelTensor) – Normal vector tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Boundary condition operator tensor

abstract initial_condition(x, v, mu)

Compute the initial condition.

Parameters:

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Initial condition tensor

abstract collision_kernel(w, t, x, v, mu)

Compute the collision kernel for the PDE.

Parameters:

• w (MultiLabelTensor) – Solution tensor

• t (LabelTensor) – Temporal coordinate tensor

• x (LabelTensor) – Spatial coordinate tensor

• v (LabelTensor) – Velocity coordinate tensor

• mu (LabelTensor) – Parameter tensor

Return type:

Tensor

Returns:

Collision kernel tensor