Convection

exponax.normalized.NormalizedConvectionStepper

Bases: BaseStepper

Source code in exponax/normalized/_convection.py

class NormalizedConvectionStepper(BaseStepper):
    normalized_coefficients: tuple[float, ...]
    normalized_convection_scale: float
    dealiasing_fraction: float

    def __init__(
        self,
        num_spatial_dims: int,
        num_points: int,
        *,
        normalized_coefficients: tuple[float, ...] = (0.0, 0.0, 0.01 * 0.1),
        normalized_convection_scale: float = 1.0 * 0.1,
        order: int = 2,
        dealiasing_fraction: float = 2 / 3,
        num_circle_points: int = 16,
        circle_radius: float = 1.0,
    ):
        """
        By default: Behaves like a Burgers with

        ``` Burgers(
            D=D, L=1, N=N, dt=0.1, diffusivity=0.01,
        )
        ```
        """
        self.normalized_coefficients = normalized_coefficients
        self.normalized_convection_scale = normalized_convection_scale
        self.dealiasing_fraction = dealiasing_fraction
        super().__init__(
            num_spatial_dims=num_spatial_dims,
            domain_extent=1.0,  # Derivative operator is just scaled with 2 * jnp.pi
            num_points=num_points,
            dt=1.0,
            num_channels=num_spatial_dims,
            order=order,
            num_circle_points=num_circle_points,
            circle_radius=circle_radius,
        )

    def _build_linear_operator(self, derivative_operator: Array) -> Array:
        # Now the linear operator is unscaled
        linear_operator = sum(
            jnp.sum(
                c * (derivative_operator) ** i,
                axis=0,
                keepdims=True,
            )
            for i, c in enumerate(self.normalized_coefficients)
        )
        return linear_operator

    def _build_nonlinear_fun(self, derivative_operator: Array):
        return ConvectionNonlinearFun(
            self.num_spatial_dims,
            self.num_points,
            derivative_operator=derivative_operator,
            dealiasing_fraction=self.dealiasing_fraction,
            scale=self.normalized_convection_scale,
        )

__init__

__init__(
    num_spatial_dims: int,
    num_points: int,
    *,
    normalized_coefficients: tuple[float, ...] = (
        0.0,
        0.0,
        0.01 * 0.1,
    ),
    normalized_convection_scale: float = 1.0 * 0.1,
    order: int = 2,
    dealiasing_fraction: float = 2 / 3,
    num_circle_points: int = 16,
    circle_radius: float = 1.0
)

By default: Behaves like a Burgers with

Burgers( D=D, L=1, N=N, dt=0.1, diffusivity=0.01, )

Source code in exponax/normalized/_convection.py

def __init__(
    self,
    num_spatial_dims: int,
    num_points: int,
    *,
    normalized_coefficients: tuple[float, ...] = (0.0, 0.0, 0.01 * 0.1),
    normalized_convection_scale: float = 1.0 * 0.1,
    order: int = 2,
    dealiasing_fraction: float = 2 / 3,
    num_circle_points: int = 16,
    circle_radius: float = 1.0,
):
    """
    By default: Behaves like a Burgers with

    ``` Burgers(
        D=D, L=1, N=N, dt=0.1, diffusivity=0.01,
    )
    ```
    """
    self.normalized_coefficients = normalized_coefficients
    self.normalized_convection_scale = normalized_convection_scale
    self.dealiasing_fraction = dealiasing_fraction
    super().__init__(
        num_spatial_dims=num_spatial_dims,
        domain_extent=1.0,  # Derivative operator is just scaled with 2 * jnp.pi
        num_points=num_points,
        dt=1.0,
        num_channels=num_spatial_dims,
        order=order,
        num_circle_points=num_circle_points,
        circle_radius=circle_radius,
    )

__call__

__call__(
    u: Float[Array, "C ... N"]
) -> Float[Array, "C ... N"]

Performs a check

Source code in exponax/_base_stepper.py

def __call__(
    self,
    u: Float[Array, "C ... N"],
) -> Float[Array, "C ... N"]:
    """
    Performs a check
    """
    expected_shape = (self.num_channels,) + spatial_shape(
        self.num_spatial_dims, self.num_points
    )
    if u.shape != expected_shape:
        raise ValueError(
            f"Expected shape {expected_shape}, got {u.shape}. For batched operation use `jax.vmap` on this function."
        )
    return self.step(u)