Struct fem_2d::fem_domain::basis::HierCurlBasisFn

pub struct HierCurlBasisFn<BSpace: HierCurlBasisFnSpace> {
    pub jac: Vec<Vec<M2D>>,
    pub jac_inv: Vec<Vec<M2D>>,
    pub det_jac: Vec<Vec<f64>>,
    pub para_scale: V2D,
    /* private fields */
}

A Hierarchical-Type Curl-Conforming Vectorial Basis Function

This basis function has the following vectorial components in the u, v and w directions:

• F_u(u, v, i, j) = N_i(u) * T_j(v) * J^-1_u(u, v)
• F_v(u, v, i, j) = T_i(u) * N_j(v) * J^-1_v(u, v)
• F_w(u, v, i, j) = T_i(u) * T_j(v) * J_z(u, v) (Not Yet Implemented)

Where the Functions N, and T are the Normal and Tangentially directed Function spaces defined by the HierCurlBasisFnSpace. This structure is Generic over any HierCurlBasisFnSpace.

The Jacobian is defined by the Elem’s mapping to real space (and the mapping between the Elems and its descendant, in the case of sub-sampling)

Fields

jac: Vec<Vec<M2D>>

Transformation matrices (or Jacobians) at each sample point. Describes transformation from real space to sampled parametric space

jac_inv: Vec<Vec<M2D>>

det_jac: Vec<Vec<f64>>

Determinants of the “Sampling Jacobian” at each point

para_scale: V2D

Parametric scaling factors (used to scale derivatives in parametric space as necessary)

Implementations

impl<BSpace: HierCurlBasisFnSpace> HierCurlBasisFn<BSpace>

pub fn f_u(&self, [i, j]: [usize; 2], [m, n]: [usize; 2]) -> V2D

Evaluate the u-directed basis function at some point (m, n)

pub fn f_v(&self, [i, j]: [usize; 2], [m, n]: [usize; 2]) -> V2D

Evaluate the v-directed basis function at some point (m, n)

pub fn f_u_d1( &self, [i, j]: [usize; 2], [m, n]: [usize; 2], para_scale: &V2D ) -> V2D

Evaluate the first derivative of the u-directed basis with respect to another Elem’s parametric space

pub fn f_v_d1( &self, [i, j]: [usize; 2], [m, n]: [usize; 2], para_scale: &V2D ) -> V2D

Evaluate the first derivative of the v-directed basis with respect to another Elem’s parametric space

pub fn f_u_d2( &self, [i, j]: [usize; 2], [m, n]: [usize; 2], para_scale: &V2D ) -> V2D

Evaluate the second derivative of the u-directed basis with respect to another Elem’s parametric space

pub fn f_v_d2( &self, [i, j]: [usize; 2], [m, n]: [usize; 2], para_scale: &V2D ) -> V2D

Evaluate the second derivative of the v-directed basis with respect to another Elem’s parametric space

pub fn f_u_dd( &self, [i, j]: [usize; 2], [m, n]: [usize; 2], para_scale: &V2D ) -> V2D

Evaluate the gradient of the u-directed basis with respect to another Elem’s parametric space

pub fn f_v_dd( &self, [i, j]: [usize; 2], [m, n]: [usize; 2], para_scale: &V2D ) -> V2D

Evaluate the gradient of the v-directed basis with respect to another Elem’s parametric space

pub fn glq_scale(&self) -> f64

The size of the parametric area relative to the unit-parametric area

pub fn edge_glq_scale(&self, edge_idx: usize) -> f64

The size of the parametric space relative to the unit-parametric space (along a single edge)

pub fn u_glq_scale(&self) -> f64

The scale of the u-axis relative to the unit parametric space

pub fn v_glq_scale(&self) -> f64

The scale of the v-axis relative to the unit parametric space

pub fn deriv_scale(&self) -> &V2D

The scale of both axes relative to the unit parametric space

pub fn sample_scale(&self, [m, n]: [usize; 2]) -> f64

The determinant of the Jacobian at some point (m, n)

pub fn max_uv_ratio(&self, [m, n]: [usize; 2]) -> f64

Maximum of uv_ratio and vu_ratio

pub fn uv_ratio(&self, [m, n]: [usize; 2]) -> f64

The ratio of the du/dx to dv/dy at some point (m, n)

pub fn vu_ratio(&self, [m, n]: [usize; 2]) -> f64

The ratio of the dv/dy to du/dx at some point (m, n)

Trait Implementations

impl<BSpace: Clone + HierCurlBasisFnSpace> Clone for HierCurlBasisFn<BSpace>

fn clone(&self) -> HierCurlBasisFn<BSpace>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<BSpace: Debug + HierCurlBasisFnSpace> Debug for HierCurlBasisFn<BSpace>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<BSpace: HierCurlBasisFnSpace> HierBasisFn for HierCurlBasisFn<BSpace>

fn defined_over( elem: &Elem, desc_elem: Option<&Elem>, [u_points, v_points]: [&[f64]; 2], [i_max, j_max]: [usize; 2], compute_d2: bool ) -> Self

Create a Basis Function instance defined over some Elem (and optionally mapped over some descendant Elem)

Arguments

• elem : the element to sample over
• desc_elem : the descendant element to sample over. If None, the BasisFn is defined over the entire Elem
• u_points : the glq points defined over (-1.0, 1.0) for the u-axis
• v_points : the glq points defined over (-1.0, 1.0) for the v-axis
• i_max : maximum u-directed expansion order
• j_max : maximum v-directed expansion order
• compute_2d : whether or not to compute the second derivatives of the Basis Functions

If a descendant Elem is provided, the raw_points are mapped (according to GLQ rules) to match the parametric bounds of the descendant Elem