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use super::glq::*;
use super::{HierCurlIntegral, IntegralResult};
use crate::fem_domain::basis::{HierCurlBasisFn, HierCurlBasisFnSpace};
use crate::fem_domain::domain::{
dof::basis_spec::BasisDir, mesh::element::Materials, mesh::space::V2D,
};
/// <∇ × u, ∇ × ρ>
pub mod curl_curl {
use super::*;
/// The L2 Inner-Product of the Curl of two Hierarchical Basis Functions
pub struct CurlCurl {
u_weights: Vec<f64>,
v_weights: Vec<f64>,
}
impl HierCurlIntegral for CurlCurl {
fn with_weights(u_weights: &[f64], v_weights: &[f64]) -> Self {
Self {
u_weights: u_weights.to_vec(),
v_weights: v_weights.to_vec(),
}
}
fn integrate<BSpace: HierCurlBasisFnSpace>(
&self,
p_dir: BasisDir,
q_dir: BasisDir,
p_orders: [usize; 2],
q_orders: [usize; 2],
p_basis: &HierCurlBasisFn<BSpace>,
q_basis: &HierCurlBasisFn<BSpace>,
materials: &Materials,
) -> IntegralResult {
IntegralResult::Full(
(1.0 / materials.mu_rel.re)
// * p_basis.glq_scale()
// * q_basis.glq_scale()
* match (p_dir, q_dir) {
(BasisDir::U, BasisDir::U) => {
real_gauss_quad(&self.u_weights, &self.v_weights, |m, n| {
let p_curl = p_basis
.f_u_d1(p_orders, [m, n], q_basis.deriv_scale())
.dot_with(&CURL_OP);
let q_curl = q_basis
.f_u_d1(q_orders, [m, n], p_basis.deriv_scale())
.dot_with(&CURL_OP);
p_curl * q_curl * max_uv_ratios(p_basis, q_basis, [m, n])
})
}
(BasisDir::U, BasisDir::V) => {
real_gauss_quad(&self.u_weights, &self.v_weights, |m, n| {
let p_curl = p_basis
.f_u_d1(p_orders, [m, n], q_basis.deriv_scale())
.dot_with(&CURL_OP);
let q_curl = q_basis
.f_v_d1(q_orders, [m, n], p_basis.deriv_scale())
.dot_with(&CURL_OP);
p_curl * q_curl
})
}
(BasisDir::V, BasisDir::U) => {
real_gauss_quad(&self.u_weights, &self.v_weights, |m, n| {
let p_curl = p_basis
.f_v_d1(p_orders, [m, n], q_basis.deriv_scale())
.dot_with(&CURL_OP);
let q_curl = q_basis
.f_u_d1(q_orders, [m, n], p_basis.deriv_scale())
.dot_with(&CURL_OP);
p_curl * q_curl
})
}
(BasisDir::V, BasisDir::V) => {
real_gauss_quad(&self.u_weights, &self.v_weights, |m, n| {
let p_curl = p_basis
.f_v_d1(p_orders, [m, n], q_basis.deriv_scale())
.dot_with(&CURL_OP);
let q_curl = q_basis
.f_v_d1(q_orders, [m, n], p_basis.deriv_scale())
.dot_with(&CURL_OP);
p_curl * q_curl * max_vu_ratios(p_basis, q_basis, [m, n])
})
}
(_, _) => 0.0,
},
)
}
fn integrate_by_parts<BSpace: HierCurlBasisFnSpace>(
&self,
p_dir: BasisDir,
q_dir: BasisDir,
p_orders: [usize; 2],
q_orders: [usize; 2],
p_basis: &HierCurlBasisFn<BSpace>,
q_basis: &HierCurlBasisFn<BSpace>,
materials: &Materials,
) -> IntegralResult {
let surface_term = (1.0 / materials.mu_rel.re)
* p_basis.glq_scale()
* q_basis.glq_scale()
* match (p_dir, q_dir) {
(BasisDir::U, BasisDir::U) => {
real_gauss_quad_inner(&self.u_weights, &self.v_weights, |m, n| {
let p_d2 = p_basis.f_u_d2(p_orders, [m, n], q_basis.deriv_scale());
let p_dd = p_basis.f_u_dd(p_orders, [m, n], q_basis.deriv_scale());
let p = V2D::from([p_dd[1] + p_d2[0], p_d2[1] + p_dd[0]]);
let q = q_basis.f_u(q_orders, [m, n]);
V2D::dot(p, q) / q_basis.glq_scale().powi(2)
* max_uv_ratios(p_basis, q_basis, [m, n])
}) * -1.0
}
(BasisDir::U, BasisDir::V) => {
real_gauss_quad_inner(&self.u_weights, &self.v_weights, |m, n| {
let p_d2 = p_basis.f_u_d2(p_orders, [m, n], q_basis.deriv_scale());
let p_dd = p_basis.f_u_dd(p_orders, [m, n], q_basis.deriv_scale());
let p = V2D::from([p_dd[1] + p_d2[0], p_d2[1] + p_dd[0]]);
let q = q_basis.f_v(q_orders, [m, n]);
V2D::dot(p, q) / q_basis.glq_scale().powi(2)
})
}
(BasisDir::V, BasisDir::U) => {
real_gauss_quad_inner(&self.u_weights, &self.v_weights, |m, n| {
let p_d2 = p_basis.f_v_d2(p_orders, [m, n], q_basis.deriv_scale());
let p_dd = p_basis.f_v_dd(p_orders, [m, n], q_basis.deriv_scale());
let p = V2D::from([p_dd[1] + p_d2[0], p_d2[1] + p_dd[0]]);
let q = q_basis.f_u(q_orders, [m, n]);
V2D::dot(p, q) / q_basis.glq_scale().powi(2)
})
}
(BasisDir::V, BasisDir::V) => {
real_gauss_quad_inner(&self.u_weights, &self.v_weights, |m, n| {
let p_d2 = p_basis.f_v_d2(p_orders, [m, n], q_basis.deriv_scale());
let p_dd = p_basis.f_v_dd(p_orders, [m, n], q_basis.deriv_scale());
let p = V2D::from([p_dd[1] + p_d2[0], p_d2[1] + p_dd[0]]);
let q = q_basis.f_v(q_orders, [m, n]);
V2D::dot(p, q) / q_basis.glq_scale().powi(2)
* max_vu_ratios(p_basis, q_basis, [m, n])
}) * -1.0
}
(_, _) => 0.0,
};
let edge_terms = (0..4)
.map(|edge_idx| {
-1.0 * (1.0 / materials.mu_rel.re)
* p_basis.edge_glq_scale(edge_idx)
* q_basis.edge_glq_scale(edge_idx)
* match (p_dir, q_dir, edge_idx) {
(BasisDir::U, BasisDir::U, 0 | 1) => real_gauss_quad_edge(
&self.u_weights,
&self.v_weights,
edge_idx,
|m, n| {
let p_curl = p_basis
.f_u_d1(p_orders, [m, n], q_basis.deriv_scale())
.dot_with(&CURL_OP);
let q = q_basis
.f_u(q_orders, [m, n])
.dot_with(&EDGE_UNIT_VECTORS[edge_idx]);
p_curl * q / q_basis.glq_scale()
* max_uv_ratios(p_basis, q_basis, [m, n])
},
),
(BasisDir::V, BasisDir::U, 0 | 1) => real_gauss_quad_edge(
&self.u_weights,
&self.v_weights,
edge_idx,
|m, n| {
let p_curl = p_basis
.f_v_d1(p_orders, [m, n], q_basis.deriv_scale())
.dot_with(&CURL_OP);
let q = q_basis
.f_u(q_orders, [m, n])
.dot_with(&EDGE_UNIT_VECTORS[edge_idx]);
p_curl * q / q_basis.glq_scale()
},
),
(BasisDir::U, BasisDir::V, 2 | 3) => {
real_gauss_quad_edge(
&self.u_weights,
&self.v_weights,
edge_idx,
|m, n| {
let p_curl = p_basis
.f_u_d1(p_orders, [m, n], q_basis.deriv_scale())
.dot_with(&CURL_OP);
let q = q_basis
.f_v(q_orders, [m, n])
.dot_with(&EDGE_UNIT_VECTORS[edge_idx]);
p_curl * q / q_basis.glq_scale()
},
) * -1.0
}
(BasisDir::V, BasisDir::V, 2 | 3) => {
real_gauss_quad_edge(
&self.u_weights,
&self.v_weights,
edge_idx,
|m, n| {
let p_curl = p_basis
.f_v_d1(p_orders, [m, n], q_basis.deriv_scale())
.dot_with(&CURL_OP);
let q = q_basis
.f_v(q_orders, [m, n])
.dot_with(&EDGE_UNIT_VECTORS[edge_idx]);
p_curl * q / q_basis.glq_scale()
* max_vu_ratios(p_basis, q_basis, [m, n])
},
) * -1.0
}
(_, _, _) => 0.0,
}
})
.collect::<Vec<f64>>()
.try_into()
.unwrap();
IntegralResult::ByParts(surface_term, edge_terms)
}
}
const CURL_OP: V2D = V2D::from([-1.0, 1.0]);
const EDGE_UNIT_VECTORS: [V2D; 4] = [
V2D::from([-1.0, 0.0]),
V2D::from([1.0, 0.0]),
V2D::from([0.0, -1.0]),
V2D::from([0.0, 1.0]),
];
#[inline]
fn max_uv_ratios<BSpace: HierCurlBasisFnSpace>(
p_basis: &HierCurlBasisFn<BSpace>,
q_basis: &HierCurlBasisFn<BSpace>,
[m, n]: [usize; 2],
) -> f64 {
((p_basis.det_jac[m][n] >= q_basis.det_jac[m][n]) as u8) as f64 * p_basis.uv_ratio([m, n])
+ ((p_basis.det_jac[m][n] < q_basis.det_jac[m][n]) as u8) as f64
* q_basis.uv_ratio([m, n])
// p_basis.uv_ratio([m, n])
}
#[inline]
fn max_vu_ratios<BSpace: HierCurlBasisFnSpace>(
p_basis: &HierCurlBasisFn<BSpace>,
q_basis: &HierCurlBasisFn<BSpace>,
[m, n]: [usize; 2],
) -> f64 {
((p_basis.det_jac[m][n] >= q_basis.det_jac[m][n]) as u8) as f64 * p_basis.vu_ratio([m, n])
+ ((p_basis.det_jac[m][n] < q_basis.det_jac[m][n]) as u8) as f64
* q_basis.vu_ratio([m, n])
// p_basis.vu_ratio([m, n])
}
}
/// <u, ρ>
pub mod inner {
use super::*;
/// The L2 Inner product of two Basis Functions
pub struct L2Inner {
u_weights: Vec<f64>,
v_weights: Vec<f64>,
}
impl HierCurlIntegral for L2Inner {
fn with_weights(u_weights: &[f64], v_weights: &[f64]) -> Self {
Self {
u_weights: u_weights.to_vec(),
v_weights: v_weights.to_vec(),
}
}
fn integrate<BSpace: HierCurlBasisFnSpace>(
&self,
p_dir: BasisDir,
q_dir: BasisDir,
p_orders: [usize; 2],
q_orders: [usize; 2],
p_basis: &HierCurlBasisFn<BSpace>,
q_basis: &HierCurlBasisFn<BSpace>,
materials: &Materials,
) -> IntegralResult {
IntegralResult::Full(
materials.eps_rel.re
* p_basis.glq_scale()
* q_basis.glq_scale()
* match (p_dir, q_dir) {
(BasisDir::U, BasisDir::U) => {
real_gauss_quad(&self.u_weights, &self.v_weights, |m, n| {
V2D::dot(
p_basis.f_u(p_orders, [m, n]),
q_basis.f_u(q_orders, [m, n]),
) * partial_max(
p_basis.sample_scale([m, n]),
q_basis.sample_scale([m, n]),
)
})
}
(BasisDir::U, BasisDir::V) => {
real_gauss_quad(&self.u_weights, &self.v_weights, |m, n| {
V2D::dot(
p_basis.f_u(p_orders, [m, n]),
q_basis.f_v(q_orders, [m, n]),
) * partial_max(
p_basis.sample_scale([m, n]),
q_basis.sample_scale([m, n]),
)
})
}
(BasisDir::V, BasisDir::U) => {
real_gauss_quad(&self.u_weights, &self.v_weights, |m, n| {
V2D::dot(
p_basis.f_v(p_orders, [m, n]),
q_basis.f_u(q_orders, [m, n]),
) * partial_max(
p_basis.sample_scale([m, n]),
q_basis.sample_scale([m, n]),
)
})
}
(BasisDir::V, BasisDir::V) => {
real_gauss_quad(&self.u_weights, &self.v_weights, |m, n| {
V2D::dot(
p_basis.f_v(p_orders, [m, n]),
q_basis.f_v(q_orders, [m, n]),
) * partial_max(
p_basis.sample_scale([m, n]),
q_basis.sample_scale([m, n]),
)
})
}
(_, _) => 0.0,
},
)
}
fn integrate_by_parts<BSpace: HierCurlBasisFnSpace>(
&self,
p_dir: BasisDir,
q_dir: BasisDir,
p_orders: [usize; 2],
q_orders: [usize; 2],
p_basis: &HierCurlBasisFn<BSpace>,
q_basis: &HierCurlBasisFn<BSpace>,
materials: &Materials,
) -> IntegralResult {
IntegralResult::Full(
materials.eps_rel.re
* p_basis.glq_scale()
* q_basis.glq_scale()
* match (p_dir, q_dir) {
(BasisDir::U, BasisDir::U) => {
real_gauss_quad_inner(&self.u_weights, &self.v_weights, |m, n| {
V2D::dot(
p_basis.f_u(p_orders, [m, n]),
q_basis.f_u(q_orders, [m, n]),
) * partial_max(
p_basis.sample_scale([m, n]),
q_basis.sample_scale([m, n]),
)
})
}
(BasisDir::U, BasisDir::V) => {
real_gauss_quad_inner(&self.u_weights, &self.v_weights, |m, n| {
V2D::dot(
p_basis.f_u(p_orders, [m, n]),
q_basis.f_v(q_orders, [m, n]),
) * partial_max(
p_basis.sample_scale([m, n]),
q_basis.sample_scale([m, n]),
)
})
}
(BasisDir::V, BasisDir::U) => {
real_gauss_quad_inner(&self.u_weights, &self.v_weights, |m, n| {
V2D::dot(
p_basis.f_v(p_orders, [m, n]),
q_basis.f_u(q_orders, [m, n]),
) * partial_max(
p_basis.sample_scale([m, n]),
q_basis.sample_scale([m, n]),
)
})
}
(BasisDir::V, BasisDir::V) => {
real_gauss_quad_inner(&self.u_weights, &self.v_weights, |m, n| {
V2D::dot(
p_basis.f_v(p_orders, [m, n]),
q_basis.f_v(q_orders, [m, n]),
) * partial_max(
p_basis.sample_scale([m, n]),
q_basis.sample_scale([m, n]),
)
})
}
(_, _) => 0.0,
},
)
}
}
fn partial_max(v1: f64, v2: f64) -> f64 {
std::cmp::max_by(v1, v2, |a, b| a.partial_cmp(b).unwrap())
}
}