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add more integration schemes

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Magnus Ulimoen
2020-04-11 19:44:40 +02:00
parent 29499c0c0c
commit 596605a8b7
1 changed files with 122 additions and 20 deletions
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142
sbp/src/integrate.rs
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@@ -1,13 +1,97 @@
use super::Float;
use ndarray::{Array3, Zip};
use ndarray::Array3;
pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
pub trait ButcherTableau {
const S: usize = Self::B.len();
const A: &'static [&'static [Float]];
const B: &'static [Float];
const C: &'static [Float];
}
pub struct Rk4;
impl ButcherTableau for Rk4 {
const A: &'static [&'static [Float]] = &[&[0.5], &[0.0, 0.5], &[0.0, 0.0, 1.0]];
const B: &'static [Float] = &[1.0 / 6.0, 1.0 / 3.0, 1.0 / 3.0, 1.0 / 6.0];
const C: &'static [Float] = &[0.5, 0.5, 1.0];
}
pub struct Rk4_38;
impl ButcherTableau for Rk4_38 {
const A: &'static [&'static [Float]] = &[&[1.0 / 3.0], &[-1.0 / 3.0, 1.0], &[1.0, -1.0, 1.0]];
const B: &'static [Float] = &[1.0 / 8.0, 3.0 / 8.0, 3.0 / 8.0, 1.0 / 8.0];
const C: &'static [Float] = &[1.0 / 3.0, 2.0 / 3.0, 1.0];
}
pub struct EulerMethod;
impl ButcherTableau for EulerMethod {
const A: &'static [&'static [Float]] = &[&[]];
const B: &'static [Float] = &[1.0];
const C: &'static [Float] = &[];
}
pub struct MidpointMethod;
impl ButcherTableau for MidpointMethod {
const A: &'static [&'static [Float]] = &[&[0.5]];
const B: &'static [Float] = &[0.0, 1.0];
const C: &'static [Float] = &[1.0 / 2.0];
}
/// Bit exessive...
const SQRT_5: Float = 2.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275;
pub struct Rk6;
impl ButcherTableau for Rk6 {
const A: &'static [&'static [Float]] = &[
&[4.0 / 7.0],
&[115.0 / 112.0, -5.0 / 16.0],
&[589.0 / 630.0, 5.0 / 18.0, -16.0 / 45.0],
&[
229.0 / 1200.0 - 29.0 / 6000.0 * SQRT_5,
119.0 / 240.0 - 187.0 / 1200.0 * SQRT_5,
-14.0 / 75.0 + 34.0 / 375.0 * SQRT_5,
-3.0 / 100.0 * SQRT_5,
],
&[
71.0 / 2400.0 - 587.0 / 12000.0 * SQRT_5,
187.0 / 480.0 - 391.0 / 2400.0 * SQRT_5,
-38.0 / 75.0 + 26.0 / 375.0 * SQRT_5,
27.0 / 80.0 - 3.0 / 400.0 * SQRT_5,
(1.0 + SQRT_5) / 4.0,
],
&[
-49.0 / 480.0 + 43.0 / 160.0 * SQRT_5,
-425.0 / 96.0 + 51.0 / 32.0 * SQRT_5,
52.0 / 15.0 - 4.0 / 5.0 * SQRT_5,
-27.0 / 16.0 + 3.0 / 16.0 * SQRT_5,
5.0 / 4.0 - 3.0 / 4.0 * SQRT_5,
5.0 / 2.0 - 1.0 / 2.0 * SQRT_5,
],
];
const B: &'static [Float] = &[
1.0 / 12.0,
0.0,
0.0,
0.0,
5.0 / 12.0,
5.0 / 12.0,
1.0 / 12.0,
];
const C: &'static [Float] = &[
4.0 / 7.0,
5.0 / 7.0,
6.0 / 7.0,
(5.0 - SQRT_5) / 10.0,
(5.0 + SQRT_5) / 10.0,
1.0,
];
}
pub fn integrate<'a, BTableau, F: 'a, RHS, MT, C>(
rhs: RHS,
prev: &F,
fut: &mut F,
time: &mut Float,
dt: Float,
k: &mut [F; 4],
k: &mut [F],
constants: C,
mut mutables: &mut MT,
@@ -15,8 +99,10 @@ pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
C: Copy,
F: std::ops::Deref<Target = Array3<Float>> + std::ops::DerefMut<Target = Array3<Float>>,
RHS: Fn(&mut F, &F, Float, C, &mut MT),
BTableau: ButcherTableau,
{
assert_eq!(prev.shape(), fut.shape());
assert!(k.len() >= BTableau::S);
for i in 0.. {
let simtime;
@@ -25,26 +111,24 @@ pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
fut.assign(prev);
simtime = *time;
}
1 | 2 => {
i if i < BTableau::S => {
fut.assign(prev);
fut.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
simtime = *time + dt / 2.0;
for (&a, k) in BTableau::A[i - 1].iter().zip(k.iter()) {
if a == 0.0 {
continue;
}
fut.scaled_add(a * dt, &k);
}
simtime = *time + dt * BTableau::C[i - 1];
}
3 => {
_ if i == BTableau::S => {
fut.assign(prev);
fut.scaled_add(dt, &k[i - 1]);
simtime = *time + dt;
}
4 => {
Zip::from(&mut **fut)
.and(&**prev)
.and(&*k[0])
.and(&*k[1])
.and(&*k[2])
.and(&*k[3])
.apply(|y1, &y0, &k1, &k2, &k3, &k4| {
*y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4)
});
for (&b, k) in BTableau::B.iter().zip(k.iter()) {
if b == 0.0 {
continue;
}
fut.scaled_add(b * dt, &k);
}
*time += dt;
return;
}
@@ -56,3 +140,21 @@ pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
rhs(&mut k[i], &fut, simtime, constants, &mut mutables);
}
}
pub(crate) fn rk4<'a, F: 'a, RHS, MT, C>(
rhs: RHS,
prev: &F,
fut: &mut F,
time: &mut Float,
dt: Float,
k: &mut [F; 4],
constants: C,
mutables: &mut MT,
) where
C: Copy,
F: std::ops::Deref<Target = Array3<Float>> + std::ops::DerefMut<Target = Array3<Float>>,
RHS: Fn(&mut F, &F, Float, C, &mut MT),
{
integrate::<Rk6, F, RHS, MT, C>(rhs, prev, fut, time, dt, k, constants, mutables)
}