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adaptive integration option

This commit is contained in:
Magnus Ulimoen 2020-04-19 20:45:06 +02:00
parent 597e1ab4a0
commit 5003c0d55c
3 changed files with 147 additions and 0 deletions
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30
sbp/benches/euler.rs
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@ -1,6 +1,7 @@
use criterion::{black_box, criterion_group, criterion_main, Criterion};
use sbp::euler::System;
use sbp::operators::{SbpOperator2d, Upwind4, UpwindOperator2d, SBP4};
use sbp::Float;
fn advance_system<SBP: SbpOperator2d>(universe: &mut System<SBP>, n: usize) {
for _ in 0..n {
@ -14,6 +15,19 @@ fn advance_system_upwind<UO: UpwindOperator2d>(universe: &mut System<UO>, n: usi
}
}
fn advance_embedded<UO: UpwindOperator2d>(universe: &mut System<UO>, embedded: bool) {
let dt = 0.2 / std::cmp::max(universe.nx(), universe.ny()) as Float;
let t = 1.0;
if embedded {
let mut dt = dt;
universe.advance_adaptive(t, &mut dt, 1e-2);
} else {
for _ in 0..(t / dt).round() as isize {
universe.advance_upwind(dt);
}
}
}
fn performance_benchmark(c: &mut Criterion) {
let mut group = c.benchmark_group("EulerSystem");
group.sample_size(25);
@ -48,7 +62,23 @@ fn performance_benchmark(c: &mut Criterion) {
advance_system(&mut universe, black_box(20))
})
});
group.finish();
let mut group = c.benchmark_group("adaptive integration");
group.sample_size(10);
let mut universe = System::new(x.into_owned(), y.into_owned(), Upwind4);
group.bench_function("static dt", |b| {
b.iter(|| {
universe.init_with_vortex(0.0, 0.0);
advance_embedded(&mut universe, false);
})
});
group.bench_function("adaptive dt", |b| {
b.iter(|| {
universe.init_with_vortex(0.0, 0.0);
advance_embedded(&mut universe, true);
})
});
group.finish();
}

44
sbp/src/euler.rs
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@ -99,6 +99,13 @@ impl<SBP: SbpOperator2d> System<SBP> {
pub fn y(&self) -> ArrayView2<Float> {
self.grid.0.y.view()
}
pub fn nx(&self) -> usize {
self.grid.0.nx()
}
pub fn ny(&self) -> usize {
self.grid.0.ny()
}
}
impl<UO: UpwindOperator2d> System<UO> {
@ -127,6 +134,43 @@ impl<UO: UpwindOperator2d> System<UO> {
);
std::mem::swap(&mut self.sys.0, &mut self.sys.1);
}
pub fn advance_adaptive(&mut self, dt: Float, guess_dt: &mut Float, maxerr: Float) {
let bc = BoundaryCharacteristics {
north: BoundaryCharacteristic::This,
south: BoundaryCharacteristic::This,
east: BoundaryCharacteristic::This,
west: BoundaryCharacteristic::This,
};
let op = &self.op;
let grid = &self.grid;
let wb = &mut self.wb.0;
let mut rhs_upwind = |k: &mut Field, y: &Field, _time: Float| {
let (grid, metrics) = grid;
let boundaries = boundary_extractor(y, grid, &bc);
RHS_upwind(op, k, y, metrics, &boundaries, wb)
};
let mut time = 0.0;
let mut sys2 = self.sys.0.clone();
while time < dt {
integrate::integrate_embedded_rk::<integrate::BogackiShampine, _, _>(
&mut rhs_upwind,
&self.sys.0,
&mut self.sys.1,
&mut sys2,
&mut time,
*guess_dt,
&mut self.k,
);
let err = self.sys.0.h2_err(&sys2, &self.op);
if err < maxerr {
time += *guess_dt;
std::mem::swap(&mut self.sys.0, &mut self.sys.1);
*guess_dt *= 1.05;
} else {
*guess_dt *= 0.8;
}
}
}
}
#[derive(Clone, Debug)]

73
sbp/src/integrate.rs
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@ -8,6 +8,10 @@ pub trait ButcherTableau {
const C: &'static [Float];
}
pub trait EmbeddedButcherTableau: ButcherTableau {
const BSTAR: &'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]];
@ -87,6 +91,51 @@ impl ButcherTableau for Rk6 {
];
}
pub struct Fehlberg;
impl ButcherTableau for Fehlberg {
#[rustfmt::skip]
const A: &'static [&'static [Float]] = &[
&[1.0 / 4.0],
&[3.0 / 32.0, 9.0 / 32.0],
&[1932.0 / 2197.0, -7200.0 / 2197.0, 7296.0 / 2197.0],
&[439.0 / 216.0, -8.0, 3680.0 / 513.0, -845.0 / 4104.0],
&[-8.0 / 27.0, 2.0, -3544.0 / 2565.0, 1859.0 / 4104.0, -11.0 / 40.0],
];
#[rustfmt::skip]
const B: &'static [Float] = &[
16.0 / 135.0, 0.0, 6656.0 / 12825.0, 28561.0 / 56430.0, -9.0 / 50.0, 2.0 / 55.0,
];
const C: &'static [Float] = &[0.0, 1.0 / 4.0, 3.0 / 8.0, 12.0 / 13.0, 1.0, 1.0 / 2.0];
}
impl EmbeddedButcherTableau for Fehlberg {
const BSTAR: &'static [Float] = &[
25.0 / 216.0,
0.0,
1408.0 / 2565.0,
2197.0 / 4104.0,
-1.0 / 5.0,
0.0,
];
}
pub struct BogackiShampine;
impl ButcherTableau for BogackiShampine {
const A: &'static [&'static [Float]] = &[
&[1.0 / 2.0],
&[0.0, 3.0 / 4.0],
&[2.0 / 9.0, 1.0 / 3.0, 4.0 / 9.0],
];
const B: &'static [Float] = &[2.0 / 9.0, 1.0 / 3.0, 4.0 / 9.0, 0.0];
const C: &'static [Float] = &[0.0, 1.0 / 2.0, 3.0 / 4.0, 1.0];
}
impl EmbeddedButcherTableau for BogackiShampine {
const BSTAR: &'static [Float] = &[7.0 / 24.0, 1.0 / 4.0, 1.0 / 3.0, 1.0 / 8.0];
}
#[allow(clippy::too_many_arguments)]
pub fn integrate<BTableau: ButcherTableau, F, RHS>(
mut rhs: RHS,
@ -140,6 +189,30 @@ pub fn integrate<BTableau: ButcherTableau, F, RHS>(
}
}
#[allow(clippy::too_many_arguments)]
pub fn integrate_embedded_rk<BTableau: EmbeddedButcherTableau, F, RHS>(
rhs: RHS,
prev: &F,
fut: &mut F,
fut2: &mut F,
time: &mut Float,
dt: Float,
k: &mut [F],
) where
for<'r> &'r F: std::convert::Into<ArrayView3<'r, Float>>,
for<'r> &'r mut F: std::convert::Into<ArrayViewMut3<'r, Float>>,
RHS: FnMut(&mut F, &F, Float),
{
integrate::<BTableau, F, RHS>(rhs, prev, fut, time, dt, k);
fut2.into().assign(&prev.into());
for (&b, k) in BTableau::BSTAR.iter().zip(k.iter()) {
if b == 0.0 {
continue;
}
fut2.into().scaled_add(b * dt, &k.into());
}
}
#[cfg(feature = "rayon")]
#[allow(clippy::too_many_arguments)]
pub fn integrate_multigrid<BTableau: ButcherTableau, F, RHS>(