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add h2 operator

This commit is contained in:
Magnus Ulimoen 2020-04-12 19:27:18 +02:00
parent a9e4a7e0cc
commit 90f72847fb
10 changed files with 208 additions and 17 deletions
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42
sbp/src/euler.rs
View File

@ -283,12 +283,26 @@ impl Field {
.map(move |x| x * factor)
};
let hxiterator = itermaker(self.nx(), 1.0 / (self.nx() - 1) as Float);
let hxiterator = itermaker(
self.nx(),
if SBP::is_h2() {
1.0 / (self.nx() - 2) as Float
} else {
1.0 / (self.nx() - 1) as Float
},
);
// Repeating to get the form
// [[hx0, hx1, ..., hxn], [hx0, hx1, ..., hxn], ..., [hx0, hx1, ..., hxn]]
let hxiterator = hxiterator.into_iter().cycle().take(self.nx() * self.ny());
let hyiterator = itermaker(self.ny(), 1.0 / (self.ny() - 1) as Float);
let hyiterator = itermaker(
self.ny(),
1.0 / if SBP::is_h2() {
(self.ny() - 2) as Float
} else {
(self.ny() - 1) as Float
},
);
// Repeating to get the form
// [[hy0, hy0, ..., hy0], [hy1, hy1, ..., hy1], ..., [hym, hym, ..., hym]]
let hyiterator = hyiterator
@ -801,7 +815,11 @@ fn SAT_characteristics<SBP: SbpOperator>(
) {
// North boundary
{
let hi = (k.ny() - 1) as Float / SBP::h()[0];
let hi = if SBP::is_h2() {
(k.ny() - 2) as Float / SBP::h()[0]
} else {
(k.ny() - 1) as Float / SBP::h()[0]
};
let sign = -1.0;
let tau = 1.0;
let slice = s![y.ny() - 1, ..];
@ -819,7 +837,11 @@ fn SAT_characteristics<SBP: SbpOperator>(
}
// South boundary
{
let hi = (k.ny() - 1) as Float / SBP::h()[0];
let hi = if SBP::is_h2() {
(k.ny() - 2) as Float / SBP::h()[0]
} else {
(k.ny() - 1) as Float / SBP::h()[0]
};
let sign = 1.0;
let tau = -1.0;
let slice = s![0, ..];
@ -837,7 +859,11 @@ fn SAT_characteristics<SBP: SbpOperator>(
}
// West Boundary
{
let hi = (k.nx() - 1) as Float / SBP::h()[0];
let hi = if SBP::is_h2() {
(k.nx() - 2) as Float / SBP::h()[0]
} else {
(k.nx() - 1) as Float / SBP::h()[0]
};
let sign = 1.0;
let tau = -1.0;
let slice = s![.., 0];
@ -855,7 +881,11 @@ fn SAT_characteristics<SBP: SbpOperator>(
}
// East Boundary
{
let hi = (k.nx() - 1) as Float / SBP::h()[0];
let hi = if SBP::is_h2() {
(k.nx() - 2) as Float / SBP::h()[0]
} else {
(k.nx() - 1) as Float / SBP::h()[0]
};
let sign = -1.0;
let tau = 1.0;
let slice = s![.., y.nx() - 1];

2
sbp/src/lib.rs
View File

@ -1,3 +1,5 @@
#![feature(str_strip)]
#[cfg(feature = "f32")]
pub type Float = f32;
#[cfg(not(feature = "f32"))]

24
sbp/src/maxwell.rs
View File

@ -449,7 +449,11 @@ fn SAT_characteristics<SBP: SbpOperator>(
Boundary::This => y.slice(s![.., .., 0]),
};
// East boundary
let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as Float);
let hinv = if SBP::is_h2() {
(nx - 2) as Float / SBP::h()[0]
} else {
(nx - 1) as Float / SBP::h()[0]
};
for ((((mut k, v), g), &kx), &ky) in k
.slice_mut(s![.., .., nx - 1])
.gencolumns_mut()
@ -483,7 +487,11 @@ fn SAT_characteristics<SBP: SbpOperator>(
let g = match boundaries.east {
Boundary::This => y.slice(s![.., .., nx - 1]),
};
let hinv = 1.0 / (SBP::h()[0] / (nx - 1) as Float);
let hinv = if SBP::is_h2() {
(nx - 2) as Float / SBP::h()[0]
} else {
(nx - 1) as Float / SBP::h()[0]
};
for ((((mut k, v), g), &kx), &ky) in k
.slice_mut(s![.., .., 0])
.gencolumns_mut()
@ -522,7 +530,11 @@ fn SAT_characteristics<SBP: SbpOperator>(
let g = match boundaries.north {
Boundary::This => y.slice(s![.., 0, ..]),
};
let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as Float);
let hinv = if SBP::is_h2() {
(ny - 2) as Float / SBP::h()[0]
} else {
(ny - 1) as Float / SBP::h()[0]
};
for ((((mut k, v), g), &kx), &ky) in k
.slice_mut(s![.., ny - 1, ..])
.gencolumns_mut()
@ -555,7 +567,11 @@ fn SAT_characteristics<SBP: SbpOperator>(
let g = match boundaries.south {
Boundary::This => y.slice(s![.., ny - 1, ..]),
};
let hinv = 1.0 / (SBP::h()[0] / (ny - 1) as Float);
let hinv = if SBP::is_h2() {
(ny - 2) as Float / SBP::h()[0]
} else {
(ny - 1) as Float / SBP::h()[0]
};
for ((((mut k, v), g), &kx), &ky) in k
.slice_mut(s![.., 0, ..])
.gencolumns_mut()

14
sbp/src/operators.rs
View File

@ -17,6 +17,9 @@ pub trait SbpOperator: Send + Sync {
Self::diffxi(prev.reversed_axes(), fut.reversed_axes())
}
fn h() -> &'static [Float];
fn is_h2() -> bool {
false
}
}
pub trait UpwindOperator: SbpOperator {
@ -42,6 +45,7 @@ pub(crate) fn diff_op_1d(
block: ndarray::ArrayView2<Float>,
diag: ndarray::ArrayView1<Float>,
symmetric: bool,
is_h2: bool,
prev: ArrayView1<Float>,
mut fut: ArrayViewMut1<Float>,
) {
@ -49,7 +53,11 @@ pub(crate) fn diff_op_1d(
let nx = prev.shape()[0];
assert!(nx >= 2 * block.len_of(ndarray::Axis(0)));
let dx = 1.0 / (nx - 1) as Float;
let dx = if is_h2 {
1.0 / (nx - 2) as Float
} else {
1.0 / (nx - 1) as Float
};
let idx = 1.0 / dx;
let first_elems = prev.slice(::ndarray::s!(..block.len_of(::ndarray::Axis(1))));
@ -91,6 +99,10 @@ mod upwind4;
pub use upwind4::Upwind4;
mod upwind9;
pub use upwind9::Upwind9;
mod upwind4h2;
pub use upwind4h2::Upwind4h2;
mod traditional4;
pub use traditional4::SBP4;
mod traditional8;

1
sbp/src/operators/traditional4.rs
View File

@ -29,6 +29,7 @@ impl SbpOperator for SBP4 {
ndarray::arr2(Self::BLOCK).view(),
ndarray::arr1(Self::DIAG).view(),
false,
false,
prev,
fut,
)

1
sbp/src/operators/traditional8.rs
View File

@ -33,6 +33,7 @@ impl SbpOperator for SBP8 {
ndarray::arr2(Self::BLOCK).view(),
ndarray::arr1(Self::DIAG).view(),
false,
false,
prev,
fut,
)

2
sbp/src/operators/upwind4.rs
View File

@ -281,6 +281,7 @@ impl SbpOperator for Upwind4 {
ndarray::arr2(Self::BLOCK).view(),
ndarray::arr1(Self::DIAG).view(),
false,
false,
prev,
fut,
)
@ -405,6 +406,7 @@ impl UpwindOperator for Upwind4 {
ndarray::arr2(Self::DISS_BLOCK).view(),
ndarray::arr1(Self::DISS_DIAG).view(),
true,
false,
prev,
fut,
)

95
sbp/src/operators/upwind4h2.rs Normal file
View File

@ -0,0 +1,95 @@
use super::{SbpOperator, UpwindOperator};
use crate::Float;
use ndarray::{ArrayView1, ArrayViewMut1};
#[derive(Debug)]
pub struct Upwind4h2 {}
impl Upwind4h2 {
#[rustfmt::skip]
const HBLOCK: &'static [Float] = &[
0.91e2/0.720e3, 0.325e3/0.384e3, 0.595e3/0.576e3, 0.1909e4/0.1920e4,
];
#[rustfmt::skip]
const DIAG: &'static [Float] = &[
-1.43229166666667e-02, 1.40625000000000e-01, -7.38281250000000e-01, 0.00000000000000e+00, 7.38281250000000e-01, -1.40625000000000e-01, 1.43229166666667e-02
];
#[rustfmt::skip]
const BLOCK: &'static [[Float; 7]] = &[
[-3.95604395604396e+00, 5.41758241758242e+00, -1.94505494505495e+00, 4.83516483516484e-01, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
[-8.09025641025641e-01, 0.00000000000000e+00, 1.03948717948718e+00, -2.47384615384615e-01, 1.69230769230769e-02, 0.00000000000000e+00, 0.00000000000000e+00],
[2.37983193277311e-01, -8.51680672268908e-01, 0.00000000000000e+00, 7.35966386554622e-01, -1.36134453781513e-01, 1.38655462184874e-02, 0.00000000000000e+00],
[-6.14632442814737e-02, 2.10581456259822e-01, -7.64623712240265e-01, 0.00000000000000e+00, 7.42535358826611e-01, -1.41435306443164e-01, 1.44054478784704e-02],
];
#[rustfmt::skip]
const DISS_BLOCK: &'static [[Float; 7]; 4] = &[
[-2.76989342315976e-01, 5.19355016842454e-01, -3.46236677894969e-01, 1.03871003368491e-01, 0.00000000000000e+00, 0.00000000000000e+00, 0.00000000000000e+00],
[7.75570158484731e-02, -1.62342481638964e-01, 1.47715500579822e-01, -7.98531117124082e-02, 1.69230769230769e-02, 0.00000000000000e+00, 0.00000000000000e+00],
[-4.23630758836198e-02, 1.21027405937249e-01, -1.91609307039399e-01, 1.82272708078206e-01, -8.31932773109244e-02, 1.38655462184874e-02, 0.00000000000000e+00],
[1.32037874021759e-02, -6.79734450144910e-02, 1.89370108794365e-01, -2.78654929966754e-01, 2.16081718177056e-01, -8.64326872708224e-02, 1.44054478784704e-02],
];
#[rustfmt::skip]
const DISS_DIAG: &'static [Float; 7] = &[
1.43229166666667e-02, -8.59375000000000e-02, 2.14843750000000e-01, -2.86458333333333e-01, 2.14843750000000e-01, -8.59375000000000e-02, 1.43229166666667e-02,
];
}
impl SbpOperator for Upwind4h2 {
fn diff1d(prev: ArrayView1<Float>, fut: ArrayViewMut1<Float>) {
super::diff_op_1d(
ndarray::arr2(Self::BLOCK).view(),
ndarray::arr1(Self::DIAG).view(),
false,
true,
prev,
fut,
)
}
fn h() -> &'static [Float] {
Self::HBLOCK
}
fn is_h2() -> bool {
true
}
}
#[test]
fn upwind4h2_test() {
let nx = 20;
let x = crate::utils::h2linspace(0.0, 1.0, nx);
let mut res = ndarray::Array1::zeros(nx);
Upwind4h2::diff1d(x.view(), res.view_mut());
let ans = &x * 0.0 + 1.0;
approx::assert_abs_diff_eq!(&res, &ans, epsilon = 1e-4);
res.fill(0.0);
let y = &x * &x / 2.0;
Upwind4h2::diff1d(y.view(), res.view_mut());
let ans = &x;
approx::assert_abs_diff_eq!(&res, &ans, epsilon = 1e-4);
res.fill(0.0);
let y = &x * &x * &x / 3.0;
Upwind4h2::diff1d(y.view(), res.view_mut());
let ans = &x * &x;
approx::assert_abs_diff_eq!(&res, &ans, epsilon = 1e-2);
}
impl UpwindOperator for Upwind4h2 {
fn diss1d(prev: ArrayView1<Float>, fut: ArrayViewMut1<Float>) {
super::diff_op_1d(
ndarray::arr2(Self::DISS_BLOCK).view(),
ndarray::arr1(Self::DISS_DIAG).view(),
true,
true,
prev,
fut,
)
}
}

2
sbp/src/operators/upwind9.rs
View File

@ -50,6 +50,7 @@ impl SbpOperator for Upwind9 {
ndarray::arr2(Self::BLOCK).view(),
ndarray::arr1(Self::DIAG).view(),
false,
false,
prev,
fut,
)
@ -66,6 +67,7 @@ impl UpwindOperator for Upwind9 {
ndarray::arr2(Self::DISS_BLOCK).view(),
ndarray::arr1(Self::DISS_DIAG).view(),
true,
false,
prev,
fut,
)

42
sbp/src/utils.rs
View File

@ -19,6 +19,7 @@ pub struct ExtendedGrid {
/// x: [x0, x1, ..., xn]
/// which results in x being broadcasted to nx/ny size
/// x: linspace:start:end:num
/// x: linspace:h2:start:end:num
/// where x will be from start to end inclusive, with num steps
/// x: [[x00, x01, .., x0n], [x10, x11, .., x1n], ... [xm0, xm1, ..., xmn]]
/// which is the full grid x
@ -49,11 +50,15 @@ pub fn json_to_grids(json: JsonValue) -> Result<Vec<ExtendedGrid>, String> {
let to_array_form = |mut x: JsonValue| {
if let Some(s) = x.take_string() {
if s.starts_with("linspace") {
if let Some(s) = s.strip_prefix("linspace:") {
let (s, h2) = if let Some(s) = s.strip_prefix("h2:") {
(s, true)
} else {
(s, false)
};
// linspace:start:stop:steps
let mut iter = s.split(':');
let name = iter.next().unwrap();
assert_eq!(name, "linspace");
let start = iter.next();
let start: Float = match start {
@ -73,9 +78,11 @@ pub fn json_to_grids(json: JsonValue) -> Result<Vec<ExtendedGrid>, String> {
if iter.next().is_some() {
return Err(format!("linspace: contained more than expected"));
}
Ok(ArrayForm::Array1(ndarray::Array::linspace(
start, end, steps,
)))
Ok(ArrayForm::Array1(if h2 {
h2linspace(start, end, steps)
} else {
ndarray::Array::linspace(start, end, steps)
}))
} else {
Err(format!("Could not parse gridline"))
}
@ -285,3 +292,26 @@ pub fn json_to_vortex(mut json: JsonValue) -> super::euler::VortexParameters {
eps,
}
}
pub fn h2linspace(start: Float, end: Float, n: usize) -> ndarray::Array1<Float> {
let h = 1.0 / (n - 2) as Float;
ndarray::Array1::from_shape_fn(n, |i| match i {
0 => start,
i if i == n - 1 => end,
i => h * (i as Float - 0.5),
})
}
#[test]
fn test_h2linspace() {
let x = h2linspace(0.0, 1.0, 50);
approx::assert_abs_diff_eq!(x[0], 0.0, epsilon = 1e-6);
approx::assert_abs_diff_eq!(x[49], 1.0, epsilon = 1e-6);
let hend = x[1] - x[0];
let h = x[2] - x[1];
approx::assert_abs_diff_eq!(x[49] - x[48], hend, epsilon = 1e-6);
approx::assert_abs_diff_eq!(2.0 * hend, h, epsilon = 1e-6);
for i in 1..48 {
approx::assert_abs_diff_eq!(x[i + 1] - x[i], h, epsilon = 1e-6);
}
}