use rk4 in maxwell
This commit is contained in:
Magnus Ulimoen
parent
e957a4fff7
commit
3229554d6b
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@ -1,14 +1,14 @@
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use criterion::{black_box, criterion_group, criterion_main, Criterion};
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use sbp::maxwell::System;
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use sbp::operators::{SbpOperator, Upwind4, UpwindOperator, SBP4};
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use sbp::MaxwellSystem;
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fn advance_system<SBP: SbpOperator>(universe: &mut MaxwellSystem<SBP>, n: usize) {
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fn advance_system<SBP: SbpOperator>(universe: &mut System<SBP>, n: usize) {
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for _ in 0..n {
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universe.advance(0.01);
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}
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}
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fn advance_system_upwind<UO: UpwindOperator>(universe: &mut MaxwellSystem<UO>, n: usize) {
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fn advance_system_upwind<UO: UpwindOperator>(universe: &mut System<UO>, n: usize) {
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for _ in 0..n {
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universe.advance_upwind(0.01);
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}
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@ -23,8 +23,7 @@ fn performance_benchmark(c: &mut Criterion) {
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let x = ndarray::Array2::from_shape_fn((h, w), |(_, i)| i as f32 / (w - 1) as f32);
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let y = ndarray::Array2::from_shape_fn((h, w), |(j, _)| j as f32 / (h - 1) as f32);
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let mut universe =
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MaxwellSystem::<Upwind4>::new(w, h, x.as_slice().unwrap(), y.as_slice().unwrap());
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let mut universe = System::<Upwind4>::new(w, h, x.as_slice().unwrap(), y.as_slice().unwrap());
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group.bench_function("advance", |b| {
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b.iter(|| {
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universe.set_gaussian(0.5, 0.5);
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@ -32,8 +31,7 @@ fn performance_benchmark(c: &mut Criterion) {
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})
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});
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let mut universe =
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MaxwellSystem::<Upwind4>::new(w, h, x.as_slice().unwrap(), y.as_slice().unwrap());
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let mut universe = System::<Upwind4>::new(w, h, x.as_slice().unwrap(), y.as_slice().unwrap());
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group.bench_function("advance_upwind", |b| {
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b.iter(|| {
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universe.set_gaussian(0.5, 0.5);
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@ -41,8 +39,7 @@ fn performance_benchmark(c: &mut Criterion) {
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})
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});
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let mut universe =
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MaxwellSystem::<SBP4>::new(w, h, x.as_slice().unwrap(), y.as_slice().unwrap());
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let mut universe = System::<SBP4>::new(w, h, x.as_slice().unwrap(), y.as_slice().unwrap());
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group.bench_function("advance_trad4", |b| {
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b.iter(|| {
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universe.set_gaussian(0.5, 0.5);
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82
src/lib.rs
82
src/lib.rs
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@ -3,9 +3,8 @@ use wasm_bindgen::prelude::*;
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pub mod euler;
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mod grid;
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pub(crate) mod integrate;
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mod maxwell;
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pub mod maxwell;
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pub mod operators;
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pub use crate::maxwell::{Field, WorkBuffers};
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pub(crate) use grid::Grid;
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#[cfg(feature = "wee_alloc")]
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@ -19,13 +18,13 @@ pub fn set_panic_hook() {
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}
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#[wasm_bindgen]
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pub struct MaxwellUniverse(MaxwellSystem<operators::Upwind4>);
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pub struct MaxwellUniverse(maxwell::System<operators::Upwind4>);
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#[wasm_bindgen]
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impl MaxwellUniverse {
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#[wasm_bindgen(constructor)]
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pub fn new(width: usize, height: usize, x: &[f32], y: &[f32]) -> Self {
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Self(MaxwellSystem::new(width as usize, height as usize, x, y))
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Self(maxwell::System::new(width as usize, height as usize, x, y))
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}
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pub fn init(&mut self, x0: f32, y0: f32) {
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@ -41,87 +40,18 @@ impl MaxwellUniverse {
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}
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pub fn get_ex_ptr(&self) -> *const u8 {
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self.0.sys.0.ex().as_ptr() as *const u8
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self.0.field().ex().as_ptr() as *const u8
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}
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pub fn get_ey_ptr(&self) -> *const u8 {
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self.0.sys.0.ey().as_ptr() as *const u8
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self.0.field().ey().as_ptr() as *const u8
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}
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pub fn get_hz_ptr(&self) -> *const u8 {
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self.0.sys.0.hz().as_ptr() as *const u8
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self.0.field().hz().as_ptr() as *const u8
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}
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}
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pub struct MaxwellSystem<SBP: operators::SbpOperator> {
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sys: (Field, Field),
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wb: WorkBuffers,
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grid: Grid<SBP>,
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}
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impl<SBP: operators::SbpOperator> MaxwellSystem<SBP> {
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pub fn new(width: usize, height: usize, x: &[f32], y: &[f32]) -> Self {
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assert_eq!((width * height), x.len());
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assert_eq!((width * height), y.len());
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let grid = Grid::new_from_slice(height, width, x, y).expect(
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"Could not create grid. Different number of elements compared to width*height?",
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);
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Self {
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sys: (Field::new(width, height), Field::new(width, height)),
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grid,
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wb: WorkBuffers::new(width, height),
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}
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}
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pub fn set_gaussian(&mut self, x0: f32, y0: f32) {
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let (ex, hz, ey) = self.sys.0.components_mut();
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ndarray::azip!(
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(ex in ex, hz in hz, ey in ey,
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&x in &self.grid.x, &y in &self.grid.y)
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{
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*ex = 0.0;
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*ey = 0.0;
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*hz = gaussian(x, x0, y, y0)/32.0;
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});
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}
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pub fn advance(&mut self, dt: f32) {
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maxwell::advance(
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&self.sys.0,
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&mut self.sys.1,
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dt,
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&self.grid,
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Some(&mut self.wb),
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);
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std::mem::swap(&mut self.sys.0, &mut self.sys.1);
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}
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}
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impl<UO: operators::UpwindOperator> MaxwellSystem<UO> {
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/// Using artificial dissipation with the upwind operator
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pub fn advance_upwind(&mut self, dt: f32) {
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maxwell::advance_upwind(
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&self.sys.0,
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&mut self.sys.1,
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dt,
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&self.grid,
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Some(&mut self.wb),
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);
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std::mem::swap(&mut self.sys.0, &mut self.sys.1);
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}
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}
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fn gaussian(x: f32, x0: f32, y: f32, y0: f32) -> f32 {
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use std::f32;
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let x = x - x0;
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let y = y - y0;
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let sigma = 0.05;
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1.0 / (2.0 * f32::consts::PI * sigma * sigma) * (-(x * x + y * y) / (2.0 * sigma * sigma)).exp()
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}
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#[wasm_bindgen]
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pub struct EulerUniverse(euler::System<operators::Upwind4>);
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211
src/maxwell.rs
211
src/maxwell.rs
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@ -1,7 +1,8 @@
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use super::integrate::integrate_rk4;
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use super::operators::{SbpOperator, UpwindOperator};
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use super::Grid;
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use ndarray::azip;
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use ndarray::prelude::*;
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use ndarray::{azip, Zip};
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#[derive(Clone, Debug)]
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pub struct Field(pub(crate) Array3<f32>);
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@ -67,121 +68,91 @@ impl Field {
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}
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}
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pub(crate) fn advance_upwind<UO>(
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prev: &Field,
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fut: &mut Field,
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dt: f32,
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grid: &Grid<UO>,
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work_buffers: Option<&mut WorkBuffers>,
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) where
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UO: UpwindOperator,
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{
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assert_eq!(prev.0.shape(), fut.0.shape());
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let mut wb: WorkBuffers;
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let (y, k, tmp) = if let Some(x) = work_buffers {
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(&mut x.y, &mut x.buf, &mut x.tmp)
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} else {
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wb = WorkBuffers::new(prev.nx(), prev.ny());
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(&mut wb.y, &mut wb.buf, &mut wb.tmp)
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};
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let boundaries = BoundaryTerms {
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north: Boundary::This,
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south: Boundary::This,
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west: Boundary::This,
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east: Boundary::This,
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};
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for i in 0..4 {
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// y = y0 + c*kn
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y.assign(&prev);
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match i {
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0 => {}
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1 | 2 => {
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y.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
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}
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3 => {
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y.scaled_add(dt, &k[i - 1]);
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}
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_ => {
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unreachable!();
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}
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};
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RHS_upwind(&mut k[i], &y, grid, &boundaries, tmp);
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}
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Zip::from(&mut fut.0)
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.and(&prev.0)
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.and(&*k[0])
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.and(&*k[1])
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.and(&*k[2])
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.and(&*k[3])
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.apply(|y1, &y0, &k1, &k2, &k3, &k4| *y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4));
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pub struct System<SBP: SbpOperator> {
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sys: (Field, Field),
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wb: WorkBuffers,
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grid: Grid<SBP>,
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}
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impl<SBP: SbpOperator> System<SBP> {
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pub fn new(width: usize, height: usize, x: &[f32], y: &[f32]) -> Self {
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assert_eq!((width * height), x.len());
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assert_eq!((width * height), y.len());
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let grid = Grid::new_from_slice(height, width, x, y).expect(
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"Could not create grid. Different number of elements compared to width*height?",
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);
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Self {
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sys: (Field::new(width, height), Field::new(width, height)),
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grid,
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wb: WorkBuffers::new(width, height),
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}
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}
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pub fn field(&self) -> &Field {
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&self.sys.0
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}
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pub fn set_gaussian(&mut self, x0: f32, y0: f32) {
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let (ex, hz, ey) = self.sys.0.components_mut();
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ndarray::azip!(
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(ex in ex, hz in hz, ey in ey,
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&x in &self.grid.x, &y in &self.grid.y)
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{
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*ex = 0.0;
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*ey = 0.0;
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*hz = gaussian(x, x0, y, y0)/32.0;
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});
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}
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pub fn advance(&mut self, dt: f32) {
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integrate_rk4(
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RHS,
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&self.sys.0,
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&mut self.sys.1,
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dt,
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&self.grid,
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&mut self.wb.k,
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&mut self.wb.tmp,
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);
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std::mem::swap(&mut self.sys.0, &mut self.sys.1);
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}
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}
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impl<UO: UpwindOperator> System<UO> {
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/// Using artificial dissipation with the upwind operator
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pub fn advance_upwind(&mut self, dt: f32) {
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integrate_rk4(
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RHS_upwind,
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&self.sys.0,
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&mut self.sys.1,
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dt,
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&self.grid,
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&mut self.wb.k,
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&mut self.wb.tmp,
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);
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std::mem::swap(&mut self.sys.0, &mut self.sys.1);
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}
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}
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fn gaussian(x: f32, x0: f32, y: f32, y0: f32) -> f32 {
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use std::f32;
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let x = x - x0;
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let y = y - y0;
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let sigma = 0.05;
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1.0 / (2.0 * f32::consts::PI * sigma * sigma) * (-(x * x + y * y) / (2.0 * sigma * sigma)).exp()
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}
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#[allow(non_snake_case)]
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/// Solving (Au)_x + (Bu)_y
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/// with:
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/// A B
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/// [ 0, 0, 0] [ 0, 1, 0]
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/// [ 0, 0, -1] [ 1, 0, 0]
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/// [ 0, -1, 0] [ 0, 0, 0]
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pub(crate) fn advance<SBP>(
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prev: &Field,
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fut: &mut Field,
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dt: f32,
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grid: &Grid<SBP>,
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work_buffers: Option<&mut WorkBuffers>,
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) where
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SBP: SbpOperator,
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{
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assert_eq!(prev.0.shape(), fut.0.shape());
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let mut wb: WorkBuffers;
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let (y, k, tmp) = if let Some(x) = work_buffers {
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(&mut x.y, &mut x.buf, &mut x.tmp)
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} else {
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wb = WorkBuffers::new(prev.nx(), prev.ny());
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(&mut wb.y, &mut wb.buf, &mut wb.tmp)
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};
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let boundaries = BoundaryTerms {
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north: Boundary::This,
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south: Boundary::This,
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west: Boundary::This,
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east: Boundary::This,
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};
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for i in 0..4 {
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// y = y0 + c*kn
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y.assign(&prev);
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match i {
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0 => {}
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1 | 2 => {
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y.scaled_add(1.0 / 2.0 * dt, &k[i - 1]);
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}
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3 => {
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y.scaled_add(dt, &k[i - 1]);
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}
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_ => {
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unreachable!();
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}
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};
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RHS(&mut k[i], &y, grid, &boundaries, tmp);
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}
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Zip::from(&mut fut.0)
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.and(&prev.0)
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.and(&*k[0])
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.and(&*k[1])
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.and(&*k[2])
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.and(&*k[3])
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.apply(|y1, &y0, &k1, &k2, &k3, &k4| *y1 = y0 + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4));
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}
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#[allow(non_snake_case)]
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///
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/// This flux is rotated by the grid metrics
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/// (Au)_x + (Bu)_y = 1/J [
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/// (J xi_x Au)_xi + (J eta_x Au)_eta
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@ -194,12 +165,17 @@ fn RHS<SBP: SbpOperator>(
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k: &mut Field,
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y: &Field,
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grid: &Grid<SBP>,
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boundaries: &BoundaryTerms,
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tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
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) {
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fluxes(k, y, grid, tmp);
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SAT_characteristics(k, y, grid, boundaries);
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let boundaries = BoundaryTerms {
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north: Boundary::This,
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south: Boundary::This,
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west: Boundary::This,
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east: Boundary::This,
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};
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SAT_characteristics(k, y, grid, &boundaries);
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azip!((k in &mut k.0,
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&detj in &grid.detj.broadcast((3, y.ny(), y.nx())).unwrap()) {
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@ -212,13 +188,18 @@ fn RHS_upwind<UO: UpwindOperator>(
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k: &mut Field,
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y: &Field,
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grid: &Grid<UO>,
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boundaries: &BoundaryTerms,
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tmp: &mut (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
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) {
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fluxes(k, y, grid, tmp);
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dissipation(k, y, grid, tmp);
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SAT_characteristics(k, y, grid, boundaries);
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let boundaries = BoundaryTerms {
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north: Boundary::This,
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south: Boundary::This,
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west: Boundary::This,
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east: Boundary::This,
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};
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SAT_characteristics(k, y, grid, &boundaries);
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azip!((k in &mut k.0,
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&detj in &grid.detj.broadcast((3, y.ny(), y.nx())).unwrap()) {
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@ -576,8 +557,7 @@ fn SAT_characteristics<SBP: SbpOperator>(
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}
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pub struct WorkBuffers {
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y: Field,
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buf: [Field; 4],
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k: [Field; 4],
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tmp: (Array2<f32>, Array2<f32>, Array2<f32>, Array2<f32>),
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}
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@ -586,8 +566,7 @@ impl WorkBuffers {
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let arr2 = Array2::zeros((ny, nx));
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let arr3 = Field::new(nx, ny);
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Self {
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y: arr3.clone(),
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buf: [arr3.clone(), arr3.clone(), arr3.clone(), arr3],
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k: [arr3.clone(), arr3.clone(), arr3.clone(), arr3],
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tmp: (arr2.clone(), arr2.clone(), arr2.clone(), arr2),
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}
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}
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