colin/fdtd-coremem
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broken: expand to two dimensions.

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Broken because there seems to be a scaling issue, and also the previous
1d simulation has no effect when ported to this new 2d world.
This commit is contained in:
Colin
2020-07-14 23:26:27 -07:00
parent 80cb3a9d52
commit a82c2f60e7
4 changed files with 126 additions and 86 deletions
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1
Cargo.toml
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@@ -8,3 +8,4 @@ edition = "2018"
[dependencies]
ansi_term = "0.12"
ndarray = "0.13"

18
examples/coremem.rs
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@@ -1,18 +1,18 @@
use coremem::SimState;
use coremem::render::ColorTermRenderer;
use coremem::render::NumericTermRenderer;
use coremem::consts;
use std::{thread, time};
fn main() {
let mut state = SimState::new(16);
state.impulse_b(0, 1.0/consts::C);
state.impulse_e(0, 1.0);
state.impulse_b(7, 1.0/consts::C);
state.impulse_e(7, 1.0);
state.impulse_b(15, 1.0/consts::C);
state.impulse_e(15, 1.0);
let mut state = SimState::new(16, 4);
state.impulse_bz(0, 0, 1.0/consts::C);
//state.impulse_ey(0, 0, 1.0);
state.impulse_bz(7, 0, 1.0/consts::C);
//state.impulse_ey(7, 0, 1.0);
state.impulse_bz(15, 0, 1.0/consts::C);
//state.impulse_ey(15, 0, 1.0);
loop {
ColorTermRenderer.render(&state);
NumericTermRenderer.render(&state);
state.step();
thread::sleep(time::Duration::from_millis(100));
}

156
src/lib.rs
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@@ -5,6 +5,8 @@
//!
//! [1] https://www.eecs.wsu.edu/~schneidj/ufdtd/ufdtd.pdf
use ndarray::Array2;
pub mod render;
// Some things to keep in mind:
@@ -23,104 +25,136 @@ pub mod consts {
#[derive(Default)]
pub struct SimState {
cells: Vec<Cell>,
cells: Array2<Cell>,
}
impl SimState {
pub fn new(size: usize) -> Self {
pub fn new(width: usize, height: usize) -> Self {
Self {
cells: vec![Cell::default(); size],
cells: Array2::default((height, width))
}
}
pub fn step(&mut self) {
let mut working_cells = vec![Cell::default(); self.cells.len()];
let mut working_cells = self.cells.clone();
//let mut working_cells = vec![Cell::default(); self.cells.len()];
// first advance all the magnetic fields
for (i, left_cell) in self.cells.iter().enumerate() {
let right_cell = match self.cells.get(i+1) {
Some(&cell) => cell,
_ => Cell::default(),
};
working_cells[i] = left_cell.step_b(right_cell);
for down_y in 1..self.height() {
for right_x in 1..self.width() {
let cell = self.get(right_x-1, down_y-1);
let right_cell = self.get(right_x, down_y-1);
let down_cell = self.get(right_x-1, down_y);
working_cells[[down_y-1, right_x-1]] = cell.step_b(right_cell, down_cell);
}
}
std::mem::swap(&mut working_cells, &mut self.cells);
for (i, right_cell) in working_cells.iter().enumerate() {
let left_cell = match i {
0 => Cell::default(),
_ => working_cells[i-1],
};
self.cells[i] = right_cell.step_e(left_cell);
// now advance electic fields
for y in 1..self.height() {
for x in 1..self.width() {
let cell = self.get(x, y);
let left_cell = self.get(x-1, y);
let up_cell = self.get(x, y-1);
working_cells[[y, x]] = cell.step_e(left_cell, up_cell);
}
}
std::mem::swap(&mut working_cells, &mut self.cells);
}
pub fn impulse_e(&mut self, idx: usize, e: f32) {
self.cells[idx].ez += e;
pub fn impulse_ex(&mut self, x: usize, y: usize, ex: f32) {
self.cells[[y, x]].ex += ex;
}
pub fn impulse_ey(&mut self, x: usize, y: usize, ey: f32) {
self.cells[[y, x]].ey += ey;
}
pub fn impulse_bz(&mut self, x: usize, y: usize, bz: f32) {
self.cells[[y, x]].bz += bz;
}
pub fn impulse_b(&mut self, idx: usize, y: f32) {
self.cells[idx].by += y;
pub fn width(&self) -> usize {
self.cells.shape()[1]
}
pub fn cells(&self) -> &[Cell] {
&*self.cells
pub fn height(&self) -> usize {
self.cells.shape()[0]
}
pub fn get(&self, x: usize, y: usize) -> Cell {
self.cells[[y, x]]
}
}
/// Conceptually, one cell looks like this:
///
/// +-------------+
/// | |
/// .Ez .By . next cell
/// | |
/// +-------------+
/// +-------.-------+
/// | Ex |
/// | |
/// | |
/// .Ey .Bz .
/// | |
/// | |
/// | |
/// +-------.-------+
///
/// Where +By points up and +Ez points into the page, and the cell has a unit length of 1.
/// Where the right hand rule indicates that positive Bz is pointing out of the page, towards the
/// reader.
///
/// The dot on bottom is Ex of the cell at (x, y+1) and the dot on the right is the Ey of the cell at
/// (x+1, y). The `+` only indicates the corner of the cell -- nothing of interest is measured at
/// the pluses.
#[derive(Copy, Clone, Default)]
pub struct Cell {
/// electric field
ez: f32,
/// magnetic field
by: f32,
ex: f32,
ey: f32,
bz: f32,
}
impl Cell {
pub fn ez(&self) -> f32 {
self.ez
pub fn ex(&self) -> f32 {
self.ex
}
pub fn by(&self) -> f32 {
self.by
pub fn ey(&self) -> f32 {
self.ey
}
fn step_b(self, right: Cell) -> Self {
pub fn bz(&self) -> f32 {
self.bz
}
fn step_b(self, right: Cell, down: Cell) -> Self {
// Maxwell's equation: del x E = -dB/dt
// Expands: dB_y/dt = dE_z/dx
// Discretize: (delta B_y) / (delta t) = (delta E_z)/(delta x)
// Rearrange: delta B_y = (delta t)/(delta x) * (delta E_z)
//
// light travels C meters per second, therefore (delta x)/(delta t) = c if we use SI units.
// XXX: this differs from [1], which says we should use Z_0 = 1/(epsilon c) here instead of c.
let delta_e = right.ez - self.ez; //< delta E_z
let delta_b = delta_e / consts::C; //< delta B_y
// Expand: dE_y/dx - dE_x/dy = -dB_z/dt
// Rearrange: dB_z/dt = dE_x/dy - dE_y/dx
// Discretize: (delta B_z)/(delta t) = (delta E_x)/(delta y) - (delta E_y)/(delta x)
//
// light travels C meters per second, therefore (delta x)/(delta t) = (delta y)/(delta t) = c if we use SI units.
// Simplify: delta B_z = (delta E_x)/c - (delta E_y)/c
let delta_ex = down.ex - self.ex;
let delta_ey = right.ey - self.ey;
let delta_bz = (delta_ex - delta_ey) / consts::C;
Cell {
ez: self.ez,
by: self.by + delta_b,
ex: self.ex,
ey: self.ey,
bz: self.bz + delta_bz,
}
}
fn step_e(self, left: Cell) -> Self {
fn step_e(self, left: Cell, up: Cell) -> Self {
// Maxwell's equation: del x B = mu_0 eps_0 dE/dt
// Expands: dB_y/dx = mu_0 eps_0 dE_y/dt
// Rearrange: dE_y/dt = 1/(mu_0 eps_0) dB_y/dx
// Discretize: (delta E_y)/(delta t) = 1/(mu_0 eps_0) (delta dB_y)/(delta x)
// Rearrange: delta E_y = (delta t)/(delta x) 1/(mu_0 eps_0) (delta B_y)
// Substitute c as in step_b: delta E_y = (mu_0 eps_0)/c (delta B_y)
// Note that c = 1/sqrt(mu_0 eps_0), so this becomes:
// delta E_y = c (delta B_y)
// XXX once again this differs from [1]
let delta_b = self.by - left.by; //< delta B_y
let delta_e = delta_b * consts::C; //< delta E_z
// N.B: c = 1/sqrt(mu_0 eps_0) so:
// Rearrange: dE/dt = c^2 del x B
// Expand: dE_x/dt = c^2 dB_z/dy (1); dE_y/dt = -c^2 dB_z/dx (2)
//
// Discretize (1): (delta E_x)/(delta t) = c^2 (delta B_z)/(delta y)
// Recall: (delta y)/(delta t) = c, as from step_b
// Substitute: (delta E_x) = c (delta B_z,y)
//
// Discretize (2): (delta E_y)/(delta t) = -c^2 (delta B_z)/(delta x)
// Substitute c: (delta E_y) = -c (delta B_z,x)
let delta_bz_y = self.bz - up.bz;
let delta_ex = consts::C * delta_bz_y;
let delta_bz_x = self.bz - left.bz;
let delta_ey = consts::C * delta_bz_x;
Cell {
ez: self.ez + delta_e,
by: self.by,
ex: self.ex + delta_ex,
ey: self.ey + delta_ey,
bz: self.bz,
}
}
}

37
src/render.rs
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@@ -6,13 +6,17 @@ pub struct NumericTermRenderer;
impl NumericTermRenderer {
pub fn render(&self, state: &SimState) {
print!("B: ");
for cell in state.cells() {
print!("{:>10.1e} ", cell.by());
}
print!("\nE:");
for cell in state.cells() {
print!("{:>10.1e} ", cell.ez());
for y in 0..state.height() {
for x in 0..state.width() {
let cell = state.get(x, y);
print!(" {:>10.1e}", cell.ex());
}
print!("\n");
for x in 0..state.width() {
let cell = state.get(x, y);
print!("{:>10.1e} {:>10.1e}", cell.ey(), cell.bz());
}
print!("\n");
}
print!("\n");
}
@@ -26,14 +30,15 @@ fn clamp(v: f32, range: f32) -> f32 {
impl ColorTermRenderer {
pub fn render(&self, state: &SimState) {
let square = "█";
for cell in state.cells() {
let b_value = clamp(cell.by() * consts::C * 128.0, 255.0);
let b_color = RGB(0, b_value.max(0.0) as _, b_value.abs() as _);
let e_value = clamp(cell.ez() * 128.0, 255.0);
let e_color = RGB(e_value.abs() as _, e_value.max(0.0) as _, 0);
print!("{}{}", e_color.paint(square), b_color.paint(square));
}
print!("\n");
unimplemented!()
// let square = "█";
// for cell in state.cells() {
// let b_value = clamp(cell.by() * consts::C * 128.0, 255.0);
// let b_color = RGB(0, b_value.max(0.0) as _, b_value.abs() as _);
// let e_value = clamp(cell.ez() * 128.0, 255.0);
// let e_color = RGB(e_value.abs() as _, e_value.max(0.0) as _, 0);
// print!("{}{}", e_color.paint(square), b_color.paint(square));
// }
// print!("\n");
}
}