fdtd-solver.js

/**

 * FDTDSolver — 2D Finite-Difference Time-Domain wave equation solver.

 * Loaded as a plain script; class is defined on the global scope.

 */

/**

 * @typedef {Object} FDTDSolverConfig

 * @property {number} nx - grid width in cells

 * @property {number} ny - grid height in cells

 * @property {number} dx - spatial step size

 * @property {number} dt - time step size

 * @property {number} c  - wave speed

 * @property {number} dampingWidth - absorbing boundary layer width in cells

 */

/**

 * @typedef {Object} BarrierConfig

 * @property {'single'|'double'} mode

 * @property {number} barrierCol - x-index of the barrier column

 * @property {number} slitWidth  - slit width in grid cells

 * @property {number} slitSeparation - center-to-center distance (double-slit only)

 * @property {number} ny - grid height for centering

 */

class FDTDSolver {
  /**

   * @param {FDTDSolverConfig} config

   */
  constructor(config) {
    this.config = config;
    this.nx = config.nx;
    this.ny = config.ny;
    this.dx = config.dx;
    this.dt = config.dt;
    this.c = config.c;
    this.dampingWidth = config.dampingWidth;

    const size = this.nx * this.ny;
    this.uPrev = new Float32Array(size);
    this.uCurr = new Float32Array(size);
    this.uNext = new Float32Array(size);
    this.barrier = new Uint8Array(size);

    this.time = 0;
    this.paused = false;
  }

  /** Zero all amplitude arrays and reset time counter. */
  reset() {
    this.uPrev.fill(0);
    this.uCurr.fill(0);
    this.uNext.fill(0);
    this.time = 0;
  }

  /**

   * Advance n time steps using the FDTD update equation.

   * @param {number} n - number of sub-steps

   */
  step(n) {
    if (this.paused) return;

    const { nx, ny, c, dt, dx, dampingWidth } = this;
    const C = c * dt / dx;
    const C2 = C * C;

    for (let s = 0; s < n; s++) {
      // 1. FDTD update for interior cells
      for (let y = 1; y < ny - 1; y++) {
        for (let x = 1; x < nx - 1; x++) {
          const idx = y * nx + x;
          const neighbors =
            this.uCurr[idx + 1] +       // i+1, j
            this.uCurr[idx - 1] +       // i-1, j
            this.uCurr[idx + nx] +      // i, j+1
            this.uCurr[idx - nx];       // i, j-1
          this.uNext[idx] =
            2.0 * this.uCurr[idx] -
            this.uPrev[idx] +
            C2 * (neighbors - 4.0 * this.uCurr[idx]);
        }
      }

      // 2. Enforce barrier cells to zero (Dirichlet boundary)
      const size = nx * ny;
      for (let i = 0; i < size; i++) {
        if (this.barrier[i] === 1) {
          this.uNext[i] = 0;
        }
      }

      // 3. Absorbing boundary damping on all four edges.
      // For columns near the source, skip top/bottom damping so the
      // plane wave source stays uniform and doesn't get eaten at the edges.
      const sourceCol = dampingWidth + 2;
      for (let y = 0; y < ny; y++) {
        for (let x = 0; x < nx; x++) {
          const dLeft = x;
          const dRight = nx - 1 - x;
          const dTop = y;
          const dBottom = ny - 1 - y;

          // For columns at or near the source, only damp left/right edges
          const nearSource = (x >= sourceCol - 1 && x <= sourceCol + 1);
          const dMin = nearSource
            ? Math.min(dLeft, dRight)
            : Math.min(dLeft, dRight, dTop, dBottom);

          if (dMin < dampingWidth) {
            const ratio = (dampingWidth - dMin) / dampingWidth;
            const damping = 1.0 - 0.99 * ratio * ratio * ratio;
            const idx = y * nx + x;
            this.uNext[idx] *= damping;
            this.uCurr[idx] *= damping;
            this.uPrev[idx] *= damping;
          }
        }
      }

      // 4. Rotate arrays: prev ← curr, curr ← next
      const temp = this.uPrev;
      this.uPrev = this.uCurr;
      this.uCurr = this.uNext;
      this.uNext = temp;

      // 5. Apply soft source injection
      if (this.wavelength) {
        this.applySource(this.time, this.wavelength);
      }

      this.time += this.dt;
    }
  }

  /**

   * Populate the barrier array from a BarrierConfig.

   * @param {BarrierConfig} config

   */
  setBarrier(config) {
    const { mode, barrierCol, slitWidth, slitSeparation, ny } = config;
    const nx = this.nx;

    // Clear existing barrier
    this.barrier.fill(0);

    // Support custom slit center for per-slit barriers (orthogonal polarization)
    const centerY = config._slitCenter != null ? config._slitCenter : Math.floor(ny / 2);
    const halfSlit = Math.floor(slitWidth / 2);

    if (mode === 'single') {
      // Fill entire barrier column, then carve out the slit
      for (let y = 0; y < ny; y++) {
        this.barrier[y * nx + barrierCol] = 1;
      }
      // Open the slit: centered opening of slitWidth cells
      const slitStart = centerY - halfSlit;
      const slitEnd = slitStart + slitWidth;
      for (let y = slitStart; y < slitEnd; y++) {
        if (y >= 0 && y < ny) {
          this.barrier[y * nx + barrierCol] = 0;
        }
      }
    } else if (mode === 'double') {
      // Fill entire barrier column
      for (let y = 0; y < ny; y++) {
        this.barrier[y * nx + barrierCol] = 1;
      }
      // Two slits symmetric about center, separated by slitSeparation (center-to-center)
      const halfSep = Math.floor(slitSeparation / 2);
      const slit1Center = centerY - halfSep;
      const slit2Center = centerY + halfSep;

      // Open slit 1
      const slit1Start = slit1Center - halfSlit;
      const slit1End = slit1Start + slitWidth;
      for (let y = slit1Start; y < slit1End; y++) {
        if (y >= 0 && y < ny) {
          this.barrier[y * nx + barrierCol] = 0;
        }
      }

      // Open slit 2
      const slit2Start = slit2Center - halfSlit;
      const slit2End = slit2Start + slitWidth;
      for (let y = slit2Start; y < slit2End; y++) {
        if (y >= 0 && y < ny) {
          this.barrier[y * nx + barrierCol] = 0;
        }
      }
    }
  }

  /**

   * Soft additive source injection along the source column.

   * @param {number} time

   * @param {number} wavelength

   */
  applySource(time, wavelength) {
    const { nx, ny, c, dx, dampingWidth } = this;
    const sourceCol = dampingWidth + 2;
    const A = this.sourceAmplitude != null ? this.sourceAmplitude : 1.0;
    const phase = 2.0 * Math.PI * time * c / (wavelength * dx);

    // Source width: how many cells of the column emit waves (centered)
    const sw = this.sourceWidth != null ? Math.min(this.sourceWidth, ny) : ny;
    const centerY = Math.floor(ny / 2);
    const halfSW = Math.floor(sw / 2);
    const yStart = Math.max(0, centerY - halfSW);
    const yEnd = Math.min(ny, centerY - halfSW + sw);

    // Hard source: force the amplitude at the source column.
    // This prevents backward-traveling waves from interfering with the
    // source and creating a standing wave pattern (point-source artifacts).
    const val = A * Math.sin(phase);
    for (let y = yStart; y < yEnd; y++) {
      this.uCurr[y * nx + sourceCol] = val;
    }
  }

  /**

   * Returns the current amplitude field.

   * @returns {Float32Array}

   */
  getAmplitude() {
    return this.uCurr;
  }
}

window.FDTDSolver = FDTDSolver;