Densify evaluation set to 289 points; evaluation-point overlay now a toggle, default off - concept-collection/fastandaccurate

concept-collection / fastandaccurate

Densify evaluation set to 289 points; evaluation-point overlay now a toggle, default off

Jeremy Magland <jmagland@flatironinstitute.org> committed 2 days ago commit 7fcfeb0fa557 parent 66784cb Browse files

6 changed files+38−22

docs/problems/laplace-dirichlet-2d.mdmodified+5−5View file

@@ -50,9 +50,9 @@ site's interactive views, but such runs are not recorded.

5050

5151 ## What is scored

5252

53-Each instance fixes 65 evaluation points: 16 rays at angles

54-θ_j = 2πj/16 + 0.13 (j = 0, …, 15), radial fractions

55-ρ ∈ {0.25, 0.5, 0.75, 0.9} along each ray (the point at fraction ρ on ray

53+Each instance fixes 289 evaluation points: 32 rays at angles

54+θ_j = 2πj/32 + 0.13 (j = 0, …, 31), radial fractions

55+ρ ∈ {0.1, 0.2, …, 0.9} along each ray (the point at fraction ρ on ray

5656 θ is ρ r(θ) (cos θ, sin θ)), ordered radius-major, plus the origin last.

5757 The solver returns u at exactly these points. Reported errors are

5858

@@ -95,10 +95,10 @@ manifest) and prob is a struct with fields

9595 | `prob.curveD` | first derivative of the curve with respect to t |

9696 | `prob.curveDD` | second derivative |

9797 | `prob.g` | `@(t) -> g`, Dirichlet data at boundary parameter t |

98-| `prob.evalXY` | 65×2, the evaluation points |

98+| `prob.evalXY` | 289×2, the evaluation points |

9999 | `prob.vizXY` | m×2, visualization grid points (m = 0 when not requested) |

100100

101-The return value is a struct: `out.uEval` (65×1, required) and

101+The return value is a struct: `out.uEval` (289×1, required) and

102102 `out.uGrid` (m×1; `[]` when `prob.vizXY` is empty). The solver must not

103103 reconstruct the sources analytically or otherwise special-case the known

104104 solution; submissions are reviewed for this.

src/app/components/DomainView.tsxmodified+2−2View file

@@ -55,7 +55,7 @@ export function DomainView({ inst }: { inst: Laplace2dInstance }) {

5555 ctx.fillStyle = token("--text-2");

5656 for (const p of evalPoints(inst)) {

5757 ctx.beginPath();

58- ctx.arc(X(p.x), Y(p.y), 2, 0, 2 * Math.PI);

58+ ctx.arc(X(p.x), Y(p.y), 1.4, 0, 2 * Math.PI);

5959 ctx.fill();

6060 }

6161

@@ -83,7 +83,7 @@ export function DomainView({ inst }: { inst: Laplace2dInstance }) {

8383 <figure style={{ margin: 0 }}>

8484 <canvas ref={canvasRef} />

8585 <figcaption className="field-caption" style={{ maxWidth: 360 }}>

86- The domain, the 65 evaluation points where solutions are scored

86+ The domain, the evaluation points where solutions are scored

8787 (dots), and the exact solution's sources a distance {inst.d} outside

8888 the boundary (crosses).

8989 </figcaption>

src/app/components/SolutionSection.tsxmodified+17−2View file

@@ -41,6 +41,7 @@ export function SolutionSection({ inst }: { inst: Laplace2dInstance }) {

4141 const [busy, setBusy] = useState(false);

4242 const [error, setError] = useState<string | null>(null);

4343 const [computed, setComputed] = useState<Computed | null>(null);

44+ const [showMarks, setShowMarks] = useState(false);

4445

4546 const exact = useMemo(() => exactGridValues(inst), [inst]);

4647

@@ -113,6 +114,14 @@ export function SolutionSection({ inst }: { inst: Laplace2dInstance }) {

113114 <button className="primary" onClick={compute} disabled={busy}>

114115 {busy ? "computing…" : "Compute in this browser"}

115116 </button>

117+ <label className="small">

118+ <input

119+ type="checkbox"

120+ checked={showMarks}

121+ onChange={(e) => setShowMarks(e.target.checked)}

122+ />{" "}

123+ show evaluation points on the error map

124+ </label>

116125 </div>

117126 {error && <p className="small" style={{ color: "var(--series-2)" }}>{error}</p>}

118127 <div className="row">

@@ -139,9 +148,15 @@ export function SolutionSection({ inst }: { inst: Laplace2dInstance }) {

139148 inst={inst}

140149 values={errField}

141150 mode="logmag"

142- overlayPoints={marks}

151+ overlayPoints={showMarks ? marks : undefined}

143152 title="Pointwise error (log scale)"

144- caption="Absolute difference from the exact solution; the color scale spans 8 decades below the maximum. Dots mark the 65 evaluation points where the reported errors are measured."

153+ caption={

154+ "Absolute difference from the exact solution; the color scale " +

155+ "spans 8 decades below the maximum." +

156+ (showMarks

157+ ? ` Dots mark the ${marks.length} evaluation points where the reported errors are measured.`

158+ : "")

159+ }

145160 />

146161 )}

147162 </div>

src/app/pages/ProblemPage.tsxmodified+2−2View file

@@ -339,8 +339,8 @@ export function ProblemPage({ problemId }: { problemId: string }) {

339339 Compute one solve at a chosen resolution and compare the field with

340340 the exact solution, on a shared color scale. The error map shows the

341341 absolute pointwise difference on a log scale; the errors reported in

342- the results above are measured at the 65 evaluation points, marked

343- as dots on the error map.

342+ the results above are measured at the evaluation points, which can

343+ be shown on the error map.

344344 </p>

345345 <SolutionSection inst={inst} />

346346 </>

src/problems/laplace2d/exact.tsmodified+6−6View file

@@ -49,15 +49,15 @@ export function exactU(inst: Laplace2dInstance, x: number, y: number): number {

4949 return u;

5050 }

5151

52-/** The 65 evaluation points: 16 rays, radial fractions

53- * [0.25, 0.5, 0.75, 0.9], plus the origin. Order matches

54- * build_problem.m: radius outer, angle inner, origin last. */

52+/** The 289 evaluation points: 32 rays, radial fractions 0.1..0.9, plus

53+ * the origin. Order matches build_problem.m: radius outer, angle inner,

54+ * origin last. */

5555 export function evalPoints(inst: Laplace2dInstance): { x: number; y: number }[] {

56- const rho = [0.25, 0.5, 0.75, 0.9];

56+ const rho = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9];

5757 const pts: { x: number; y: number }[] = [];

5858 for (const r of rho) {

59- for (let j = 0; j < 16; j++) {

60- const th = (2 * Math.PI * j) / 16 + 0.13;

59+ for (let j = 0; j < 32; j++) {

60+ const th = (2 * Math.PI * j) / 32 + 0.13;

6161 const rr = r * boundaryR(inst, th);

6262 pts.push({ x: rr * Math.cos(th), y: rr * Math.sin(th) });

6363 }

src/problems/laplace2d/matlab/build_problem.mmodified+6−5View file

@@ -18,7 +18,7 @@ function prob = build_problem(a, k, d, wantGrid)

1818 % curveD @(t) -> [x' y'] first derivative

1919 % curveDD @(t) -> [x'' y''] second derivative

2020 % g @(t) -> g Dirichlet data at boundary parameter t

21-% evalXY 65 x 2 points where uEval is required

21+% evalXY 289 x 2 points where uEval is required

2222 % vizXY m x 2 grid points where uGrid is requested

2323 % (m = 0 when no visualization is wanted)

2424

@@ -41,10 +41,11 @@ prob.curveDD = @(t) [(-a*k*k*cos(k*t) - 1 - a*cos(k*t)).*cos(t) + 2*a*k*sin(k*t)

4141 (-a*k*k*cos(k*t) - 1 - a*cos(k*t)).*sin(t) - 2*a*k*sin(k*t).*cos(t)];

4242 prob.g = @(t) laplace2d_bdata(t, a, k, sx, sy, c);

4343

44-% Evaluation points: 16 rays, 4 radial fractions, plus the origin.

45-% The rule must match evalPoints() in src/problems/laplace2d/exact.ts.

46-rho = [0.25; 0.5; 0.75; 0.9];

47-th = 2*pi*(0:15)'/16 + 0.13;

44+% Evaluation points: 32 rays, radial fractions 0.1..0.9, plus the origin

45+% (289 points). The rule must match evalPoints() in

46+% src/problems/laplace2d/exact.ts.

47+rho = (1:9)'/10;

48+th = 2*pi*(0:31)'/32 + 0.13;

4849 pts = zeros(numel(rho)*numel(th) + 1, 2);

4950 idx = 1;

5051 for i = 1:numel(rho)