Aditya-m04/IR_vary_f_1000 · Datasets at Hugging Face

Input stringlengths 2.85k 2.92k	Output stringlengths 170 8.17k
{ "metadata": { "case_id": "sample_523_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:14:36.645522Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m². The characteristic length is 0.25 m and aspect ratio ~1.0, indicating a square geometry. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). Physics are governed by the steady-state Poisson equa...
{ "metadata": { "case_id": "sample_126_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:23.584202Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of unit side length (1.0 m × 1.0 m) is modeled with homogeneous material conductivity k = 1.0 W/(m·K). The governing physics is steady‑state heat conduction described by the Poisson equation −∇·(k∇T) = f, where f is a spatially varying volumetric source term. All four boundaries are he...
{ "metadata": { "case_id": "sample_999_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:18:34.346160Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D unit square plate of side length 1.0 m and area 1.0 m² is modeled with homogeneous material conductivity k = 1.0 W/(m·K). Steady-state heat conduction follows the Poisson equation -∇·(k∇T) = f with spatially-varying internal source f(x,y). All boundaries—left, right, top, and bottom—are prescribed ...
{ "metadata": { "case_id": "sample_548_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:14:47.905651Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of side 1.0 m (x∈[0,1], y∈[0,1]) encloses a domain area of 1.0 m² and a total boundary length of 4.0 m. The characteristic length is 0.25 m and the aspect ratio is essentially unity. The homogeneous material has thermal conductivity k=1.0 W/(m·K). The physics follow the steady‑state he...
{ "metadata": { "case_id": "sample_019_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:10:26.441474Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of unit dimensions (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m² and characteristic length 0.25 m. The plate is homogeneous with thermal conductivity k = 1.0 W/(m·K). Physics follow steady-state heat conduction governed by the Poisson equation −∇·(k∇T) = f, where f represents a vo...
{ "metadata": { "case_id": "sample_894_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:17:28.976453Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of unit side length (0–1 m in x and y) encloses an area of 1.0 m². The material is homogeneous with thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation −∇·(k∇T) = f, where f(x,y) is the volumetric heat source term. All four boundaries ...
{ "metadata": { "case_id": "sample_412_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:13:44.932919Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of unit dimensions (1 m × 1 m) undergoes steady-state heat conduction governed by -∇·(k∇T) = f. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). All four boundaries are held at Dirichlet temperature T = 0 K, creating a thermal reference plane. The plate area is 1.0 m²...
{ "metadata": { "case_id": "sample_174_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:44.432462Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (domain area 1.0 m²) with homogeneous material conductivity k = 1.0 W/(m·K). The physics follow steady-state heat conduction governed by the Poisson equation -∇·(k∇T) = f. Boundary conditions are Dirichlet with temperature fixed at T = 0 K on all four sides (le...
{ "metadata": { "case_id": "sample_104_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:12.747065Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of unit side length (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m² and aspect ratio ≈1.0. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation -∇·(k∇T) = f with Dirichlet boundary conditions T = 0 K impo...
{ "metadata": { "case_id": "sample_838_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:16:59.839134Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate from the plate geometry family spans x ∈ [0,1] m and y ∈ [0,1] m, yielding a domain area of 1.0 m² and an aspect ratio of 1.0. The material is homogeneous with thermal conductivity k = 1.0 W/(m·K). Physics are governed by the steady-state Poisson equation -∇·(k∇T) = f, where f(x,y) is ...
{ "metadata": { "case_id": "sample_296_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:12:54.187315Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m² and characteristic length 0.25 m. The homogeneous material exhibits thermal conductivity k = 1.0 W/(m·K). Physics are governed by steady-state heat conduction via the Poisson equation -∇·(k∇T) = f, where f is a...
{ "metadata": { "case_id": "sample_107_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:14.479087Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m² and characteristic length 0.25 m. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction follows the Poisson equation −∇·(k∇T) = f with linear finite element discretizat...
{ "metadata": { "case_id": "sample_145_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:31.792305Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of unit side length (x, y ∈ [0,1] m) with area 1.0 m² and characteristic length 0.25 m. The material is homogeneous with thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation -∇·(k∇T) = f, where f represents a volumetric heat source term...
{ "metadata": { "case_id": "sample_837_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:16:59.174126Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of unit length (1 m × 1 m) and thickness negligible relative to in-plane dimensions, composed of a homogeneous material with thermal conductivity k = 1.0 W/(m·K). The governing physics is steady-state heat conduction obeying the Poisson equation −∇·(k∇T) = f, where f(x,y) represents a ...
{ "metadata": { "case_id": "sample_136_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:27.865256Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D unit square plate of dimensions x∈[0,1] m, y∈[0,1] m with homogeneous conductivity k=1.0 W/(m·K) undergoes steady-state heat conduction governed by the Poisson equation -∇·(k∇T)=f. All four boundaries impose Dirichlet conditions T=0 K. The domain area is 1.0 m² with aspect ratio ≈1.0 confirming a s...
{ "metadata": { "case_id": "sample_760_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:16:19.555688Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of unit length (x ∈ [0,1] m, y ∈ [0,1] m) with area 1.0 m² and characteristic length 0.25 m. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation -∇·(k∇T) = f. All four boundaries (left, right, bottom, top) ...
{ "metadata": { "case_id": "sample_324_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:13:07.617476Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of side length 1.0 m (x in [0,1], y in [0,1]) occupies a domain area of 1.0 m^2. The material is homogeneous with thermal conductivity k = 1.0 W/(mK). Heat transfer is governed by steady-state conduction described by the Poisson equation -div(kgrad(T)) = f, where f represents a spati...
{ "metadata": { "case_id": "sample_210_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:12:04.855715Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (area 1.0 m², characteristic length 0.25 m, aspect ratio ~1.0) undergoes steady-state heat conduction described by the Poisson equation -∇·(k∇T) = f. The material is homogeneous with conductivity k = 1.0 W/(m·K). All four boundaries (left, right, bottom, top) s...
{ "metadata": { "case_id": "sample_702_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:15:58.067448Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D unit-square plate of dimensions 1.0 m × 1.0 m (area 1.0 m²) undergoes steady-state heat conduction governed by -∇·(k∇T) = f with homogeneous conductivity k = 1.0 W/(m·K). All four boundaries (left x=0, right x=1, bottom y=0, top y=1) are held at Dirichlet temperature T = 0, establishing a zero-refe...
{ "metadata": { "case_id": "sample_150_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:33.380325Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D unit square plate measuring x∈[0,1] m and y∈[0,1] m with area 1.0 m² and near-unity aspect ratio. The homogeneous material has conductivity k=1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation -∇·(k∇T)=f. All four boundaries (left, right, top, bottom) have Dirichlet condi...
{ "metadata": { "case_id": "sample_265_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:12:34.765080Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D unit square plate of dimensions x∈[0,1] m and y∈[0,1] m with homogeneous material conductivity k=1.0 W/(m·K). The steady-state heat conduction is governed by the Poisson equation -∇·(k∇T)=f. All four boundaries (left, right, top, bottom) have Dirichlet conditions with temperature fixed at zero. The...
{ "metadata": { "case_id": "sample_298_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:12:55.680333Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...	{ "problem": "A 2D square plate of unit side length (x,y ∈ [0,1] m) with homogeneous material conductivity k = 1.0 W/(m·K) undergoes steady-state heat conduction governed by -∇·(k∇T) = f. All four boundaries are held at zero temperature (Dirichlet BCs: T=0 on left, right, top, and bottom edges). The domain area is 1....

{ "metadata": { "case_id": "sample_523_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:14:36.645522Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m². The characteristic length is 0.25 m and aspect ratio ~1.0, indicating a square geometry. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). Physics are governed by the steady-state Poisson equa...

{ "metadata": { "case_id": "sample_126_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:23.584202Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of unit side length (1.0 m × 1.0 m) is modeled with homogeneous material conductivity k = 1.0 W/(m·K). The governing physics is steady‑state heat conduction described by the Poisson equation −∇·(k∇T) = f, where f is a spatially varying volumetric source term. All four boundaries are he...

{ "metadata": { "case_id": "sample_999_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:18:34.346160Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D unit square plate of side length 1.0 m and area 1.0 m² is modeled with homogeneous material conductivity k = 1.0 W/(m·K). Steady-state heat conduction follows the Poisson equation -∇·(k∇T) = f with spatially-varying internal source f(x,y). All boundaries—left, right, top, and bottom—are prescribed ...

{ "metadata": { "case_id": "sample_548_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:14:47.905651Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of side 1.0 m (x∈[0,1], y∈[0,1]) encloses a domain area of 1.0 m² and a total boundary length of 4.0 m. The characteristic length is 0.25 m and the aspect ratio is essentially unity. The homogeneous material has thermal conductivity k=1.0 W/(m·K). The physics follow the steady‑state he...

{ "metadata": { "case_id": "sample_019_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:10:26.441474Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of unit dimensions (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m² and characteristic length 0.25 m. The plate is homogeneous with thermal conductivity k = 1.0 W/(m·K). Physics follow steady-state heat conduction governed by the Poisson equation −∇·(k∇T) = f, where f represents a vo...

{ "metadata": { "case_id": "sample_894_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:17:28.976453Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of unit side length (0–1 m in x and y) encloses an area of 1.0 m². The material is homogeneous with thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation −∇·(k∇T) = f, where f(x,y) is the volumetric heat source term. All four boundaries ...

{ "metadata": { "case_id": "sample_412_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:13:44.932919Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of unit dimensions (1 m × 1 m) undergoes steady-state heat conduction governed by -∇·(k∇T) = f. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). All four boundaries are held at Dirichlet temperature T = 0 K, creating a thermal reference plane. The plate area is 1.0 m²...

{ "metadata": { "case_id": "sample_174_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:44.432462Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (domain area 1.0 m²) with homogeneous material conductivity k = 1.0 W/(m·K). The physics follow steady-state heat conduction governed by the Poisson equation -∇·(k∇T) = f. Boundary conditions are Dirichlet with temperature fixed at T = 0 K on all four sides (le...

{ "metadata": { "case_id": "sample_104_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:12.747065Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of unit side length (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m² and aspect ratio ≈1.0. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation -∇·(k∇T) = f with Dirichlet boundary conditions T = 0 K impo...

{ "metadata": { "case_id": "sample_838_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:16:59.839134Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate from the plate geometry family spans x ∈ [0,1] m and y ∈ [0,1] m, yielding a domain area of 1.0 m² and an aspect ratio of 1.0. The material is homogeneous with thermal conductivity k = 1.0 W/(m·K). Physics are governed by the steady-state Poisson equation -∇·(k∇T) = f, where f(x,y) is ...

{ "metadata": { "case_id": "sample_296_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:12:54.187315Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m² and characteristic length 0.25 m. The homogeneous material exhibits thermal conductivity k = 1.0 W/(m·K). Physics are governed by steady-state heat conduction via the Poisson equation -∇·(k∇T) = f, where f is a...

{ "metadata": { "case_id": "sample_107_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:14.479087Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (x ∈ [0,1] m, y ∈ [0,1] m) with domain area 1.0 m² and characteristic length 0.25 m. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction follows the Poisson equation −∇·(k∇T) = f with linear finite element discretizat...

{ "metadata": { "case_id": "sample_145_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:31.792305Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of unit side length (x, y ∈ [0,1] m) with area 1.0 m² and characteristic length 0.25 m. The material is homogeneous with thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation -∇·(k∇T) = f, where f represents a volumetric heat source term...

{ "metadata": { "case_id": "sample_837_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:16:59.174126Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of unit length (1 m × 1 m) and thickness negligible relative to in-plane dimensions, composed of a homogeneous material with thermal conductivity k = 1.0 W/(m·K). The governing physics is steady-state heat conduction obeying the Poisson equation −∇·(k∇T) = f, where f(x,y) represents a ...

{ "metadata": { "case_id": "sample_136_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:27.865256Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D unit square plate of dimensions x∈[0,1] m, y∈[0,1] m with homogeneous conductivity k=1.0 W/(m·K) undergoes steady-state heat conduction governed by the Poisson equation -∇·(k∇T)=f. All four boundaries impose Dirichlet conditions T=0 K. The domain area is 1.0 m² with aspect ratio ≈1.0 confirming a s...

{ "metadata": { "case_id": "sample_760_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:16:19.555688Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of unit length (x ∈ [0,1] m, y ∈ [0,1] m) with area 1.0 m² and characteristic length 0.25 m. The homogeneous material has thermal conductivity k = 1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation -∇·(k∇T) = f. All four boundaries (left, right, bottom, top) ...

{ "metadata": { "case_id": "sample_324_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:13:07.617476Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of side length 1.0 m (x in [0,1], y in [0,1]) occupies a domain area of 1.0 m^2. The material is homogeneous with thermal conductivity k = 1.0 W/(m*K). Heat transfer is governed by steady-state conduction described by the Poisson equation -div(k*grad(T)) = f, where f represents a spati...

{ "metadata": { "case_id": "sample_210_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:12:04.855715Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate measuring 1.0 m by 1.0 m (area 1.0 m², characteristic length 0.25 m, aspect ratio ~1.0) undergoes steady-state heat conduction described by the Poisson equation -∇·(k∇T) = f. The material is homogeneous with conductivity k = 1.0 W/(m·K). All four boundaries (left, right, bottom, top) s...

{ "metadata": { "case_id": "sample_702_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:15:58.067448Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D unit-square plate of dimensions 1.0 m × 1.0 m (area 1.0 m²) undergoes steady-state heat conduction governed by -∇·(k∇T) = f with homogeneous conductivity k = 1.0 W/(m·K). All four boundaries (left x=0, right x=1, bottom y=0, top y=1) are held at Dirichlet temperature T = 0, establishing a zero-refe...

{ "metadata": { "case_id": "sample_150_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:11:33.380325Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D unit square plate measuring x∈[0,1] m and y∈[0,1] m with area 1.0 m² and near-unity aspect ratio. The homogeneous material has conductivity k=1.0 W/(m·K). Steady-state heat conduction is governed by the Poisson equation -∇·(k∇T)=f. All four boundaries (left, right, top, bottom) have Dirichlet condi...

{ "metadata": { "case_id": "sample_265_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:12:34.765080Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D unit square plate of dimensions x∈[0,1] m and y∈[0,1] m with homogeneous material conductivity k=1.0 W/(m·K). The steady-state heat conduction is governed by the Poisson equation -∇·(k∇T)=f. All four boundaries (left, right, top, bottom) have Dirichlet conditions with temperature fixed at zero. The...

{ "metadata": { "case_id": "sample_298_solution000001", "solver": "FEniCSx", "dimensionality": "2D", "geometry_family": "plate", "timestamp": "2026-02-17T15:12:55.680333Z" }, "geometry": { "bbox": [ 0.0, 1.0, 0.0, 1.0, 0.0, 0.0 ], "volume": 1.0, ...

{ "problem": "A 2D square plate of unit side length (x,y ∈ [0,1] m) with homogeneous material conductivity k = 1.0 W/(m·K) undergoes steady-state heat conduction governed by -∇·(k∇T) = f. All four boundaries are held at zero temperature (Dirichlet BCs: T=0 on left, right, top, and bottom edges). The domain area is 1....