2D Laplace Equation Solver

∇²φ = 0 models electrostatics, gravity, heat, and fluid flow. Draw conductors at fixed potentials; watch equipotential lines and electric field lines emerge via SOR iteration.

Draw Mode

+V (hot)

−V (cold)

Erase

Brush size 6px

Solver

Over-relax ω 1.80 Iter/frame 20

Convergence

Residual: —
Iterations: —

Physics

∇²φ = 0
E = −∇φ

Mean value:
φ(x)=avg(nbrs)

SOR: ω∈(1,2)
optimal ω→2