HPC Tier Module
Poisson (Multigrid)
A geometric multigrid V-cycle for the 3D Poisson equation, with true error against a known solution.
This tool runs inside GDBS HPC. What it computes and the authorities it applies are below.
The problem
Demonstrating multigrid convergence and confirming it against a known solution usually requires a numerical-PDE setup outside the browser.
The local-first solution
This plugin calls the real multigrid engine in the browser to run a geometric V-cycle for the 3D Poisson equation on a toroidal grid, rendering residual convergence and, for the sine mode, the true L2 error against the exact solution.
What it does
Geometric multigrid V-cycle for 3D Poisson on a toroidal grid
Selectable sine-mode (exact known) or Gaussian source term
Residual convergence history per V-cycle
True L2 and Linf error vs the exact solution for the sine mode
3D solution surface plus mid-plane heatmap with the GeoNum trust verdict
Honest scope
For the sine mode the exact solution is known, so the reported L2 and Linf are true errors rather than asserted accuracy, validated by the engine's native multigrid test suite. The trust verdict is the engine's own GeoNum measurement, passed through.
Authorities cited
- Brandt (1977). Multi-Level Adaptive Solutions to Boundary-Value Problems. Math. Comp. 31, 333.
- Trottenberg, Oosterlee, Schuller (2001). Multigrid. Academic Press.
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Run a multigrid V-cycle
Run the solver in the browser and save the result to Sandbox, attach it to a Worklog case, or route it into a Gate client portal. Nothing is uploaded to anyone's cloud.