Poisson and Laplace equations

Steady boundary-value problems: a sparse direct Poisson solve, the relaxation iterations that preceded it, finite elements, and multigrid.

Poisson’s equation: a potential with sources

Poisson's equation: a potential with sources

Richardson’s relaxation: iterating toward Laplace’s solution

Richardson's relaxation: iterating toward Laplace's solution

Finite elements: Galerkin’s hat functions on an uneven mesh

Finite elements: Galerkin's hat functions on an uneven mesh

Multigrid: a solver whose cost does not grow with the grid

Multigrid: a solver whose cost does not grow with the grid