The Multigrid Workbench: Discretization Techniques

Any (partial) differential equation must be discretized before it can be treated computationally. The most common techniques are

Many text books on numerical methods for partial differential equations provide background information on these methods.

For the multigrid workbench the example problem is discretized by five point differences. Here the (square) domain is replaced by an equidistant mesh with gridlines.

Each node is represented by an unknown

and the partial derivatives are replaced by

so that Laplace's equation becomes a system of linear equations of the form

This banded system may be solved by direct elimination techniques, however, much faster are (linear) iterative methods, like the multigrid method.

Ulrich Ruede , Thu Feb 2 21:05:32 MEZ 1995
Updated by Craig C. Douglas