

Olaf Steinbach :Artificial Multilevel Preconditioners
The use of multilevel preconditioners such as the BPX
preconditioner is based on an appropriate hierarchy
of the underlying finite or boundary element spaces which
can be obtained by refinement starting from a given
coarse grid. In practical applications, however, the coarse grid may be already huge such that geometric
multilevel strategies can not be applied. Using ideas
from fast boundary element methods, in particular
clustering algorithms, it is possible to define an
artificial multilevel hierarchy for piecewise constant
finite or boundary element spaces. From this one can
easily derive efficient preconditioners for both
finite and boundary element methods.
