# Dynamic Load-Balancing For PDE Solvers

Using Adaptive Unstructured Meshes

**Chris Walshaw and Martin Berzins**

### Abstract:

Modern PDE solvers written for time-dependent problems increasingly employ
adaptive unstructured meshes (see Flaherty et al. [1])
in order to both increase efficiency and control
the numerical error. If a distributed memory parallel computer
is to be used, there arises the significant problem of dividing up the domain
equally amongst the processors whilst minimising the inter-subdomain
dependencies. A number of graph based algorithms have recently been
proposed for steady state calculations, for example [2]
& [3]. This paper considers an extension to
such methods which renders them
more suitable for time-dependent problems in which the mesh may be
changed frequently.

**1**-
J. E. Flaherty, P. J. Paslow, M. S. Shepherd, and J. D. Vasilakis.
Adaptive Methods for Partial Differential Equations.
In
*Proc. of Workshop on Adaptive Computational Methods for
Partial Differential Equations, Rensseleer Poly. Inst., 1988*, SIAM,
Philadelphia, 1989.

**2**-
B. Hendrickson and R. Leland.
An Improved Spectral Graph Partitioning Algorithm for Mapping
Parallel Computations.
Tech. Rep. SAND 92-1460, Sandia National Labs, Albuquerque, NM.,
1992.

**3**-
H. D. Simon.
Partitioning of Unstructured Problems for Parallel Processing.
Tech. Rep. RNR-91-08, NASA Ames Research Center (to appear in
Computing Systems in Engineering), 1991.

* *

Fri Aug 13 13:42:55 BST 2004