Nodal Reordering Strategies

The availability of high performance computing
clusters has allowed scientists and engineers to
study more challenging problems. However, new
algorithms need to be developed to take advantage of
the new computer architecture. Since the solution
of linear systems still demands most of the
computational effort in many problems (such as the
approximation of partial differential equation
models) iterative methods and, in particular,
efficient preconditioners need to be developed. In
this study, we consider application of incomplete
LU (ILU) preconditioners for finite element models
to partial differential equations. We study two
implementations of the ILU preconditioner: a
stucture-based method and a threshold-based method.
Since finite elements lead to large, sparse systems,
reordering the node numbers can have a substantial
influence on the effectiveness of these
preconditioners.

Autorentext

Fellow of the Society of Actuaries. Member of the American Academy of Actuaries. MS Mathematics, BS Mathematics, BS Computer Science from Virginia Tech. Tae Kwon Do Blackbelt. Currently working as an actuarial consultant for Mercer in New York City.

Klappentext

The availability of high performance computing clusters has allowed scientists and engineers to study more challenging problems. However, new algorithms need to be developed to take advantage of the new computer architecture. Since the solution of linear systems still demands most of the computational effort in many problems (such as the approximation of partial differential equation models) iterative methods and, in particular, efficient preconditioners need to be developed. In this study, we consider application of incomplete LU (ILU) preconditioners for finite element models to partial differential equations. We study two implementations of the ILU preconditioner: a stucture-based method and a threshold-based method. Since finite elements lead to large, sparse systems, reordering the node numbers can have a substantial influence on the effectiveness of these preconditioners.