A graph theoretic process that models level-based, incomplete LU factorization (ILU(`)) of sparse unsymmetric matrices is developed. The model leads to two incomplete fill path theorems that are generalizations of the original fill path theorem of Rose, Tarjan, and Lueker. Our S-level incomplete fill path theorem leads to the development of new, embarrassingly parallel algorithms for computing ...

In this paper, a new variant of the Jacobi-Davidson method is presented that is specifically designed for real unsymmetric matrix pencils. Whenever a pencil has a complex conjugated pair of eigenvalues, the method computes the two dimensional real invariant subspace spanned by the two corresponding complex conjugated eigenvectors. This is beneficial for memory costs and in many cases it also ac...

A scheme is presented for analising nite-element triangulations. The method takes a random triangulated planar graph and gives a multifrontal way to solve the corresponding physical problem, so that the maximum bandwidth of each front is guaranteed to be \optimal". The interesting characteristic of this scheme is that it introduces large-grained parallelism dictated by the domain structure. A w...

Benchmarks for parallel processing of large models is an urgent need for High Performance Computing (HPC) as today’s model size reaches millions of degrees of freedom. Explicit solvers as in the case of crash dynamics or fluid dynamics do not require matrix based equation solvers and inherently exhibit good scalability on large numbers of processors. Where as analysis requiring implicit solvers...

Noise, Vibration and Harshness (NVH) is a critical consideration in the design of automotive and aerospace vehicles for comfort, and fatigue of components arising from interior structural and acoustic pressure fluctuations due to external structural or acoustic loading. In the low to mid frequency range, current NVH models, obtained by direct, unsymmetric, coupled Eulerian Finite Element discre...