Multiphysics and multiscale simulations often need to solve discretized sparse
algebraic systems that are highly indefinite, nonsymmetric and extremely
ill-conditioned. For such problems, factorization based algorithms are often
at the core of the solvers toolchain. Compared to pure iterative methods,
the higher computation and communication costs in factorization methods
present serious hurdles to utilizing extreme-scale hardware.
I will present several research vignettes aimed at reducing those costs.
By incorporating data-sparse low-rank structures, such as
hierarchical matrix algebra, we can obtain lower arithmetic complexity
as well as robust preconditioner. By replicating small amount of data
in sparse factorization, we can avoid communication with provablly
lower communication complexity. By means of asynchronous, custermized
broadcast/reduction, we can reduce the dominating latency cost in
sparse triangular solution. The effectiveness of these techniques will be
demonstrated with our open source software STRUMPACK and SuperLU.
Sherry Li is a Senior Scientist at Lawrence Berkeley National Laboratory.
She has worked on diverse problems in high performance scientific
computations, including parallel computing, sparse matrix computations,
high precision arithmetic, and combinatorial scientific computing
She has (co)authored over 100 publications. She is the lead developer
of SuperLU sparse direct solver library, and has contributed
to several other widely-used mathematical libraries, including
ARPREC, LAPACK, STRUMPACK, and XBLAS. She received Ph.D. in Computer Science
from UC Berkeley in 1996. She is a SIAM Fellow and an ACM Senior Member.