Hierarchical Low-rank Matrix Factorizations
Asynchronous Iterative Solvers
Combinatorial Scientific Computing
Zoltan and Zoltan2: partitioning and load balancing
**Former projects:**
Extreme-scale Algorithms and Software (EASIR)
Support preconditioners
Ice Sheet Modeling
Sensor placement for water contamination detection
Parallel Solvers for Circuit Simulation (Xyce)
#### Hierarchical Low-rank Matrix Factorizations

Many linear systems have naturally low-rank properties. Examples of such structure include H, H2, HSS, and HODLR matrices. In collaboration with Professor Eric Darve at Stanford, we are investigating a novel hierarchical low-rank solver algorithm. The algorithm may either be used as a fast sparse direct solver or as a preconditioner. I am the PI for this Sandia/LDRD project.

#### Asynchronous Iterative Solvers

Communication and synchronization can be very expensive on extreme-scale parallel systems. We investigate how asynchronous methods may be used to solve linear systems more efficiently on systems with high concurrency. The project involves both multithreaded on-node solvers and optimized Schwarz domain decomposition between nodes. Collaboration with Georgia Tech (Edmond Chow), Temple (Daniel Szyld), and UTK.

#### Combinatorial Scientific Computing

My main research area is combinatorial scientific computing (CSC). I was formerly a principal investigator for the CSCAPES project (2006-2011).

The Institute for Combinatorial Scientific Computing and Petascale Simulations (CSCAPES, pronounced "seascapes") is one of the four Institutes established nationwide in September 2006 as the new component of the second cycle of the DOE initiative Scientific Discovery through Advanced Computing (SciDAC). The CSCAPES Institute has a two-fold purpose:

- To accelerate the development and deployment of fundamental enabling technologies in high performance computing, by creating algorithms and software tools for key combinatorial problems in scientific computing at the petascale, and
- To foster the next generation of researchers capable of effectively applying combinatorial techniques to scientific computing, by training graduate students and post-doctoral associates, conducting outreach workshops and tutorials, and publishing in the scientific literature.

The focus areas of CSCAPES are load balancing in parallel computation, automatic differentiation, and advanced methods for sparse matrix computations. To realize its goals, CSCAPES is committed to working closely with other SciDAC Institutes, Centers for Enabling Technologies, and Science Application Partnerships, as well as with relevant bodies in academia and industry, internationally.
The CSCAPES Institute is a collaborative effort among investigators from Purdue University, Old Dominion University, Sandia National Laboratories, Argonne National Laboratory, Ohio State University, and Colorado State University. The Institute is funded by DOE's Office of Science.

CSCAPES Homepage

#### Zoltan and Zoltan2: partitioning, load balancing, ordering, coloring

Zoltan
is a toolkit for data management in parallel (distributed) computing.
It is the leading tool for partitioning and dynamic load balancing for scientific computing.
We have recently developed a fully parallel hypergraph partitioner in Zoltan.
Zoltan is open-source software and available for download, either separately or as part of

Trilinos.

Zoltan2 is a new Trilinos package for partitioning and combinatorial scientific computing, and can be viewed as a complete redesign and refactor of Zoltan. We have recently developed novel 2D partitioning method for scale-free graphs, which will eventually be deployed in Zoltan2. We are pursuing both shared-memory and distributed-memory parallel algorithms.

#### Extreme-Scale Algorithms and Software Institute (EASIR)

EASIR is a math/CS research institute funded by DOE Office of Science. Participants include Sandia, Oak Ridge, U. of Tennessee - Knoxville, UC Berkeley, and UIUC. The goal is to improve performance for scientific computing on many-core and emerging architectures, with focus on future extreme-scale computers. Algorithmic resilience is another research component.
I am interested in communication-avoiding algorithms for linear algebra and manycore preconditioners.

#### Ice Sheet Modeling

We will model cracks and fracture in ice sheets and their impact on global climate. Computational tools include XFEM, multigrid solvers, and load balancing for parallel computing.

This project is led by Columbia University, and part of

ISICLES.

#### Support preconditioners

Support preconditioners is an emerging class of preconditioners for
symmetric linear systems with strong theoretical properties.
I have made important contributions in this area, see
my list of

publications.
Learn more about support preconditioners at

www.preconditioners.com.

#### Sensor placement for water contamination detection

Sandia has in collaboration with the EPA developed an early warning system for detecting contamination of drinking water. This is part of the TEVA (Threat Ensemble Vulnerability Assessment) and SPOT (Sensor Placement Optimization Toolkit) projects.

(Press release.) My contribution has been in optimization methods for sensor placement, in particular memory-efficient Lagrangian methods. The EPA/Sandia/Argonne team was a finalist for the prestigous

2008 Edelman award in operations research. (

Description of the finalists.)

#### Parallel Solvers for Circuit Simulation (Xyce)

Xyce is a parallel circuit simulator, similar to SPICE. A key problem is to solve highly ill-conditioned sparse linear systems of equations. Traditionally, direct solvers are used, but these do not scale well in parallel. Most iterative solvers (preconditioners) do not work well. I work on both direct and iterative methods that are suitable for parallel computing.