Sponsored
Research Projects
Current
Projects
The goal of the project is to develop novel preconditioning techniques for sparse and dense linear systems. These techniques will use a sequence of linear transformations to obtain a preconditioned system from the original one. Techniques will be developed to analyze the preconditioned system, and schemes will be developed to improve the effectiveness of the preconditioner. The resulting preconditioners will be robust, effective, and inexpensive. These preconditioning techniques will be implemented, analyzed, and tested on a variety of problems. |
The goal of this
project is to develop a coupled, hybrid hydrodynamic computational model for
simulation and prediction of complex water wave processes from the deep ocean
to the shoreline. The model will be physically comprehensive, with total
domain scales on the order of hundred's of
kilometers, yet with a nearshore grid resolution
less than a meter. To include this great range of scales, a number of diverse
hydrodynamic models, with various but overlapping physical and practical
constraints, will be integrated to create a hybrid
hydrodynamic software tool. The method of interfacing the different
hydrodynamic models will be founded in distributed
computing techniques, thereby allowing for utilization of computer cluster
resources. In addition, each of the individual models in the hybrid system will be parallelized, leading to the creation of a
massively parallel and distributed simulation platform. |
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Past Projects
In this project we developed a new class of robust and parallelizable preconditioners for the solution of sparse linear systems arising from partial differential equations. The approach was based on a hierarchical decomposition of the matrices associated with the linear system, and was designed to improve the effectiveness of the preconditioner without compromising the parallelism inherent in the computation. A formal methodology was developed for construction, application, and analysis of these preconditioners. Effectiveness of these techniques were tested on problems in incompressible fluid simulations. Parallel implementations of these preconditioners were developed and their performance evaluated for various multiprocessor platforms.
In this project we developed preconditioned iterative methods for solving the linear systems arising in inductance and capacitance extraction problems. Solvers for the inductance problem used a novel solenoidal basis approach to precondition a reduced system implicitly, leading to rapid convergence of the iterative methods. Fast approximations to the matrix-vector products with dense system matrices were computed using efficient hierarchical methods.
We developed a software package called ParIS for parasitic
extraction of based on novel algorithms.
The package provides the capability of fast parasitic extraction on a variety
of parallel computers.
In this project we developed innovative
techniques and software for fast methods in particle dynamics and their
applications. The project addressed algorithmic issues, serial and parallel
performance, portability, and I/O requirements in the context of selected
applications. Specifically, the project made research contributions in the
following areas: · Error Control and Boundary Conditions for Hierarchical Treecodes · Robust Parallel Algorithms and Libraries for Dynamic Environments Data Analysis and I/O Control |
Simulations of solid-liquid flows are of great interest to numerous industries using sedimenting and fluidized suspensions, lubricated transport, and hydraulic fracturing of hydrocarbon reservoirs. The state-of-the-art preconditioners and iterative methods are unable to solve the ill-conditioned, large, sparse linear systems that arise in 3D simulations. We have proposed a novel multilevel approach that is a robust and effective preconditioner for these systems in addition to being efficiently parallelizable. Using this preconditioner, flows with thousands of particles can now be simulated on parallel computers such as the SGI Origin2000. Such simulations were not possible with existing methods. A unique feature of this approach is that a well-conditioned basis for the zero-divergence fluid space is explicitly computed. As a result, this technique is ideally suited for those engineering applications where conservation laws must be strictly enforced. We plan to extend the multilevel approach to non-Newtonian fluid flows with larger number of particles. There, issues related to visualization, data analysis, distributed object-oriented computing, and performance evaluation of software assume great importance - these will also be the focus of our continuing research.
The core issue in
many scientific applications is the solution of extremely large, sparse
linear systems on parallel computers. In general, this is
achieved by using a preconditioned iterative method. However, the
ultimate goal of finding robust, effective, and parallelizable
preconditioners has been elusive. We have developed parallel preconditioners
based on the multilevel technique described earlier that are very effective
for linear systems arising from partial differential equations. We have also
developed several novel algorithms, e.g., the balance scheme,
that use projection-based techniques to transform the original linear
system into a favorably conditioned reduced system. The reduced system can be
solved efficiently on parallel computers using well known
iterative methods. |
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Updated by Vivek Sarin on January 13, 2006