**Linear Algebra Problems**
We designed new generation of algorithms to solve extremely large
dense systems of linear equations with 10 million (and more) unknowns.
The algorithms are accurate and insensitive to condition number of
the main matrix. They work well on current parallel architectures,
including clusters of multi-cores and Graphics Processing Units (GPUs).
**Integral Equation-Based Electromagnetic Problems**
The discretization of integral equation-based electromagnetic problems,
including antenna design, leads to dense system of linear equations.
The algorithm to solve such systems of linear equations essentially
utilizes the new generation of algorithms mentioned above. It can
solve electromagnetic problems with 10 million (and more) unknowns.
Due to compact nature of computer resources required by the new
algorithms, only computer memory for a few vectors is required.
**Statistical machine learning (SML)**
SML is one of the topics of artificial intelligence. SML deals with
the design and development of algorithms and techniques that allow
computers to "learn". The major focus of machine learning research
is to extract information from data automatically, by computational
and statistical methods. We investigate the use of statistical
machine learning methods within the framework of Bayesian statistics
and apply them to engineering and scientific problems of interest
to aircraft design community. We offer environments satysfying
customer modeling requirements, including innovative techniques with
highly optimized algorithms on current and future computer platforms.
**Selecting Low Discrepancy Sequences for computational problems**
The term Low Discrepancy Sequences (LDS) has a precise mathematical
definition. Intuitively, we can say it is a sequence of N points
which are more uniform than any pseudo-randomly generated sequence.
There are mathematical algorithms developed to avoid clustering
as observed with pseudo-random number generators. The LDS are
applicable to a wide range of scientific and engineering areas,
including:
**Operations Research**
Design trade studies with performance and support impact assessment,
aircraft configuration optimization, verification studies.
**Micro-electromechanical systems (MEMS)**
Automotive, aerospace, biology, chemistry, computer science,
medicine, optics, and telecommunications.
**Computer simulations for all aspects of MEMS design**
Aerodynamic, electro-magnetic, mechanical, optical, structural,
and thermal.