Leader:  Dr. Yalchin Efendiev

Co-Leaders:  Dr. Nancy Amato and Dr. Bani Mallick

Research Core 1 addresses topics related to systematic modeling and simulation approaches for multiscale problems able to make accurate predictions and account for uncertainties due to modeling and measurement errors.


Synergy with Other Research Cores

Robust and fast parallel algorithms are essential for inverse problems (Core 2) and data assimilation (Core 3). Without fast algorithms that can quantify uncertainties and make reliable predictions across the scales, one cannot solve complex inverse and optimization problems. Multiscale algorithms deliver the solution fields at different scales which are used for visualization purposes (Core 3).


Research Directions

In a problem-solving environment, it is important that forward modeling and simulations satisfy the following requirements:

(1) model errors and uncertainties can be quantified;

(2) simulations across scales can be performed efficiently and fast in parallel;

(3) numerical errors can be estimated (deterministically and statistically); and

(4) probabilistic predictions with a confidence level can be performed.

Research Thrusts & Example Projects


Research Thrust 1: Numerical analysis at fundamental (resolved) scales;

Development of compatible, stable, and accurate approximation methods

Development of adaptive methods with a posteriori error estimates

Development of efficient iterative solution methods

Example project: Numerical methods for transport equations

Research Thrust 2: Modeling and simulation for bridging scales; 

Development of analytical modeling approaches for bridging the scales

Development of numerical approaches for bridging the scales and propagation of uncertainties across the scales

Example project: Multiscale simulation techniques for bridging scales


Research Thrust 3: Data analysis and predictive statistical modeling

Statistical data analysis and modeling 

Solving differential equations in the presence of uncertainties

Example project: Hierarchical Bayesian Approaches for Statistical Modeling

Research Thrust 4: Parallel computing

Strategies for exploiting the adaptive, hierarchical discretizations arising from the numerical methods on advanced computational platforms

Data structures to support multiscale problems on massive (e.g., petascale) computational platforms

Example project: High performance methods for particle transport