Computational Math & Algorithms
Research encompasses a range of disciplines seeking computational methods to solve fundamental equations. Solutions may be sought for existing equations or new equations may be developed expressly for the purpose of treating problems of Army interest. Problems in which the equations can be expressed in the form of partial differential equations stem from the basic science and engineering disciplines spanning characteristic length scales from sub-atomic to continuum, neural signals, stochastic variables and design theory. Broad classes of problems may also require considerable specialization of solutions based on the platform used to obtain them.
- PDE Based Methods
- Complex Systems
Seeks understanding of phenomena that pertain to the scientific pursuits in and across traditional scientific disciplines that lack relevant computational capabilities. Often, the problems are interdisciplinary or require the solution of multiple sets of equations with disparate intrinsic length scales. The equations, algorithms, and conceptual representation, can change with respect to both space and time when traversing scales or crossing the boundaries between scientific disciplines Multi-scale simulations are instrumental in gaining insight into material response predictions; weather and climate forecasting; chemical and biological dispersion; micro-systems; biological ecosystems; and computer and human networks. In each of these areas there is a growing need for higher fidelity computations at the individual scales as well as research into mathematics and computational algorithms bridging the scales.
- Multi-scale simulations
- Physical Processes and Mechanisms
- Emulation methods
Applied Computer Modeling and Analysis
Is focused on using predictive and reliable computational capabilities and tools to impact the design and deployment of critical Army systems and devices. Computational sciences-based enabling tools are required to perform large-scale system analysis from complex model development to detailed analytics.
- Large-scale systems and scenarios modeling
- Large-scale computing enablers
Verification, Validation, & Uncertainty Quantification
Research is focused on assuring that simulations perform as intended, considering the range of conditions where models and simulations reproduce observed behavior within acceptable tolerances and establishing confidence levels. Army applications span many fields including non-traditional and data intensive sciences and challenges fundamental understanding of VVUQ. The Computational Science Campaign will work with the other ARL Campaigns to explore, develop, and implement VVUQ tools for (i) identifying deficiencies in simulations; (ii) setting guidelines for adequacy of computational results; (iii) exploring the impact of known variability and uncertainty of input; and (iv) control of adaptive algorithms to achieve specified levels of accuracy in solutions.
- Verification and validation
- Uncertainty Quantification