Research Areas

The FASTMath SciDAC Institute is developing and deploying scalable mathematical algorithms and software tools for reliable simulation of complex physical phenomena and collaborating with Department of Energy (DOE) domain scientists to ensure the usefulness and applicability of our work. The focus of our work is strongly driven by the requirements of DOE application scientists who require fast, accurate, and robust forward simulation along with the ability to efficiently perform ensembles of simulations in optimization or uncertainty quantification studies.

Adaptive and Multiscale Discretizations

To advance efficient, architecture-aware temporal and spatial discretizations relevant to SciDAC partnerships, a set of activities coordinated across FASTMath will advance our discretization methods and associated software to support efficient, adaptive multiscale simulation workflows that employ multiple coupled models.

Algebraic Solvers

Solution of systems of algebraic equations is undoubtedly one of the most common computational kernels in scientific applications of interest to the Department of Energy. Efficient, scalable, and reliable algorithms are crucial for the success of large-scale simulations. To achieve maximal efficiency, the solvers need to exploit structure and data need to remain resident on the GPUs. We will advance our linear, nonlinear, and eigen solvers by exploiting properties of multiscale discretizations and block structures. 

Decision Support Methods

Our decision support methods encompass fundamental research in uncertainty quantification (UQ) and numerical optimization. These methods are used for quantifying confidence in simulations, improving scientific AI/ML training and inference, and solving parameter and state estimation problems for dynamic models. Our work includes innovative research in leveraging domain knowledge, estimating model fidelity, obtaining and combining information, and advancing the mathematics of digital twins.