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.

Our contributions in SciDAC-4 range from providing the foundations for next-generation application codes to developing key numerical capabilities that enabled faster time to solution, higher fidelity, and more robust simulations. In SciDAC-5, we will continue our efforts to further develop the full range of technologies to improve the reliability, accuracy, and robustness of application simulation codes.

In particular, our team will conduct research in eight foundational topical areas, covering problem discretization, solution of algebraic systems of equations, and others. We will advance numerical methods and software in each of these eight focused topical areas, prioritizing our developments based on application needs both now and as they evolve into the future. We will also more tightly integrate these methods and software together to improve overall functionality, efficiency, and performance of next-generation simulation codes.

Tools for Problem Discretization

A number of critical Department of Energy applications, characterized by complex geometry and/or physics, have greatly benefited from the application of high-order and/or adaptive mesh methods that have been developed by the FASTMath team. Over the course of the SciDAC program, these methods and tools have evolved to the point where application scientists are able to focus their attention on the development of domain-specific discretization technologies, using FASTMath tools for controlling and adapting the meshes. Our focus in FASTMath is the continued development of structured, multi-block technologies, unstructured mesh techniques, particle-mesh methods, and time discretization methods. Of critical importance in these areas is high-order discretization techniques and adaptive mesh refinement.


Tools for Solution of Algebraic Systems

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. FASTMath work focuses on both iterative and direct linear solution methods, and eigensolvers. Our work in the first half of the project in these areas centered around two primary themes. First, we are developing new algorithms and using them to better solve physics problems including advanced multigrid techniques, improved preconditioners, and new eigensystem solvers. Second, we are creating efficient many-core solution methodologies using hybrid programming techniques, communication-reducing strategies, and intelligent task-mapping methods. This work has application to fusion, nuclear structure calculation, quantum chemistry, accelerator modeling, climate, and dislocation dynamics research.


Tools for the Outer Loop

Many scientific applications of interest to the Department of Energy require the use of outer loop methods for parameter estimation, design optimization, optimization under uncertainty, and uncertainty quantification. The FASTMath work in these outer loop activities focuses on numerical optimization, uncertainty quantification, and data analysis. In the numerical optimization area, we are developing scalable methods for derivative-free optimization, constrained optimization, and multi-objective optimization. In the uncertainty quantification area, we are developing Bayesian inference and optimization methods and multi-fidelity methods. In the data analytics area, we are developing hierarchical data representations and statistical methods for data fusion with multi-modal and multi-physics data. All this work has applications in climate, fusion, high-energy physics, and nuclear physics.