FASTMath SciDAC Institute
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 work extensively with mesh-based, continuum-level models or particle-based techniques. The FASTMath team has extensive experience developing algorithms and software tools available for such simulations. 

Our current research efforts are focused on developing a full range of technologies to improve the reliability, accuracy, and robustness of application simulation codes. In particular, we are developing mesh-based methods including structured, unstructured, and mapped multiblock techniques. We will use embedded boundaries along with high-quality, high-order mesh representations to capture complex geometry, and adaptive mesh refinement to control error in multi resolution simulations. We are developing fast solvers, load-balancing methods, and new remapping techniques. We are focusing effort on robust linear, nonlinear, and eigensolvers.

By bringing these different areas into a single institute, we are able to effectively deploy new integrated capabilities such as efficient adaptivity through the software stack and coupling technologies.

One of the key challenges facing the scientific computing community is the shift to multi-/manycore nodes and million-way parallelism. Thus a pervasive theme in our work is understanding the most effective ways to implement our algorithms at scale on these architectures, with particular emphasis on hybrid programming models, architecture-aware partitioning and data layout techniques, and communication-reducing algorithms.

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.

Projects

Making block-structured grid adaptive mesh refinement software frameworks available for the development of massively parallel, multiphysics applications.

Developing, applying, and distributing unstructured mesh tools that will operate on tomorrow’s massively parallel computers for use in solving problems on complex geometries with anisotropic physics.

Supporting embedded particle–mesh methods in both structured and unstructured grid methods for a variety of applications.

Developing time integration methods tailored to multi-rate problems that arise in the context of multi-physics and multi-scale simulations.

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, nonlinear solvers, eigensolvers, and differential variational inequality schemes. 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, acceleration methods for nonlinear algebraic systems, 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.

Projects

Researching and developing iterative linear solvers, particularly multigrid and multilevel methods.

Providing factorization-based sparse solvers and preconditioners on high-end parallel machines.

Providing a full range of nonlinear solution algorithms and software implementations to enable flexible, robust, and scalable solution of science applications.

Developing scalable eigenvalue algorithms and solvers for problems with millions to billions of degrees of freedom.

Creating robust solvers for differential variational inequalities to enable consistent, efficient modeling of transitional phenomena.