Advancing Science via Applied Mathematics Applied Partial Differential Equations to develop simulation tools for solving multi-scale and multi-physics problems Phillip Colella (project webpage) Lawrence Berkeley National Laboratory

This project will develop simulation tools for solving multi-scale and multi-physics problems based on finite difference and finite-volume methods on logically-rectangular structured grids combined with block structured adaptive mesh refinement to represent multi-scale behavior. This center will build on the previous accomplishments of the first round of SciDAC investments, to achieve the following goals: to support computational scientists who wish to use multiresolution tools to solve scientific problems in support of the Department’s science objectives, including astrophysics, combustion and fusion to obtain uniformly high-performance for APDEC software, including parallel scalability to thousands of processors to hundreds of thousands of processors; and to develop new adaptive mesh refinement capabilities required by applications stakeholders, such as fourth-order finite volume methods, adaptive mesh refinement for Maxwell’s equations, high-performance solvers for anisotropic problems, new methods for treating complex geometries, and particle and hybrid particle/continuum methods.

The APDEC center will primarily support computational scientists who wish to use multiresolution tools to solve scientific problems in support of the Department of Energy missions. Potential collaborations include astrophysics, combustion and magnetic fusion. In all of these areas, there are one or more SciDAC projects that have specific requirements that can be met by APDEC. APDEC will interact with science applications developers of structured-grid adaptive methods on a variety of issues including model analysis, algorithm design, domain-specific modifications to the algorithms and software, and debugging.

Center for Enabling Technology: Applied Mathematics

Project Title: The Applied Partial Differential Equations Center for Enabling Technologies (APDEC)

Principal Investigator: Phillip Colella
Affiliation: Lawrence Berkeley National Laboratory

Project Webpage: hpcrd.lbl.gov/APDEC/

Participating Institutions and Co-Investigators:
Lawrence Berkeley National Laboratory - Phillip Colella (PI), Marcus S. Day, Daniel T. Graves, Terry J. Ligocki, Michael J. Lijewski, Daniel Martin, Peter McCorquodale, Peter Schwartz, Theodore D. Sternberg, and Brian Van Straalen
Lawrence Livermore National Laboratory - Caroline Gatti-Bono, and David Trebotich
Princeton Plasma Physics Laboratory - Ravi Samtaney
UC-Davis - Gregory Miller

Funding Partners: Office of Science — Office of Advanced Scientific Computing Research

Budget and Duration: Approximately $3.1 million per year for five years ¹

Other Media:

• Performance and scaling of locally-structured grid methods for partial differential equations, paper in SciDAC 2007 Conference Proceedings
  slides from presentation (pdf)
• APDEC: Algorithms and Software for DISCOVERY, article in Issue 4 of SciDAC Review
• Simulating Turbulent Flames, article in Issue 2 of SciDAC Review

Other SciDAC Enabling Technologies Centers
Other SciDAC Applied Mathematics efforts