Berkeley Lab's AMR Software Provides a Powerful Set of Tools for Tackling Difficult Problems in Computational Science
With the use of the adaptive mesh refinement capability developed by computational scientists at Lawrence Berkeley National Laboratory, and parallel computers powerful enough to tackle the biggest problems, new horizons are opening in scientific research. Many everyday situations, such as running an internal combustion engine or predicting weather, actually involve very complex physical processes that scientists are only now beginning to understand. At Berkeley Lab, scientists and mathematicians are developing specialized tools and algorithms for computer modeling of problems like these. The tools are general enough that most computational problems involving partial differential equations can potentially benefit from their use.
Adaptive mesh refinement, or AMR, has been under development for more than 15 years. Scientists in the National Energy Research Scientific Computing (NERSC) Division at Berkeley Lab have been at the forefront of developing the algorithms that exploit this capability to solve a variety of scientific problems. Recently, Berkeley Lab scientists have used AMR to create some of the most accurate simulations of flames to date. This research has broad applications in such areas as reducing pollution and increasing energy efficiency in vehicles and power plants. Other applications of AMR include modeling the dispersal of airborne substances in the atmosphere, studying the behavior of supernovae, modeling dendritic crystal growth, and designing future generations of particle accelerators.
AMR serves as a "numerical microscope," allowing researchers to "zoom in" on the specific regions of a problem that are most important to its solution. Rather than requiring that the whole calculation have the same spatial resolution, AMR allows different resolution in different regions of the problem. Areas of interest are covered with a finer mesh than the surrounding regions; for time-dependent problems, the finer meshes are also advanced with a smaller time step. Not having to perform the entire calculation at the finest resolution allows scientists to make the most of available computer resources, so that they can then solve bigger, harder problems.
One of the most challenging problems in computational science to which AMR is being applied is numerical modeling of combustion. Calculations of combustion processes often include a well-defined flame front; focusing the computing power on the flame, where hundreds or thousands of chemical reactions may be taking place, results in large savings in computing time and memory. As the flame develops and moves through the domain, the finer meshes automatically move with it, allowing researchers to achieve unprecedented temporal and spatial resolution of the internal flame structure.
For more information about Berkeley Lab AMR, see the article "Zooming In On Data" from the 1997-98 Berkeley Lab Highlights. For more technical detail, see What Is AMR?
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