Elliptic Solvers for Adaptive Mesh Refinement Grids

We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work. Background and Research Objectives Our objective was to develop multigrid methods which would efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final result will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of CIC-19 (Computer Research and Applications), EES-5 (Geoanalysis), T-3 (Fluid Dynamics), T-7 (Mathematical Modeling and Analysis), and XTM (Radiation Transport), and others. The focus of this work was research on FAC, AFAC and AFACX (described below) for serial and parallel environments and inclusion of the black box multigrid techniques developed by Dendy *Principal Investigator, e-mail: dquinlan @kml.gov