Project: Adaptive mesh Refinement
Project: Adaptive mesh Refinement Adaptive Mesh Refinement is a numerical technique which dynamically places high resolution numerical grids in the region of a numerical simulation where higher accuracy is needed. First proposed by Berger and Oliger in 1984, the method is crucial in solving PDE's where large gradients and widely varying dynamics and dynamical scales are present. Problems in numerical relativity exhibit such gradients and widely varying dynamics.The NCSA Relativity group effort in Adaptive Mesh Refiniment is currently centered around the DAGH library written by Manish Parashar. The DAGH system is a parallel adaptive system written in C++ which allows parallel AMR on many platforms with a minimum of end-user effort. The system uses the MPI system for it's message passing.
Simultaneously, Henry Neeman is developing his HAMR system, a library for adaptive mesh refinement, and the NCSA group is working on a simple 1D AMR code, written in 1994 by Paul Walker and Joan Massó, from which we still hope to learn information about the behaviour of adaptive mesh systems. This effort is being undertaken by a new collaboration with Mercyhurst College.
Integration of the DAGH system into the Newage Code is well underway. Similarly, an example code which can be used for documentation purposes is almost complete. With these stages complete, we hope to go into production with the full AMR implementation.The 1D effort is currently being pursued by theteam at Mercyhurst, which is trying to revive the original AMR code described in Adaptive Mesh Refinement in Numerical Relativity, so that we can continue to have a simple portable interface to 1D AMR.
Using AMR techniques implemented in the 1D AMR code, we were able to solve the single black hole problem to 100M using far less CPU and Memory which would have been required to acheive the same accuracy in a fixed-mesh setting.
The 3-D efforts are aimed at placing AMR in the G and H and New Age codes. The FOHFC formulation of the Einstein Equations shows another method of dealing with the large gradients in 3+1 simulations, and The Apparent Horizon Boundary Condition avoids the formation of these gradients altogether. Some combination of these 3 techniques (AHBC, FOFCH, and AMR) should provide a stable long-running solution to Black Hole problems.
The The BBH GC Toolkit for Computational Relativity is intimately related to the 3-D collaboration.