The 20th century saw the culmination of efforts to solve the major theoretical problems of astrophysics using analytical techniques. Indeed, most of the basic underpinnings of our current understanding of stellar and galactic dynamics, gas dynamics, stellar evolution, and planetary dynamics, were laid out by the heroic efforts of several generations of theorists from Eddington, Chandrasekhar, Schwarzchild and Milne to the likes of Parker, Mestel, Zel’dovich, Ostriker, Goldreich, Rees, Shu and Blandford. However, the complexity of most astrophysical phenomena dictates that accessible analytical techniques are increasingly becoming relegated to limiting cases. In a realistic and complete description of most cosmic phenomena, one must typically face highly non-linear interactions between objects or particles, as well as non-linear couplings between different kinds of interactions, including gravitational, electromagnetic, radiative, and gas dynamical interactions. Consequently, numerical approaches to understanding astrophysical phenomena have become indispensable, and promise to dominate the methodology of theorists well into the 21st century and presumably beyond.
The sophistication and the diversity of computational methods have grown alongside the power of computers, but there has emerged the perception amongst some theorists that we have reached certain roadblocks in this evolutionary process. While technical advances continue to be made, including massive parallelization and the development of dedicated special-purpose computers, such as GRAPE, investigators have encountered various algorithmic limitations. With the possible exception of some novel methodologies currently being explored, future progress in computational theory appears to be awaiting only the inexorable increase in raw computing power. The most advanced coding techniques, including adaptive mesh refinement (AMR), N-body tree codes, and smoothed particle hydrodynamics (SPH) and its offshoots, have been very successful, but their accuracy in the 3-dimensional realm is often problematical, especially over long time spans. The devil is often in the unresolved, small-scale details of such physical processes as turbulent cascades, turbulent energy dissipation, magnetic field line reconnection, narrow shock fronts and dynamical instabilities, among others.
Consequently, this is an appropriate time for the community to examine these algorithmic limitations to see if creative, new ways can be found to circumvent them, either for limited ranges of problems, or across the board. We therefore propose a program at IPAM aimed at stimulating exchanges among computational astrophysicists and applied mathematicians. The program would be structured to identify the barriers to algorithmic efficiency and accuracy, and to provoke the participants to either find ways of surmounting those barriers or perhaps to decisively demonstrate that certain limitations are inherently unavoidable.
The topic of astrophysical theory is chosen for a couple of reasons: first, because it is at the forefront of the development of computational techniques, as has always been the case historically. Second, astrophysical theory is an inherently rich subject calling upon every conceivable brand of numerical analysis for a very broad range of phenomena. The range of subtopics below illustrates this point.
Of course, much of what is learned from this endeavor can be applied across the board to a variety of other subjects, such as meteorology and oceanography. We will nonetheless limit the scope of this program to exclude a few important computational astrophysics topics: data analysis techniques and astronomical imaging, because we judge those to be outside the domain of astrophysical theory proper. Astronomical imaging is, in any case, the focus of a separate IPAM workshop.
There have been occasional international conferences explicitly focused on computational astrophysics. For example, in March 1998, the International Conference on Numerical Astrophysics was held in Tokyo Japan. (Proceedings published by: S.M. Miyama, K. Tomisaka, T. Hanawa: 1999, Boston: Kluwer, Astrophysics and Space Science Library vol 240).
The upcoming IPAM program, however, will be the first to bring the numericists together with applied mathematicians.
Some of the topics that will be covered in the program are:
(Bern, Physikalisches Institut)
Phillip Colella (Lawrence Berkeley National Laboratory, Mathematics)
Richard Klein (University of California at Berkeley/Lawrence Livermore National Laboratory, Astronomy)
James McWilliams (UCLA, IGPP & Atmospheric Sciences)
Joseph Monaghan (Monash University, Australia, Mathematical Sciences)
Mark Morris (UCLA, Physics & Astronomy)
Stanley Osher (IPAM, Mathematics)
Chi-Wang Shu (Brown University, Applied Mathematics)
Harold Yorke (California Institute of Technology, Astrophysics)