The investigators propose to participate in organizing the next ICOSAHOM (International Conference on Spectral And High-Order Methods) on June 22-26 2009 at the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway. They have been working in this field for several decades and have been active participants in all past ICOSAHOM meetings. Selected papers from the proceedings will be published as a special issue in a archival journal. They also plan to produce a report for the funding agency that will provide feedback from a round-table discussion we plan to organize. The theme of this round-table discussion will be the future algorithmic trends and applications of numerical methods and what is the role of high-order methods. Also, their transition to computer codes that will be used for the simulation needs of the national labs and in industry will be discussed, especially in the context of petaflop applications. To this end, they plan to invite researchers with advanced computing expertise and also have interest on high-order accuracy to participate in this panel. The invited and contributed talks will contain new theoretical and applications results of spectral and high-order methods which had not been published yet. Spectral and high-order methods have become increasingly important in diverse applications as aeroacoustics, electromagnetics, ocean modeling, seismology, energy, non-Newtonian flows, nonlinear optics, plasma dynamics, and uncertainty quantification. New developments in the last few years have addressed issues of complex geometry, high-speed flows, fast solvers for large-scale simulations, reduced order modeling, and stochastic modeling.
NSF has invested heavily in computer hardware in their last three decades in par with the rapid growth of computer industry. However, simultaneous advances are required in the development of algorithms and software in order to make effective use of the new computer resources. This conference will advance the state-of-the-art in algorithms of high accuracy that are required in order to produce credible simulation results. In addition to the senior researchers invited, we plan to sponsor young researchers, postdocs and PhD students, especially from under-represented minorities, in order to educate a new cadre of simulation scientists in these methods. Today, high-order accuracy (at least second-order) is a requirement for publishing archival work in engineering journals, and the planned panel discussion is expected to have great impact in the engineering community. In addition, the important issue of numerical versus modeling accuracy and issues related to Verification and Validation will be discussed.
