On July 20-23, 2004, the 2004 International Workshop on the Solution of Partial Differential Equations (Organizers: M. Satoh, P. Swarztrauber, J. Drake, D. Williamson) was held at Miyoshi Memorial Auditorium in Yokohama Institute for Earth Sciences. The purpose of this workshop is to discuss speed and accuracy of Partial Differential quations on the Sphere for atmosphere and ocean models to be used with limited computer resources. Every time, many researchers especially pioneers in numeric simulation model and experts on numerical algorithm participate in this workshop. Research groups from various countries take turns in organizing the workshop every other year. This year, Next- Generation Model Development Group of Global Environment Modeling Research Program, Frontier Research Center for Global Change hosted the workshop.
The workshop venue had a vibrant atmosphere with almost 70 participants from various countries. Main topics of discussion were proposition of new advection schemes such as various conservation scheme and non-negative advection scheme, grid dividing method on the sphere such as icosahedral grid and cubic grid models or Yin-Yang grid model and its discretization method, optimization issue of the current prevailing spectral method, formulation method of non-hydrostatic equation, effectiveness of adaptive grid method, proposal of test cases for verifying the validity of new model, etc. These discussions also depend on the computer environment of each researcher and therefore, they were conducted always with the viewpoint of computer resources (parallel computers, architecture, etc.). During the meeting, FRCGC and the Earth Simulator Center made various presentations, and among them, the presentation on high-resolution computation using the Earth Simulator attracted interests of many participants from abroad.
One of the characteristics of this workshop was that questions and answers were exchanged very lively. A time frame of each lecture was comparatively long and enough time for questions and answers could be taken, and especially because many of the participants had very deep backgrounds about topics. In some other conferences, showing the detailed equations and schemes is not desirable because participants cannot understand immediately. On this workshop, however, many participants requested to show the equations and schemes and lively discussions were conducted about topics in detail. Also, many participants gathered from the world leading operation centers and we could discuss on the next-generation atmosphere and ocean models, the one Next-Generation Model Development Group is now developing. Participants were able to exchange information, and deepen the grasping and mutual understanding of next-generation dynamic core strategy.
The presentation materials used in this workshop were distributed to all the participants and will be released to the public through Internet. The next workshop is scheduled to be held in Monterey in 2006.