Many  scientific and  engineering calculations  require solving  very large  systems  of linear  equations.  For  example, fluid  flow equations  such as  those encountered in standard three dimensional aerodynamics  simulations lead to systems that typically have tens of millions  of unknowns.  These systems are sparse in that each equation involves  a small number of unknowns.  A traditional, and  generally robust, way to solve such systems is  to rely on direct factorization but this approach becomes prohibitively expensive as the problem increases in size.  The consensus now is that iterative methods, i.e., methods that approximate the solution by  an iterative process, are mandatory when  dealing with large systems such as  those that arise from 3-D simulations.   Among standard iterative methods, those  based on  a combination  of preconditioning and  projection on  Krylov subspaces  are quite popular  due to  their excellent  compromise betweeng enerality  and efficiency.   A preconditioner  is any  inexpensive process  to obtain  an approximate  solution to  the original  system.  For  example, common preconditining techniques  are those based  on Incomplete LU  (ILU) factorizations that  approximately factor the  original matrix into  the product of  a lower triangular matrix  L and  an upper triangular  matrix U.   Preconditioning is  the most important  ingredient of  an iterative solution  method and  research on developing effective preconditioners has  been consistently active and flourishing for  several decades now.  Its themes vary from preconditioners for specific applications, to highly parallel techniques, divide-and-conquer type methods, and theoretical aspects on convergence analysis.

The `Preconditioning' series of conferences which started in the Twin cities, MN,  in 1999, address all these themes and many more.  The conference takes place every other year and attracts around 100 delegates worldwide on average.  The 10th of  these meetings, `Preconditioning 2017' was held at the University of British Columbia (Vancouver) from July  31 to August 2,  2017.  The goal of  the NSF funding was to provide financial support for  a few US-based  participants to this conference,  giving priority to junior and under-represented groups. Of the  10 participants supported, three were female (two students and a  post-doc), two were from under-represented groups (one African  American, one Hispanic),  and one came  from a community  college. In  addition, nine out  of these ten participants satisfied our  definition of 'junior' participant, that is a researcher who is still a graduate student or  obtained her/his doctorate no more than 6 years prior to the meeting.  Finally, three of the ten were invited speakers.  The positive impact of this support on the careers of these individuals, especially the students, and the junior awardees, is clear.  Indeed,  without financial support, most of them would not have been able to attend this important gathering. The grant also  had an excellent impact on the conference itself  by boosting participation, even if slightly, and by  improving the diversity of the participants.

Last Modified: 04/18/2018
Modified by: Yousef Saad