Applied Mathematics Research for Exascale Computing

Cover art by George Kitrinos, a derivative of " Circuit board elements background " from freedesign-file.com, used under Creative Commons Attribution 3.0. Equations from a far-field approximation of the Green's function solution to the acoustic analogy equation with thermoacoustic sources. Government nor any agency thereof, nor any of their employees or officers, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of document authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof and shall not be used for advertising or product endorsement purposes. Abstract This report details the findings and recommendations of the DOE ASCR Exascale Mathematics Working Group that was chartered to identify mathematics and algorithms research opportunities that will enable scientific applications to harness the potential of exascale computing. The working group organized a workshop, held August 21-22, 2013 in Washington, D.C., to solicit input from over seventy members of the applied mathematics community. Research gaps, approaches, and directions across the breadth of applied mathematics were discussed, and this report synthesizes these perspectives into an integrated outlook on the applied mathematics research necessary to achieve scientific breakthroughs using exascale systems.