Solving differential equations at the exascale
Garth N. Wells, University of Cambridge

Abstract: I will discuss the development of finite element algorithms and implementations for a range of applications on exascale hardware. When considering accelerators it is helpful to reflect on past attempts (since the honest efforts generally failed!) to assess why performance was disappointing. I will argue that the disappointing performance was due to a failure to assess the suitability of algorithms end-to-end; focusing on accelerating one step in a sequence of otherwise established of algorithms over-constrains approaches and dooms them to failure. Improved mathematical and algorithmic understanding now allows us to exploit exascale-type hardware efficiently. Also on the upside, I will show that recent developments in compiler technologies have made it much easier to develop high performance finite element kernels without non-standard language extensions, with excellent measured performance assessed against performance models. To make developments accessible, I will also touch upon the open-source FEniCS Project (https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Ffenicsproject.org%2F&data=05%7C02%7Chetsys%40warwick.ac.uk%7C68d2fe5375b84ba453da08dc1278beb3%7C09bacfbd47ef446592653546f2eaf6bc%7C0%7C0%7C638405557015823721%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=7HwNmQz4WsLAtX%2Bd3%2BthmVfzjzBS5bNUFFf61Kb9H%2F0%3D&reserved=0) and its approach to creating high-level, high-performance software implementations.

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