Conformal mesh adaptation on heterogeneous supercomputers

Abstract

Mesh adaptation is a technique which dynamically modifies the mesh being used to approximately solve a Partial Differential Equation (PDE) in order to improve aspects of the approximate solution including the computer time and memory used to compute it as well as its level of accuracy. Even with the use of mesh adaptation, computing ever more accurate PDE solutions requires significant computer time and memory, motivating the use of supercomputers, which are constructed as networks of cooperating computational hardware. Trends in the computer hardware industry at large are introducing heterogeneous designs for current leadership-class supercomputers, which is both an opportunity and a challenge for programs aiming to make use of these machines.

Several improvements to the design of mesh adaptation programs are presented, including solution transfer methods which preserve mass and momentum, methods for the maintenance of high-quality elements, scalable and deterministic methods for hybrid parallelization of mesh modification operations, and a combination of modification operators which reduce implementation complexity without sacrificing effectiveness.

This thesis presents implementations of mesh adaptation which are designed with memory efficient cache-friendly data structures and algorithms which can effectively leverage both distributed memory parallelism and shared memory parallelism (including GPUs). The data structures used in these implementations are widely applicable to other tasks involving meshes, and the programming paradigms introduced are general enough to be of use in most programs targeting leadership-class supercomputers. The implementations presented are being used by several simulation codes in production, and are available as open-source tools so they may continue providing value to the scientific community.