Scalable solvers for computational mechanics

Models in which every material point interacts with every other point inside a finite neighborhood are expensive in a specific way: the work per point is large, the neighborhoods overlap, and the load does not distribute evenly across a domain where some regions are fracturing and others are not. That makes them a good stress test for parallel solver design, which is what this project was about.

Load balancing, through Google Summer of Code

A Google Summer of Code 2020 project, set with Patrick Diehl, posed it: build a massively parallel solver for the two-dimensional nonlocal heat equation, as a tractable stand-in for the harder mechanics case. Pranav Gadikar (IIT Madras) took it on. The problem statement and his implementation are both open, and the load-balancing algorithm that came out of it was published as a conference paper.

The interesting part was not the heat equation. It was that the work per subdomain changes as the solution evolves, so a partition chosen once at the start degrades, and rebalancing has to cost less than the imbalance it removes.

NLMech

NLMech is the library this fed into. It uses HPX, an asynchronous many-task runtime, so computation is expressed as a dependency graph rather than as bulk-synchronous phases, which suits a problem whose costs are unevenly distributed and change over time. It is described in a paper with Patrick Diehl.

This work informed the later parallel implementation of PeriDEM, where every particle in a granular assembly carries its own deformable mechanics; see mechanics of granular media.