Section: New Results

Scalable Schwarz domain decomposition methods

Domain decomposition methods are, alongside multigrid methods, one of the dominant paradigms in contemporary large-scale partial differential equation simulation. A lightweight implementation [8] of a theoretically and numerically scalable preconditioner was developped in the context of overlapping methods. The performance of this work is assessed by numerical simulations executed on thousands of cores, for solving various highly heterogeneous elliptic problems in both 2D and 3D with billions of degrees of freedom. Such problems arise in computational science and engineering, in solid and fluid mechanics.

For example, in 3D, the initial highly heterogeneous problem of 74 million unknowns is solved in 200 seconds on 512 threads. Using 16384 threads, the problem is now made of approximately 2.3 billions unknowns, and it is solved in 215 seconds, which yields an efficiency of $\approx 90\%$. In 2D, the initial problem of 695 million unknowns is solved in 175 seconds on 512 threads. Using 16384 threads, the problem is now made of approximately 22.3 billions unknowns, and it is solved in 187 seconds, which yields an efficiency of $\approx 96\%$.