Schmitt J, Kuckuk S, Köstler H (2019)
Publication Language: English
Publication Type: Conference contribution, Abstract of lecture
Publication year: 2019
Event location: Copper Mountain, Colorado
For many linear and nonlinear systems that arise from the discretization of partial
differential equations the construction of an efficient multigrid solver is a challenging task. Here
we present a novel approach for the optimization of geometric multigrid methods that is based on
evolutionary computation, a generic program optimization technique inspired by the principle of
natural evolution. A multigrid solver is represented as a tree of mathematical expressions which
we generate based on a tailored grammar. The quality of each solver is evaluated in terms of
convergence and compute performance using automated Local Fourier Analysis (LFA) and roofline
performance modeling, respectively. Based on these objectives a multi-objective optimization is
performed using strongly typed genetic programming with a non-dominated sorting based selection.
To evaluate the model-based prediction and to target concrete applications, scalable implementations
of an evolved solver can be automatically generated with the ExaStencils code generation framework.
We demonstrate our approach by constructing multigrid solvers for Poisson’s equation with constant
and variable coefficients.
Schmitt, J., Kuckuk, S., & Köstler, H. (2019). Towards the automatic optimization of geometric multigrid methods with evolutionary computation. Paper presentation at 19th Copper Mountain Conference On Multigrid Methods, Copper Mountain, Colorado.
Schmitt, Jonas, Sebastian Kuckuk, and Harald Köstler. "Towards the automatic optimization of geometric multigrid methods with evolutionary computation." Presented at 19th Copper Mountain Conference On Multigrid Methods, Copper Mountain, Colorado 2019.