Exceptional Speedups with GenEO

Exceptional Speedups

Up to 50× performance gains with GenEO preconditioning on large-scale problems

Our GenEO preconditioning approach has achieved remarkable speedups on large-scale problems, demonstrating the power of domain decomposition methods at exascale.

1. Overview

The Generic Energy-Minimizing Coarse Space (GenEO) preconditioner has proven exceptionally effective for large-scale simulations, achieving up to 50× speedup on challenging industrial problems.

2. Key Achievement

50× Speedup

Cobra cavity benchmark
45 million degrees of freedom
2,916 CPU cores

3. Technical Details

3.1. Problem Characteristics

  • Application: Cobra cavity industrial benchmark

  • Problem Size: 45 million degrees of freedom (DoFs)

  • Computing Resources: 2,916 CPU cores

  • Method: GenEO (Generalized Eigenvalue in Overlapping domains) preconditioning

3.2. Performance Metrics

  • Baseline: Standard domain decomposition methods

  • Optimized: GenEO-enhanced solver pipeline

  • Speedup: Up to 50× reduction in solution time

  • Scalability: Strong scaling maintained across thousands of cores

4. Method Innovation

The GenEO preconditioner enhances classical domain decomposition by:

  1. Adaptive Coarse Space Construction: Automatically builds coarse spaces based on local eigenvalue problems

  2. Robust Convergence: Maintains iteration counts independent of problem parameters

  3. Parallel Efficiency: Scales effectively to thousands of cores

  4. Mixed-Precision Support: Additional gains through adaptive precision strategies

5. Impact on Applications

This breakthrough enables:

  • Industrial Simulations: Complex geometries (aerospace, automotive) now tractable at full resolution

  • Real-Time Analysis: Faster turnaround for design optimization loops

  • Larger Problems: Previously infeasible problem sizes now accessible

  • Energy Efficiency: Reduced computational time = lower energy consumption

6. Related Work Packages

7. Publications & Resources

  • Conference presentations at domain decomposition workshops

  • Integration in production solvers (Feel++, FreeFEM)

  • Available through Exa-MA software stack

← Back to Results | View Work Packages | Next: Exascale Computing →