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Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures
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Mixed-Precision for Linear Solvers in Global Geophysical Flows.

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Summary
This summary is machine-generated.

Using half precision (16 bits) in elliptic solvers for atmosphere and ocean models can significantly speed up computations. This study demonstrates a 4x speed-up with minimal impact on solution quality for weather and climate models.

Keywords:
high performance computinglinear solverreduced precisionsemi‐implicit timesteppinguncertainty quantification

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Climate modeling

Background:

  • Semi-implicit (SI) time-stepping schemes are crucial for efficient atmosphere and ocean models.
  • Elliptic solvers are computationally intensive components of these models.
  • Modern supercomputers demand efficient numerical algorithms.

Purpose of the Study:

  • To investigate computational savings using mixed precision arithmetic in elliptic solvers.
  • To evaluate the impact of reduced precision (down to 16 bits) on solver convergence and solution quality.
  • To assess performance on actual reduced precision hardware.

Main Methods:

  • A novel SI shallow-water model on a sphere was developed, mimicking weather and climate models.
  • A non-symmetric Krylov-subspace Generalized Conjugated-Residual (GCR) solver with strong preconditioning was employed.
  • Mixed precision analysis was performed using an emulator, with performance measured on reduced precision hardware.

Main Results:

  • Key components of the elliptic solver, including preconditioning and linear operator application, can utilize half precision.
  • A speed-up factor of 4 was achieved using half precision compared to double precision.
  • This speed-up was observed across various problem sizes and for standard dynamical-core test cases.

Conclusions:

  • Half precision arithmetic is viable for specific components of elliptic solvers in geophysical flow models.
  • Significant computational performance gains are achievable without compromising solution accuracy.
  • This approach offers a pathway to more efficient weather and climate modeling on supercomputers.