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Sundriyal, Shivam ; Büttner, Markus ; Kenter, Tobias ; Aizinger, Vadym:
Customized Precision for Discontinuous Galerkin Methods using Adaptive Spectral Block Floating Point.
In:
Proceedings of the Platform for Advanced Scientific Computing Conference. -
New York, NY
: Association for Computing Machinery
,
2026
. - 22
ISBN 979-8-4007-2734-4
DOI: https://doi.org/10.1145/3815572.3815758
Volltext
Angaben zu Projekten
| Projekttitel: |
Offizieller Projekttitel Projekt-ID Performance-optimiertes Co-Design von Ozeanmodellierungssoftware auf FPGAs 502500606 |
|---|---|
| Projektfinanzierung: |
Deutsche Forschungsgemeinschaft |
Abstract
Discontinuous Galerkin (DG) methods offer high-order accuracy and geometric flexibility, but come with significant memory demands for storing degrees of freedom of the numerical solution -this remains a major performance bottleneck for large-scale simulations. Building on prior work introducing a 64-bit Adaptive Spectral Block Floating Point (ASBFP) format for modal 1D DG discretizations, we develop a more general framework that supports arbitrary polynomial order and arbitrary bit-width allocations. The extended ASBFP design constructs shared- and biased-exponent structures tailored to exploit the spectral decay of solution coefficients in modal DG bases, enabling fine-grained control over precision while providing both reduced- and extended-precision representations within a unified encoding model. Numerical tests in one dimension show that the generalized ASBFP format maintains the expected accuracy and convergence behaviour while substantially reducing the memory footprint across a wide range of DG orders.
We further extend the ASBFP methodology to multi-dimensional DG discretization based on tensor-product polynomial spaces. By identifying patterns in the decay of modal coefficients for multidimensional tensor-product bases and encoding hierarchical exponent offsets accordingly, this tensor-product-aware scheme enables more aggressive compression while maintaining numerical fidelity comparable to FP64 baselines. Together, these developments provide a flexible family of degree-aware spectral block floating-point formats for high-order DG methods in one and multiple dimensions.