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DTSTAMP:20260522T162631Z
LOCATION:Bldg. 6 - Room 003
DTSTART;TZID=Europe/Stockholm:20260629T113000
DTEND;TZID=Europe/Stockholm:20260629T120000
UID:submissions.pasc-conference.org_PASC26_sess167_pap125@linklings.com
SUMMARY:Customized Precision for Discontinuous Galerkin Methods Using Adap
 tive Spectral Block Floating Point
DESCRIPTION:Shivam Sundriyal and Markus Büttner (University of Bayreuth), 
 Tobias Kenter (Paderborn University), and Vadym Aizinger (University of Ba
 yreuth)\n\nDiscontinuous Galerkin (DG) methods offer high-order accuracy a
 nd geometric flexibility, but come with significant memory demands for sto
 ring 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) forma
 t for modal 1D DG discretizations, we develop a more general framework tha
 t supports \emph{arbitrary polynomial order} and \emph{arbitrary bit-width
  allocations}. The extended ASBFP design constructs shared- and biased-exp
 onent structures tailored to exploit the spectral decay of solution coeffi
 cients in modal DG bases, enabling fine-grained control over precision whi
 le providing both reduced- and extended-precision representations within a
  unified encoding model. Numerical tests in one dimension show that the ge
 neralized ASBFP format maintains the expected accuracy and convergence beh
 aviour while substantially reducing the memory footprint across a wide ran
 ge of DG orders.We further extend the ASBFP methodology to multi-dimension
 al DG discretization based on tensor-product polynomial spaces. By identif
 ying patterns in the decay of modal coefficients for multidimensional tens
 or-product bases and encoding hierarchical exponent offsets accordingly, t
 his tensor-product-aware scheme enables more aggressive compression while 
 maintaining numerical fidelity comparable to FP64 baselines. Together, the
 se developments provide a flexible family of degree-aware spectral block f
 loating-point formats for high-order DG methods in one and multiple dimens
 ions.\n\nSession Chair: Guillaume Houzeaux (Barcelona Supercomputing Cente
 r)\n\n
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