Hypercomplex Automatic Differentiation in the Eulerian Hydrocode PAGOSA

Technical Report · Wed Apr 30 04:00:00 EDT 2025

DOI:https://doi.org/10.2172/2566412· OSTI ID:2566412

Balcer, Matthew Ryan ^[1]

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1. Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Enabling the computation of partial derivatives or sensitivities in production hydrocodes is beneficial for design, optimization, sensitivity analysis, and uncertainty quantification. Traditional finite difference approximations of these sensitivities are inefficient since convergence studies of the step size is required for each parameter of interest. For these reasons, HYPercomplex Automatic Differentiation (HYPAD) was implemented in the Eulerian hydrocode PAGOSA. HYPAD is analogous to forward-mode automatic differentiation except hypercomplex numbers (numbers with multiple imaginary parts) are used instead of dual numbers. Accurate partial derivatives can be computed of all state variables with respect to multiple input variables in a single run. The method was implemented using operator overloading to handle hypercomplex algebra. HYPAD was demonstrated and verified on Sod’s shock tube problem to compute derivatives of the state variables with respect to a material parameter, initial conditions, and geometry.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: 89233218CNA000001
• OSTI ID: 2566412
• Report Number(s): LA-UR--25-24530
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING