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physics.comp-ph2025
Boosting the Efficiency of the Differential Algebra-based Fast Multipole Method Using Symbolic Differential Algebra
He Zhang
The Fast Multipole Method (FMM) computes pairwise interactions between particles with an efficiency that scales linearly with the number of particles. The method works by grouping…
physics.comp-ph2025
Higher-Order Automatic Differentiation Using Symbolic Differential Algebra: Bridging the Gap between Algorithmic and Symbolic Differentiation
He Zhang
In scientific computation, it is often necessary to calculate higher-order derivatives of a function. Currently, two primary methods for higher-order automatic differentiation exis…