A novel parallelizable convergence accelerating method: Pointwise Frequency Damping

TL;DR

This paper introduces a new parallelizable method for accelerating steady-state flow solvers by predicting asymptotic limits pointwise, ensuring identical serial and parallel results, with demonstrated speedups of 2.5 to 4 times.

Contribution

The novel method predicts asymptotic limits for each parameter based on historical data, enabling parallel acceleration without result discrepancies.

Findings

Achieved speedup factors of 2.5 to 4 in diverse flow cases.

Method guarantees identical results in serial and parallel computations.

Applicable to large-scale industrial mesh computations.

Abstract

This paper proposes a novel class of data-driven acceleration methods for steady-state flow field solvers. The core innovation lies in predicting and assigning the asymptotic limit value for each parameter during iterations based on its own historical data, rather than processing and assigning the entire flow field at once. This approach fundamentally guarantees identical results between serial and parallel computations. Subsequently, a formula for representing the asymptotic limit based on historical data is derived and discretized, yielding a purely algebraic expression.Furthermore, the applicability scope of the method is discussed, along with the underlying reasons for its acceleration capability. A quantitative expression for estimating the speedup ratio is also provided. Extensive validation cases were tested, ranging from the simplest inviscid airfoil flow to complex three-dimensional viscous transonic cruise flow around a aircraft, and solving asymmetric linear systems via GMRES. These tests consistently demonstrate significant acceleration effects with speedup factors ranging from 2.5 to 4. Combined with the near-zero computational overhead of the purely algebraic formulation during the solving process and the inherently parallel-compatible pointwise prediction principle, the results strongly indicate that this method is highly suitable for large-scale industrial mesh computations.