Accuracy and Numerical Stability Investigations of Hessian-Free Force-Gradient Integrators (4/7)
by
Kevin Schäfers(University of Wuppertal)
→
Europe/Berlin
Description
In this talk, we will discuss Hessian-free force-gradient integrators in the context of gauge field simulations in lattice QCD. The force-gradient approach offers substantial performance enhancements, particularly for larger lattice volumes where higher-order integrators exhibit greater efficiency. However, conventional force-gradient integrators require the evaluation of the force-gradient term involving the Hessian of the potential that is commonly not available in existing software and moreover is more expensive to evaluate than a standard force evaluation. In contrast, Hessian-free force-gradient integrators approximate the force-gradient updates, effectively replacing the force-gradient term with another force evaluation. Consequently, the framework can be incorporated into existing software in a straightforward way. In this talk, we will investigate two different perspectives to evaluate the performance of numerical integration schemes. Firstly, we will perform a refined error analysis and use an accuracy-related efficiency measure to evaluate the performance of an integrator. Secondly, we will perform a numerical stability analysis for conventional force-gradient integrators and their Hessian-free variants to assess the robustness of these integrators. Thereby, we define a second stability-related efficiency measure. By investigating the efficiency measures, we will detect promising integrator variants among the family of self-adjoint Hessian-free force-gradient integrators with up to eleven exponentials per time step. Different numerical tests emphasize the pros and cons of the proposed efficiency measures, as well as the superior efficiency of the proposed Hessian-free force-gradient integrators compared to commonly employed non-gradient schemes.
