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Testing and tuning symplectic integrators for the hybrid Monte Carlo algorithm in lattice QCD
Tetsuya Takaishi1, Philippe de Forcrand
1Hiroshima University of Economics, Hiroshima 731-0124, Japan.
Summary
A new second-order integrator offers a 10x reduction in integration error compared to the standard leapfrog (2LF) method. This enhanced accuracy allows for larger step sizes and a 50% increase in computational efficiency.
Area of Science:
- Computational physics
- Numerical analysis
Background:
- Standard second-order leapfrog (2LF) integrators are widely used but have limitations in accuracy and efficiency.
- Omelyan et al. recently introduced a novel second-order integrator with potential improvements.
Purpose of the Study:
- To evaluate the performance of the new second-order integrator developed by Omelyan et al.
- To compare its integration error and efficiency against the standard 2LF integrator.
- To investigate parameter tuning and optimal usage for the new integrator.
Main Methods:
- Numerical integration of physical systems using both the new second-order integrator and the standard 2LF integrator.
- Quantification of integration error using the root mean square of the energy difference (
1/2). - Comparative analysis of computational cost and efficiency.
Main Results:
- The new integrator exhibits an integration error approximately 10 times smaller than the 2LF integrator.
- The step size can be increased by a factor of three with the new integrator.
- The new integrator demonstrates about 50% greater efficiency than the 2LF integrator, considering a twofold increase in computational cost.
- Optimal parameter values for the new integrator were found to differ slightly from previously reported values and are simulation-dependent.
Conclusions:
- The new second-order integrator offers significant advantages in accuracy and efficiency over the standard 2LF integrator.
- The order of integration (positions then momenta, or vice versa) has a minor impact on performance.
- Further optimization of the integrator's parameters is possible and recommended for specific simulation contexts.
- This integrator shows promise for applications such as Trotter-Suzuki decomposition in quantum Monte Carlo simulations.
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