AN EFFICIENT METHOD TO CALCULATE FIELD THEORIES WITH DYNAMICAL FERMIONS

1991 ◽  
Vol 02 (02) ◽  
pp. 561-600 ◽  
Author(s):  
MARCIA G. DO AMARAL ◽  
M. KISCHINHEVSKY ◽  
C. ARAGÃO DE CARVALHO ◽  
F.L. TEIXEIRA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Fourth Order ◽  
Efficient Method ◽  
Field Theories ◽  
Step Size ◽  
Time Step ◽  
Acceptance Probability ◽  
Hybrid Monte Carlo ◽  
Time Step Size

We discuss the application of the Hybrid Monte Carlo method for models that describe conducting polymers, namely the Su-Schrieffer-Heeger and the Krive-Rozhavskii models. We use a fourth order Leap Frog algorithm, in order to decrease the number of Monte Carlo rejections. We also make a detailed study of which solver has the best performance in each phase of the theory as well as the dependence of the acceptance probability as a function of the time step size and other parameters.

A highly stable explicit scheme for a fourth-order nonlinear diffusion filter

2020 ◽  
Vol 11 (04) ◽  
pp. 2050030
Author(s):  
Mahipal Jetta
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Fourth Order ◽  
Nonlinear Diffusion ◽  
Splitting Scheme ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Diffusion Filter ◽  
Spatial Derivatives

The standard finite difference scheme (forward difference approximation for time derivative and central difference approximations for spatial derivatives) for fourth-order nonlinear diffusion filter allows very small time-step size to obtain stable results. The alternating directional implicit (ADI) splitting scheme such as Douglas method is highly stable but compromises accuracy for a relatively larger time-step size. In this paper, we develop [Formula: see text] stencils for the approximation of second-order spatial derivatives based on the finite pointset method. We then make use of these stencils for approximating the fourth-order partial differential equation. We show that the proposed scheme allows relatively bigger time-step size than the standard finite difference scheme, without compromising on the quality of the filtered image. Further, we demonstrate through numerical simulations that the proposed scheme is more efficient, in obtaining quality filtered image, than an ADI splitting scheme.

scholarly journals The acceptance probability in the hybrid Monte Carlo method

1990 ◽  
Vol 242 (3-4) ◽  
pp. 437-443 ◽  
Author(s):  
Sourendu Gupta ◽  
A. Irbäc ◽  
F. Karsch ◽  
B. Petersson
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Acceptance Probability ◽  
Hybrid Monte Carlo

RATE OF CONVERGENCE OF MONTE CARLO SIMULATIONS FOR THE HOBSON–ROGERS MODEL

2008 ◽  
Vol 11 (08) ◽  
pp. 889-904 ◽  
Author(s):  
FABIO ANTONELLI ◽  
VALENTINA PREZIOSO
Keyword(s):  
Monte Carlo ◽  
Rate Of Convergence ◽  
Asset Price ◽  
Approximation Error ◽  
Derivative Securities ◽  
Step Size ◽  
Time Step ◽  
No Arbitrage ◽  
Time Step Size ◽  
Theoretical Results

The Hobson–Rogers model is used to price derivative securities under the no-arbitrage condition in a stochastic volatility setting, preserving the completeness of the market. Here we are studying the rate of convergence of the Euler/Monte Carlo approximations, when pricing European, Asian and digital type options. The aim of the present work is to express the approximation error in terms of the time step size, denoted by h, used for the Euler scheme. We recover an already known result, obtained by other authors using PDE approximations, for European options. Namely we show that for a Lipschitz coefficient of the driving equations for the asset price and Lipschitz payoffs, we obtain an error of the order of [Formula: see text]. Moreover, using Malliavin Calculus techniques, we show that with a regular coefficient we may attain an error of the order of h for regular payoffs and of the order of [Formula: see text] for non Lipschitz payoffs. Finally we show some numerical simulations supporting our theoretical results.

The Acceptance Probability of the Hybrid Monte Carlo Method in High-Dimensional Problems

2010 ◽  
Author(s):  
A. Beskos ◽  
N. S. Pillai ◽  
G. O. Roberts ◽  
J. M. Sanz-Serna ◽  
A. M. Stuart ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
High Dimensional ◽  
Acceptance Probability ◽  
Hybrid Monte Carlo

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

On the Influence of Inflow Model Selection for Time-Domain Tiltrotor Aeroelastic Analysis

2021 ◽  
Author(s):  
Ethan Corle ◽  
Matthew Floros ◽  
Sven Schmitz
Keyword(s):  
Experimental Data ◽  
Particle Method ◽  
Comprehensive Analysis ◽  
Solution Stability ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Vortex Particle Method ◽  
Whirl Flutter ◽  
Vortex Particle

The methods of using the viscous vortex particle method, dynamic inflow, and uniform inflow to conduct whirl-flutter stability analysis are evaluated on a four-bladed, soft-inplane tiltrotor model using the Rotorcraft Comprehensive Analysis System. For the first time, coupled transient simulations between comprehensive analysis and a vortex particle method inflow model are used to predict whirl-flutter stability. Resolution studies are performed for both spatial and temporal resolution in the transient solution. Stability in transient analysis is noted to be influenced by both. As the particle resolution is refined, a reduction in simulation time-step size must also be performed. An azimuthal time step size of 0.3 deg is used to consider a range of particle resolutions to understand the influence on whirl-flutter stability predictions. Comparisons are made between uniform inflow, dynamic inflow, and the vortex particle method with respect to prediction capabilities when compared to wing beam-bending frequency and damping experimental data. Challenges in assessing the most accurate inflow model are noted due to uncertainty in experimental data; however, a consistent trend of increasing damping with additional levels of fidelity in the inflow model is observed. Excellent correlation is observed between the dynamic inflow predictions and the vortex particle method predictions in which the wing is not part of the inflow model, indicating that the dynamic inflow model is adequate for capturing damping due to the induced velocity on the rotor disk. Additional damping is noted in the full vortex particle method model, with the wing included, which is attributed to either an interactional aerodynamic effect between the rotor and the wing or a more accurate representation of the unsteady loading on the wing due to induced velocities.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

Sign in / Sign up

Export Citation Format

Share Document