Performance examinations of multiple time-stepping algorithms on stampede supercomputer

2015 ◽  
Author(s):  
Na Zhang ◽  
Peng Zhang ◽  
Li Zhang ◽  
Xiao Zhu ◽  
Lei Huang ◽  
...  
Keyword(s):  
Multiple Time ◽  
Time Stepping

Error Analysis of Symplectic Multiple Time Stepping

1997 ◽  
Vol 34 (5) ◽  
pp. 1792-1807 ◽  
Author(s):  
Todd R. Littell ◽  
Robert D. Skeel ◽  
Meiqing Zhang
Keyword(s):  
Error Analysis ◽  
Multiple Time ◽  
Time Stepping

scholarly journals Adaptive time-stepping using control theory for the Chemical Langevin Equation

2021 ◽  
Author(s):  
Silvana Ilie ◽  
Monjur Morshed
Keyword(s):  
Control Theory ◽  
Time Scales ◽  
Langevin Equation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Stepping ◽  
Chemical Langevin Equation ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
Adaptive Time Stepping

Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation. This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency and accuracy compared with the existing variable and constant-step methods.

Efficient multiple time-stepping algorithms of higher order

2015 ◽  
Vol 285 ◽  
pp. 133-148 ◽  
Author(s):  
Abdullah Demirel ◽  
Jens Niegemann ◽  
Kurt Busch ◽  
Marlis Hochbruck
Keyword(s):  
Higher Order ◽  
Multiple Time ◽  
Time Stepping

scholarly journals Parallel-in-time simulation of an electrical machine using MGRIT

2020 ◽  
Vol 23 (1-4) ◽  
Author(s):  
Matthias Bolten ◽  
Stephanie Friedhoff ◽  
Jens Hahne ◽  
Sebastian Schöps
Keyword(s):  
Pulse Width Modulation ◽  
Numerical Models ◽  
Induction Machine ◽  
Small Time ◽  
Electrical Machine ◽  
Multiple Time ◽  
Fine Grid ◽  
Time Stepping ◽  
Application Codes ◽  
Simulation Time

AbstractWe apply the multigrid-reduction-in-time (MGRIT) algorithm to an eddy current simulation of a two-dimensional induction machine supplied by a pulse-width-modulation signal. To resolve the fast-switching excitations, small time steps are needed, such that parallelization in time becomes highly relevant for reducing the simulation time. The MGRIT algorithm is an iterative method that allows calculating multiple time steps simultaneously by using a time-grid hierarchy. It is particularly well suited for introducing time parallelism in the simulation of electrical machines using existing application codes, as MGRIT is a non-intrusive approach that essentially uses the same time integrator as a traditional time-stepping algorithm. However, the key difficulty when using time-stepping routines of existing application codes for the MGRIT algorithm is that the cost of the time integrator on coarse time grids must be less expensive than on the fine grid to allow for speedup over sequential time stepping on the fine grid. To overcome this difficulty, we consider reducing the costs of the coarse-level problems by adding spatial coarsening. We investigate effects of spatial coarsening on MGRIT convergence when applied to two numerical models of an induction machine, one with linear material laws and a full nonlinear model. Parallel results demonstrate significant speedup in the simulation time compared to sequential time stepping, even for moderate numbers of processors.

scholarly journals Adaptive time-stepping using control theory for the Chemical Langevin Equation

2021 ◽  
Author(s):  
Silvana Ilie ◽  
Monjur Morshed
Keyword(s):  
Control Theory ◽  
Time Scales ◽  
Langevin Equation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Stepping ◽  
Chemical Langevin Equation ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
Adaptive Time Stepping

Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation. This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency and accuracy compared with the existing variable and constant-step methods.

Coupled simulation of electromagnetic induction and induced polarization effects using stretched exponential relaxation

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. WB109-WB121 ◽  
Author(s):  
Patrick Belliveau ◽  
Eldad Haber
Keyword(s):  
Time Domain ◽  
Large Scale ◽  
Induced Polarization ◽  
Multiple Time ◽  
Efficient Manner ◽  
Full Account ◽  
Frequency Dependent ◽  
Stretched Exponential ◽  
Time Stepping ◽  
The Time Domain

We have developed a new algorithm for 3D time-domain electromagnetic (EM) modeling, taking full account of induced polarization (IP) and the coupling between EM and IP effects. The algorithm can be used to model grounded source IP surveys that indicate EM induction effects and airborne time-domain EM surveys that exhibit IP effects. IP effects are most often approximated as static or modeled in the frequency domain, using frequency-dependent electrical conductivity. It is difficult to translate the frequency-dependent conductivity approach directly to the time domain in a computationally efficient manner. We take an alternative approach in which we model IP relaxations in time using the stretched exponential (SE) function. We incorporate this IP model into a direct time-stepping discretization of the quasistatic time-domain Maxwell equations. We found that modeling of IP effects with this SE approach is asymptotically equivalent to the commonly used Cole-Cole model of IP transformed to the time domain. We have implemented our algorithm using efficient numerical methods that allow it to tackle large-scale problems and are amenable to use in inversion. In particular, we have developed a parallel time-stepping technique that allows us to compute transient electric fields at multiple time steps simultaneously. We demonstrate the behavior of the SE model of IP decay and the efficiency of our algorithm by applying it to synthetic numerical examples that simulate a grounded source IP survey with significant EM effects and a concentric-loop airborne EM sounding over a chargeable body.

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