scholarly journals Large Time Step and Asymptotic Preserving Numerical Schemes for the Gas Dynamics Equations with Source Terms

2013 ◽  
Vol 35 (6) ◽  
pp. A2874-A2902 ◽  
Author(s):  
Christophe Chalons ◽  
Mathieu Girardin ◽  
Samuel Kokh
Keyword(s):  
Gas Dynamics ◽  
Large Time ◽  
Source Terms ◽  
Numerical Schemes ◽  
Gas Dynamics Equations ◽  
Time Step ◽  
Asymptotic Preserving ◽  
Large Time Step

scholarly journals ISALT: Inference-based schemes adaptive to large time-stepping for locally Lipschitz ergodic systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xingjie Helen Li ◽  
Fei Lu ◽  
Felix X.-F. Ye
Keyword(s):  
Large Time ◽  
Gradient System ◽  
Numerical Schemes ◽  
Time Step ◽  
Inference Problem ◽  
Time Dynamics ◽  
Efficient Simulation ◽  
Time Flow ◽  
Ergodic Measures ◽  
Locally Lipschitz

<p style='text-indent:20px;'>Efficient simulation of SDEs is essential in many applications, particularly for ergodic systems that demand efficient simulation of both short-time dynamics and large-time statistics. However, locally Lipschitz SDEs often require special treatments such as implicit schemes with small time-steps to accurately simulate the ergodic measures. We introduce a framework to construct inference-based schemes adaptive to large time-steps (ISALT) from data, achieving a reduction in time by several orders of magnitudes. The key is the statistical learning of an approximation to the infinite-dimensional discrete-time flow map. We explore the use of numerical schemes (such as the Euler-Maruyama, the hybrid RK4, and an implicit scheme) to derive informed basis functions, leading to a parameter inference problem. We introduce a scalable algorithm to estimate the parameters by least squares, and we prove the convergence of the estimators as data size increases.</p><p style='text-indent:20px;'>We test the ISALT on three non-globally Lipschitz SDEs: the 1D double-well potential, a 2D multiscale gradient system, and the 3D stochastic Lorenz equation with a degenerate noise. Numerical results show that ISALT can tolerate time-step magnitudes larger than plain numerical schemes. It reaches optimal accuracy in reproducing the invariant measure when the time-step is medium-large.</p>

scholarly journals Large Time Step TVD Schemes for Hyperbolic Conservation Laws

2016 ◽  
Vol 54 (5) ◽  
pp. 2775-2798 ◽  
Author(s):  
Sofia Lindqvist ◽  
Peder Aursand ◽  
Tore Flåtten ◽  
Anders Aase Solberg
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Large Time ◽  
Tvd Schemes ◽  
Time Step ◽  
Hyperbolic Conservation ◽  
Large Time Step

An explicit large time step particle-in-cell scheme for nonlinear gyrokinetic simulations in the electromagnetic regime

2016 ◽  
Vol 23 (3) ◽  
pp. 032501 ◽  
Author(s):  
R. Kleiber ◽  
R. Hatzky ◽  
A. Könies ◽  
A. Mishchenko ◽  
E. Sonnendrücker
Keyword(s):  
Large Time ◽  
Time Step ◽  
Particle In Cell ◽  
Large Time Step ◽  
Gyrokinetic Simulations
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