Splitting methods

RI McLachlan, GRW Quispel - Acta Numerica, 2002 - cambridge.org
I thought that instead of the great number of precepts of which logic is composed, I would
have enough with the four following ones, provided that I made a firm and unalterable …

[图书][B] Symplectic geometric algorithms for Hamiltonian systems

K Feng, M Qin - 2010 - Springer
It has been 16 years since Kang Feng passed away. It is our honor to publish the English
version of Symplectic Algorithm for Hamiltonian Systems, so that more readers can see the …

On the existence and the applications of modified equations for stochastic differential equations

KC Zygalakis - SIAM Journal on Scientific Computing, 2011 - SIAM
In this paper we describe a general framework for deriving modified equations for stochastic
differential equations (SDEs) with respect to weak convergence. Modified equations are …

Derivation of symmetric composition constants for symmetric integrators

M Sofroniou, G Spaletta - Optimization Methods and Software, 2005 - Taylor & Francis
This work focuses on the derivation of composition methods for the numerical integration of
ordinary differential equations, which give rise to very challenging optimization problems …

Calculating effective diffusivities in the limit of vanishing molecular diffusion

GA Pavliotis, AM Stuart, KC Zygalakis - Journal of Computational Physics, 2009 - Elsevier
In this paper we study the problem of the numerical calculation (by Monte Carlo methods) of
the effective diffusivity for a particle moving in a periodic divergent-free velocity field, in the …

Explicit volume-preserving splitting methods for divergence-free ODEs by tensor-product basis decompositions

A Zanna - IMA Journal of Numerical Analysis, 2015 - academic.oup.com
We discuss the construction of volume-preserving splitting methods based on a tensor
product of single-variable basis functions. The vector field is decomposed as the sum of …

Numerical studies of homogenization under a fast cellular flow

G Iyer, KC Zygalakis - Multiscale Modeling & Simulation, 2012 - SIAM
We consider a two dimensional particle diffusing in the presence of a fast cellular flow
confined to a finite domain. If the flow amplitude A is held fixed and the number of cells …

Parallel Numerical Methods for Model Coupling in Nutrient Cycle Simulations

M Wlotzka - 2017 - archiv.ub.uni-heidelberg.de
We present a new approach to ecosystem nutrient cycle simulations. Nutrient conversion
and fluxes between ecosystem compartments are driven by highly complex biogeochemical …

High order volume preserving integrators for three kinds of divergence-free vector fields via commutators

H Xue - Volume preserving numerical integrators for ordinary …, 2013 - bora.uib.no
In this paper, we focus on construction of high order volume preserving integrators for
divergence-free vector fields of the monomial basis, exponential basis and tensor product of …

Explicit volume-preserving splitting methods for divergence-free ODEs by tensor-product basis decompositions

AZ Munthe-Kaas - 2014 - bora.uib.no
We discuss the construction of volume-preserving splitting methods based on a tensor
product of single-variable basis functions. The vector field is decomposed as the sum of …