Software

High order integrators for sampling the invariant measure of constrained overdamped Langevin dynamics. The numerical methods are described in Adrien Laurent, Gilles Vilmart, Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds, Found. Comput. Math. 22, 649–695 (2022).

Multirevolution integrators for SDEs with fast stochastic oscillations and the nonlinear Schrödinger equation with fast white noise dispersion. The numerical methods are described in Adrien Laurent, Gilles Vilmart, Multirevolution integrators for differential equations with fast stochastic oscillations, SIAM J. Sci. Comput. 42 (2020), no. 1, A115–A139.

SK-ROCK: Optimal explicit stabilized integrator of weak order one for stiff and ergodic Itô stochastic differential equations. This algorithm is described in A. Abdulle, I. Almuslimani, and G. Vilmart, Optimal explicit stabilized integrator of weak order one for stiff and ergodic stochastic differential equations, SIAM/ASA J. Uncertain. Quantif. 6 (2018), no. 2, 937–964.

S-SDIRK: weak second order drift-implicit mean-square A-stable integrators for stiff Itô stochastic differential equations. This algorithm is described in A. Abdulle, G. Vilmart, and K.C. Zygalakis, Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations, BIT 53 (2013) 827-840.

SROCK2: weak second order explicit stabilized integrators for stiff Itô stochastic differential equations. This algorithm is described in A. Abdulle, G. Vilmart, and K.C. Zygalakis, Weak second order explicit stabilized methods for stiff stochastic differential equations, SIAM J. Sci. Comput. 35 (2013):1792-1814.
This code is a modification of the code ROCK2 (A. Abdulle, 2002), A. Abdulle & A.A. Medovikov, Second order Chebyshev methods based on orthogonal polynomials, Numer. Math. 90, no. 1 (2001), 1-18.

PIROCK: A swiss-knife integrator for stiff diffusion-advection-reaction-noise problems, which is described in A. Abdulle and G. Vilmart, PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise, J. Comp. Phys. 242 (2013), 869-888.
This code is a modification of the code ROCK2 (A. Abdulle, 2002), A. Abdulle & A.A. Medovikov, Second order Chebyshev methods based on orthogonal polynomials, Numer. Math. 90, no. 1 (2001), 1-18.

Multiple scales nonlinear PDE solver FE-HMM-NONLIN. A short matlab implementation for nonlinear elliptic and parabolic problems with multiple scales 2011, which is described in A. Abdulle and G. Vilmart, Fully discrete analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems, to appear in Mathematics of Computation, 21 pages, (2013).
This code is a nonlinear extension of the linear code FE_HMM2D by A. Abdulle and A. Nonnenmacher (C) 2009 described in A. Abdulle and A. Nonnenmacher A short and versatile finite element multiscale code for homogenization problems, Comp. Meth. Appl. Mech. Eng., Vol. 198 (2009) p. 2839-2859.

Rigid body integrator, which is described in E. Hairer and G. Vilmart, Preprocessed Discrete Moser-Veselov algorithm for the full dynamics of the rigid body, J. Phys. A: Math. Gen. 39 (2006) 13225-13235.

  • dmv10.f Fortran subroutine for the modification of order 10 of the DMV algorithm (subroutines for the versions of orders 2,4,6,8 are included).
  • dr_dmv10.f driver for DMV10 (asymmetric rigid body).
  • dmv10out.txt Output example.

Fortran implementation
Version: August 29, 2006 (latest correction of a small bug: December 28, 2007)
Yareta archive portal, DOI: 10.26037/yareta:o2ye4lqtnnemrlvzrzoj6m57ei

Rigid body integrator. Modification of DMV10 with the simultaneous computation of the tangent map, for the computation of first conjugate points. This code is described in Section 3.6 of G. Vilmart, Étude d'intégrateurs géométriques pour des équations differentielles, Ph.D. Thesis, Univ. Rennes 1 (2008) No. 3758, Univ. Genève (2008) No. 4038.

  • dmv10conj.f Fortran subroutine for the (preprocessed) DMV algorithm of order 10 with simultaneous computation of the tangent map, for the computation of first conjugate points.
  • dmvlinalg.f Linear algebra routines for DMV10CONJ
  • dr_dmv10conj.f driver for DMV10CONJ (asymmetric rigid body).
  • dmv10conjout.txt Output example.

Last update: 31-Jan-2023