Search Results - "Geometric Numerical Integration"

Geometric Numerical Integration for Hamiltonian Monte Carlo and Extrapolation

Authors: Shaw, Luke

Contributors: University/Department: Universitat Jaume I. Escola de Doctorat

Thesis Advisors: Casas, Fernando, Sanz-Serna, JM

Source: TDX (Tesis Doctorals en Xarxa)

Subject Terms: Geometric Numerical Integration, Splitting methods, Hamiltonian Monte Carlo, Symplectic Integrators, Extrapolation methods, Numerical Analysis, Ciències

File Description: application/pdf

Access URL: http://hdl.handle.net/10803/692560

Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations

Authors: Bréhier, Charles-Edouard Cohen, David

Source: Numerisk analys och simulering av PDE med slumpmässig dispersion Applied Numerical Mathematics. 186:57-83

Subject Terms: Geometric numerical integration, Stochastic partial differential equations, Strong convergence, Trace formulas, Stochastic Schrödinger equations, Splitting integrators

File Description: electronic

Access URL: https://research.chalmers.se/publication/534303
https://research.chalmers.se/publication/527569
https://arxiv.org/abs/2007.02354

High order numerical integrators for single integrand Stratonovich SDEs

Authors: Cohen, David Debrabant, Kristian Rößler, Andreas

Source: Numerisk analys och simulering av PDE med slumpmässig dispersion Applied Numerical Mathematics. 158:264-270

Subject Terms: Strong error, High order, Weak error, Stratonovich stochastic differential equation, Geometric numerical integration, B-series methods, Single integrand SDEs

File Description: electronic

Access URL: https://research.chalmers.se/publication/518714
https://research.chalmers.se/publication/520223
https://research.chalmers.se/publication/519576
https://research.chalmers.se/publication/520223/file/520223_Fulltext.pdf

Boundary-preserving numerical schemes for stochastic ordinary and partial differential equations

Authors: Ulander, Johan, 1995

Subject Terms: strong convergence, stochastic partial differential equations, Stochastic ordinary differential equations, geometric numerical integration, positivity-preserving, Lie--Trotter time splitting, boundary-preserving, weak convergence.

File Description: electronic

Access URL: https://research.chalmers.se/publication/548883
https://research.chalmers.se/publication/548883/file/548883_Fulltext.pdf

Geometric Numerical Methods: From Random Fields to Shape Matching

Authors: Jansson, Erik, 1996

Subject Terms: hydrodynamics, Stochastic partial differential equations, Lie–Poisson systems, shape analysis, geometric numerical integration, optimal transport, surface finite element methods, Gaussian random fields

File Description: electronic

Access URL: https://research.chalmers.se/publication/545974
https://research.chalmers.se/publication/545974/file/545974_Fulltext.pdf

Discrete gradients in short-range molecular dynamics simulations

Authors: Grimm, Volker Kliesch, Tobias Quispel, G. R. W.

Source: Numerical Algorithms, 96 (3), 1189–1220

Subject Terms: Parallel computing, ddc:510, Numerical and computational mathematics, Mathematical sciences, Discrete gradient, Numerical Analysis (math.NA), Molecular dynamics, Applied mathematics, 01 natural sciences, Geometric numerical integration, Linked cell method, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Mathematics

File Description: application/pdf

Access URL: http://arxiv.org/abs/2212.14344
https://publikationen.bibliothek.kit.edu/1000167557
https://doi.org/10.5445/IR/1000167557
https://publikationen.bibliothek.kit.edu/1000167557/152088221

The Lie derivative and Noether's theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators

Authors: Laurent, Adrien Busnot Laurent, Adrien Institut de Recherche Mathématique de Rennes (IRMAR) et al.

Contributors: Laurent, Adrien Busnot Laurent, Adrien Institut de Recherche Mathématique de Rennes (IRMAR) et al.

Source: Journal of Computational Dynamics. 11:10-22

Subject Terms: 58E30, 58J10, 05C05, 41A58, 37M15, 58A12, 58A12, aromatic bicomplex, volume-preservation, Euler-Lagrange complex, geometric numerical integration, aromatic Lie derivative, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 58J10, Noether's theorem, solenoidal forms, 05C05, Secondary: 41A58, 37M15, FOS: Mathematics, Mathematics - Numerical Analysis, Primary: 58E30, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

File Description: application/pdf

Access URL: http://arxiv.org/abs/2307.07984
https://hal.science/hal-04347291v2
https://doi.org/10.3934/jcd.2023011
https://hal.science/hal-04347291v2/document

Exponential integrators for nonlinear Schrödinger equations with white noise dispersion

Authors: Cohen, David Dujardin, Guillaume

Source: Stochastics and Partial Differential Equations: Analysis and Computations. 5(4):592-613

Subject Terms: Stochastic partial differential equations, Nonlinear Schrödinger equation, White noise dispersion, Numerical methods, Geometric numerical integration, Exponential integrators, Mean-square convergence

File Description: electronic

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-137244
https://doi.org/10.1007/s40072-017-0098-1

Involutive flows and discretization errors for nonlinear driftless control systems

Authors: Altafini, Claudio

Source: Systems & control letters (Print). 110:29-37

Subject Terms: Discrete-time nonlinear control systems, Nonintegrability condition, Discretization, Lie brackets, Geometric phase, Geometric numerical integration, Local error computation

File Description: electronic

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-144147
https://liu.diva-portal.org/smash/get/diva2:1172314/FULLTEXT01.pdf

High-order symplectic Lie group methods on $ SO(n) $ using the polar decomposition

Authors: Shen, Xuefeng Tran, Khoa Leok, Melvin

Source: Journal of Computational Dynamics. 9(4)

Subject Terms: Mathematical Physics, Mathematical Sciences, Geometric numerical integration, symplectic integration, variational integrator, Lie group integrator, rotation group, polar decomposition, Applied Mathematics, Numerical and Computational Mathematics, Applied mathematics, Numerical and computational mathematics

File Description: application/pdf

Access URL: https://escholarship.org/uc/item/7zv987kh
https://escholarship.org/content/qt7zv987kh/qt7zv987kh.pdf

Full Discretization of Semilinear Stochastic Wave Equations Driven by Multiplicative Noise

Authors: Anton, R. Cohen, D. Larsson, Stig et al.

Source: Siam Journal on Numerical Analysis. 54(2):1093-1119

Subject Terms: Mathematical sciences, Matematik, semilinear stochastic wave equation, multiplicative noise, strong convergence, trace formula, stochastic trigonometric methods, geometric numerical integration, partial-differential-equations, finite-element methods, additive noise, approximation

File Description: electronic

Access URL: https://gup.ub.gu.se/publication/237018
https://gup.ub.gu.se/publication/237018

Butcher series for Hamiltonian Poisson integrators through symplectic groupoids

Authors: Busnot Laurent, Adrien Cosserat, Oscar Multi-scale numerical geometric schemes (MINGUS) et al.

Contributors: Busnot Laurent, Adrien Cosserat, Oscar Multi-scale numerical geometric schemes (MINGUS) et al.

Source: https://hal.science/hal-05368917 ; 2025.

Subject Terms: Butcher series, Poisson geometry, mathematical physics, geometric numerical integration, symplectic groupoids, Hamilton-Jacobi equation, pre-Lie algebra, Hopf algebra, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

Availability: https://hal.science/hal-05368917
https://hal.science/hal-05368917v1/document
https://hal.science/hal-05368917v1/file/Paper.pdf

High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods

Authors: Bronasco, Eugen Busnot Laurent, Adrien Huguet, Baptiste, Nicolas et al.

Contributors: Bronasco, Eugen Busnot Laurent, Adrien Huguet, Baptiste, Nicolas et al.

Source: https://hal.science/hal-05368742 ; 2025.

Subject Terms: Butcher series, order conditions, Hopf algebra, post-Lie algebra, exotic series, frozen flow, Lie-group methods, ergodicity, Riemannian Langevin, Riemannian manifolds, stochastic differential equations, geometric numerical integration, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

Availability: https://hal.science/hal-05368742
https://hal.science/hal-05368742v1/document
https://hal.science/hal-05368742v1/file/paper_frozen_flow.pdf

Stochastic conformal integrators for linearly damped stochastic poisson systems

Authors: Bréhier, Charles-Édouard Cohen, David Komori, Yoshio et al.

Contributors: Bréhier, Charles-Édouard Cohen, David Komori, Yoshio et al.

Source: https://hal.science/hal-04975253 ; 2025.

Subject Terms: Stochastic differential equations, Linearly damped stochastic Poisson systems, Casimir and Hamiltonian functions, Geometric numerical integration, Stochastic conformal integrator, Strong and weak convergence, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]

Relation: info:eu-repo/semantics/altIdentifier/arxiv/2503.01540; ARXIV: 2503.01540

Availability: https://hal.science/hal-04975253
https://hal.science/hal-04975253v1/document
https://hal.science/hal-04975253v1/file/bck.pdf

The Universal Equivariance Properties of Exotic Aromatic B-Series

Authors: Laurent, Adrien Munthe-Kaas, Hans Busnot Laurent, Adrien et al.

Contributors: Laurent, Adrien Munthe-Kaas, Hans Busnot Laurent, Adrien et al.

Source: Foundations of Computational Mathematics.

Subject Terms: Probability (math.PR), geometric numerical integration, Numerical Analysis (math.NA), [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 01 natural sciences, stochastic differential equations, 15A72, 37C81, 41A58, 60H35, 65C30, 15A72, FOS: Mathematics, 65C30, equivariance, 37C81, 60H35, Butcher series, Mathematics - Numerical Analysis, 0101 mathematics, 41A58, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], exotic aromatic B-series, Mathematics - Probability

File Description: application/pdf

Access URL: http://arxiv.org/abs/2305.10993
https://hdl.handle.net/10037/35441

Discrete Dirac reduction of implicit Lagrangian systems with abelian symmetry groups

Authors: Abella, Álvaro Rodríguez Leok, Melvin Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]

Contributors: Abella, Álvaro Rodríguez Leok, Melvin Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]

Source: Digital.CSIC. Repositorio Institucional del CSIC
Consejo Superior de Investigaciones Científicas (CSIC)

Subject Terms: 37J39, 65P10, 70G65, 70H33, FOS: Physical sciences, Mathematical Physics (math-ph), Numerical Analysis (math.NA), Dynamical Systems (math.DS), 01 natural sciences, Geometric numerical integration, Discrete mechanical systems, Lagrange-Poincaré-Dirac equations, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, Mathematics - Dynamical Systems, 0101 mathematics, Reduction by symmetries, Mathematical Physics

Access URL: http://arxiv.org/abs/2202.00803
https://api.elsevier.com/content/abstract/scopus_id/85150037121
http://hdl.handle.net/10261/349433

How do Monte Carlo estimates affect stochastic geometric numerical integration?

Authors: D'Ambrosio R. Di Giovacchino S.

Source: International Journal of Computer Mathematics. 100:192-208

Subject Terms: additive noise, geometric numerical integration, Monte Carlo methods, Stochastic differential equations, stochastic Hamiltonian problems, 0101 mathematics, 01 natural sciences

Access URL: https://hdl.handle.net/11697/204785
https://doi.org/10.1080/00207160.2022.2107393

A Trigonometric Method for the Linear Stochastic Wave Equation

Authors: Cohen, David Larsson, Stig Sigg, Magdalena

Source: SIAM Journal on Numerical Analysis. 51(1):204-222

Subject Terms: Computational Mathematics, Beräkningsmatematik, Stochastic wave equation, Additive noise, Strong convergence, Trace formula, Stochastic trigonometric schemes, Geometric numerical integration

File Description: electronic

Access URL: https://gup.ub.gu.se/publication/173637
https://gup.ub.gu.se/publication/173637

Discrete quantum harmonic oscillator and Kravchuk transform

Authors: Chauleur, Quentin Faou, Erwan Centre Inria de l'Université de Lille et al.

Contributors: Chauleur, Quentin Faou, Erwan Centre Inria de l'Université de Lille et al.

Source: ISSN: 2822-7840 ; EISSN: 2804-7214.

Subject Terms: Harmonic oscillator, Kravchuk polynomials, geometric numerical integration, [MATH]Mathematics [math]

Availability: https://hal.science/hal-04819883
https://hal.science/hal-04819883v1/document
https://hal.science/hal-04819883v1/file/m2an230107.pdf
https://doi.org/10.1051/m2an/2024001

Discrete gradients in short-range molecular dynamics simulations

Authors: V Grimm T Kliesch Gilles Quispel

Subject Terms: Mathematical sciences, Applied mathematics, Numerical and computational mathematics, Discrete gradient, Geometric numerical integration, Molecular dynamics, Linked cell method, Parallel computing

Availability: https://doi.org/10.26181/26368270.v1
https://figshare.com/articles/journal_contribution/Discrete_gradients_in_short-range_molecular_dynamics_simulations/26368270