Stage-parallel fully implicit Runge-Kutta implementations with optimal multilevel preconditioners at the scaling limit

Authors: Munch, Peter, Dravins, Ivo, 1991, Kronbichler, Martin, Neytcheva, Maya, Dr, 1956

Source: eSSENCE - An eScience Collaboration SIAM Journal on Scientific Computing. 46(2):71-96

Subject Terms: implicit Runge–Kutta methods, Radau quadrature, stage-parallel preconditioning, finite element methods, matrix-free methods, geometric multigrid, massively parallel, Beräkningsvetenskap med inriktning mot numerisk analys, Scientific Computing with specialization in Numerical Analysis

File Description: print

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-492935
https://doi.org/10.1137/22M1503270

Stage-parallel preconditioners for implicit Runge-Kutta methods of arbitrarily high order, linear problems

Authors: Axelsson, Owe, Dravins, Ivo, 1991, Neytcheva, Maya, Dr, 1956

Source: Numerical Linear Algebra with Applications. 31(1)

Subject Terms: fully stage-parallel preconditioning, implicit Runge–Kutta methods, parallelization, Radau quadrature, Beräkningsvetenskap med inriktning mot numerisk analys, Scientific Computing with specialization in Numerical Analysis

File Description: electronic

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-497731
https://doi.org/10.1002/nla.2532

High Order Methods for Nonlinear Evolution Equations Governed by Semibounded or Dissipative Operators in Normed Space

Authors: Wang, Wansheng^{Aff1, IDs10915025029822_cor1}, Jin, Chengyu

Source: Journal of Scientific Computing. 104(2)

Analysis of starting approximations for implicit Runge-Kutta methods applied to ODEs based on the reverse method

Authors: Jay, Laurent O. ^{a, ⁎}, Montijano, Juan I. ^b

Source: In Applied Numerical Mathematics September 2025 215:1-14

Fine spectral analysis of preconditioned matrices and matrix-sequences arising from stage-parallel implicit Runge-Kutta methods of arbitrarily high order

Authors: Dravins, Ivo, 1991, Serra-Capizzano, Stefano, Neytcheva, Maya, Dr, 1956

Source: SIAM Journal on Matrix Analysis and Applications. 45(2):1007-1034

Subject Terms: implicit Runge--Kutta methods, Radau quadrature, preconditioning, Beräkningsvetenskap med inriktning mot numerisk analys, Scientific Computing with specialization in Numerical Analysis

File Description: print

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-497732

On convergence of implicit Runge-Kutta methods for the incompressible Navier-Stokes equations with unsteady inflow

Authors: Cai, Yunzhu ^a, Wan, Jiawei ^{b, c, ⁎}, Kareem, Ahsan ^b

Source: In Journal of Computational Physics 15 February 2025 523

Learning dynamical systems from noisy data with inverse-explicit integrators

Authors: Celledoni, Elena ^b, Eidnes, Sølve ^a, Myhr, Håkon Noren ^{b, ⁎}

Source: In Physica D: Nonlinear Phenomena February 2025 472

Implicit Runge-Kutta Methods for Accelerated Unconstrained Convex Optimization

Authors: Chen, R., Li, X.

Source: IEEE Access Access, IEEE. 8:28624-28634 2020

Spectral analysis of implicit 2 stage block Runge-Kutta preconditioners

Authors: Gander, Martin J. ¹, Outrata, Michal ^{⁎, 2}

Source: In Linear Algebra and Its Applications 15 July 2024 693:214-235

Numerical evolution of the resistive relativistic magnetohydrodynamic equations: A minimally implicit Runge-Kutta scheme

Authors: Cordero-Carrión, Isabel ^⁎, Santos-Pérez, Samuel, Martínez-Vidallach, Clara

Source: In Applied Mathematics and Computation 15 April 2023 443

Running an Atmospheric Chemistry Scheme from a Large Air Pollution Model by Using Advanced Versions of the Richardson Extrapolation

Authors: Zlatev, Zahari^Aff10, Dimov, Ivan^Aff11, Faragó, István^{Aff12, Aff13, Aff14}, Georgiev, Krassimir^Aff11, Havasi, Ágnes^{Aff12, Aff13}

Contributors: Goos, Gerhard, Founding Editor^Aff1, Hartmanis, Juris, Founding Editor^Aff2, Bertino, Elisa, Editorial Board Member^Aff3, Gao, Wen, Editorial Board Member^Aff4, Steffen, Bernhard, Editorial Board Member^Aff5, Woeginger, Gerhard, Editorial Board Member^Aff6, Yung, Moti, Editorial Board Member^Aff7, Lirkov, Ivan, editor^Aff8, Margenov, Svetozar, editor^Aff9

Source: Large-Scale Scientific Computing : 13th International Conference, LSSC 2021, Sozopol, Bulgaria, June 7–11, 2021, Revised Selected Papers. 13127:188-197

Preconditioning for block matrices with square blocks

Authors: Dravins, Ivo, 1991

Contributors: Neytcheva, Maya, Professor, Margenov, Svetozar, Professor

Source: Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology.

Subject Terms: preconditioning, block preconditioning, PDE-constrained optimization, Implicit Runge-Kutta methods, Beräkningsvetenskap med inriktning mot numerisk analys, Scientific Computing with specialization in Numerical Analysis

File Description: electronic

Access URL: https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-497750
https://uu.diva-portal.org/smash/get/diva2:1741052/FULLTEXT01.pdf

A note on approximate Jacobians of implicit Runge–Kutta methods and convergence of modified Newton iterations

Authors: Jay, Laurent O.^{Aff1, IDs10543023009948_cor1}, Sokratova, Olga

Source: BIT Numerical Mathematics. 63(4)

Efficient implementation of advanced Richardson Extrapolation in an atmospheric chemical scheme

Authors: Krassimir Georgiev, Ivan Dimov, István Faragó, Zahari Zlatev, Ágnes Havasi

Source: Zlatev, Z, Dimov, I, Faragó, I, Georgiev, K & Havasi, Á 2022, 'Efficient implementation of advanced Richardson Extrapolation in an atmospheric chemical scheme', Journal of Mathematical Chemistry, vol. 60, no. 1, pp. 219-238. https://doi.org/10.1007/s10910-021-01300-z

Subject Terms: Richardson Extrapolation, 13. Climate action, 11. Sustainability, Atmospheric chemical schemes, 0101 mathematics, 01 natural sciences, Implicit Runge–Kutta methods, Ordinary differential equations, 0105 earth and related environmental sciences

File Description: application/pdf

Access URL: https://link.springer.com/content/pdf/10.1007/s10910-021-01300-z.pdf
https://paperity.org/p/275834190/efficient-implementation-of-advanced-richardson-extrapolation-in-an-atmospheric-chemical
https://link.springer.com/article/10.1007%2Fs10910-021-01300-z
https://link.springer.com/content/pdf/10.1007/s10910-021-01300-z.pdf
https://pure.au.dk/ws/files/333843969/s10910_021_01300_z.pdf
http://hdl.handle.net/10831/83018
https://pure.au.dk/ws/files/333843969/s10910_021_01300_z.pdf
https://pure.au.dk/portal/en/publications/9a5c6d26-35b1-4485-8107-c68a7efde7c2
https://doi.org/10.1007/s10910-021-01300-z
http://www.scopus.com/inward/record.url?scp=85119519659&partnerID=8YFLogxK

The TR-BDF2 method for second order problems in structural mechanics

Authors: Bonaventura, Luca, Mármol, Macarena Gómez

Source: Computers & Mathematics with Applications. 92:13-26

Subject Terms: Structural dynamics, Highly oscillatory problems, Newmark method, Diagonally implicit Runge Kutta methods, TR-BDF2 method, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), 0101 mathematics, 01 natural sciences

File Description: application/pdf

Access URL: http://arxiv.org/pdf/2007.12363
http://arxiv.org/abs/2007.12363
https://re.public.polimi.it/handle/11311/1167866
https://doi.org/10.1016/j.camwa.2021.03.037
https://www.sciencedirect.com/science/article/pii/S0898122121001267
https://arxiv.org/pdf/2007.12363
https://dblp.uni-trier.de/db/journals/corr/corr2007.html#abs-2007-12363
https://arxiv.org/abs/2007.12363
https://hdl.handle.net/11311/1167866
https://doi.org/10.1016/j.camwa.2021.03.037

Third- and Fourth-Order ESDIRK Methods for Stiff and Differential-Algebraic Problems

Authors: Skvortsov, L. M.^{Aff1, IDS0965542522050128_cor1}

Source: Computational Mathematics and Mathematical Physics. 62(5):766-783

Bicompact Schemes for the Numerical Solution of the Reed Problem Using HOLO Algorithms

Authors: Aristova, E. N.^{Aff1, IDS2070048222020028_cor1}, Karavaeva, N. I.^{Aff1, Aff2}

Source: Mathematical Models and Computer Simulations. 14(2):187-202

Spectral analysis of implicit 2 stage block Runge-Kutta preconditioners

Authors: Gander, Martin, J, Outrata, Michal

Contributors: Université de Genève = University of Geneva (UNIGE)

Source: https://hal.science/hal-04016604 ; 2023.

Subject Terms: implicit Runge-Kutta methods two stages preconditioners GMRES bounds Classication: 65F08 65F10, implicit Runge-Kutta methods, two stages, preconditioners, GMRES, bounds Classication: 65F08, 65F10, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

Relation: hal-04016604; https://hal.science/hal-04016604; https://hal.science/hal-04016604/document; https://hal.science/hal-04016604/file/GanderOutrata_IRK2stage.pdf

Availability: https://hal.science/hal-04016604
https://hal.science/hal-04016604/document
https://hal.science/hal-04016604/file/GanderOutrata_IRK2stage.pdf

Spectral analysis of implicit s stage block Runge-Kutta preconditioners

Authors: Gander, Martin, J, Outrata, Michal

Contributors: Université de Genève = University of Geneva (UNIGE)

Source: https://hal.science/hal-04213008 ; 2023.

Subject Terms: implicit Runge-Kutta methods two stages preconditioners GMRES bounds Classification: 65F08 65F10, implicit Runge-Kutta methods, two stages, preconditioners, GMRES, bounds Classification: 65F08, 65F10, [MATH]Mathematics [math]

Relation: hal-04213008; https://hal.science/hal-04213008; https://hal.science/hal-04213008v2/document; https://hal.science/hal-04213008v2/file/2023_GanderOutrata_IRKsstage.pdf

Availability: https://hal.science/hal-04213008
https://hal.science/hal-04213008v2/document
https://hal.science/hal-04213008v2/file/2023_GanderOutrata_IRKsstage.pdf

A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier–Stokes equation

Authors: Chen, Xi ^{a, ⁎}, Li, Yuwen ^b, Drapaca, Corina ^c, Cimbala, John ^a

Source: In Journal of Computational Physics 1 December 2020 422