ORCID Profile
0000-0003-2391-4086
Current Organisation
Monash University
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Numerical Solution of Differential and Integral Equations | Numerical Analysis | Numerical and Computational Mathematics |
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2009
DOI: 10.1137/08072632X
Publisher: Elsevier BV
Date: 2017
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2021
DOI: 10.1137/20M1344512
Publisher: Elsevier BV
Date: 04-2006
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2017
DOI: 10.1137/16M1074266
Publisher: Elsevier BV
Date: 12-2018
Publisher: Elsevier BV
Date: 07-2009
Publisher: Elsevier BV
Date: 2009
Publisher: Elsevier BV
Date: 12-2019
Publisher: Elsevier BV
Date: 09-2019
Publisher: Elsevier BV
Date: 12-2021
Publisher: The Open Journal
Date: 09-06-2022
DOI: 10.21105/JOSS.04157
Publisher: Elsevier BV
Date: 07-2018
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2014
DOI: 10.1137/130918708
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2008
DOI: 10.1137/07069969X
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2008
DOI: 10.1137/070680497
Publisher: Elsevier BV
Date: 2017
Publisher: Elsevier BV
Date: 11-2015
Publisher: Springer Science and Business Media LLC
Date: 07-05-2008
Publisher: Springer Science and Business Media LLC
Date: 02-07-2013
Publisher: Springer Science and Business Media LLC
Date: 11-07-2022
DOI: 10.1007/S10915-022-01913-9
Abstract: We conduct a condition number analysis of a Hybrid High-Order (HHO) scheme for the Poisson problem. We find the condition number of the statically condensed system to be independent of the number of faces in each element, or the relative size between an element and its faces. The dependence of the condition number on the polynomial degree is tracked. Next, we consider HHO schemes on cut background meshes, which are commonly used in unfitted discretisations. It is well known that the linear systems obtained on these meshes can be arbitrarily ill-conditioned due to the presence of sliver-cut and small-cut elements. We show that the condition number arising from HHO schemes on such meshes is not as negatively effected as those arising from conforming methods. We describe how the condition number can be improved by aggregating ill-conditioned elements with their neighbours.
Publisher: World Scientific Pub Co Pte Ltd
Date: 03-2023
DOI: 10.1142/S0218202523500148
Abstract: This paper aims to develop numerical approximations of the Keller–Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized finite element method and a semi-implicit time integration. The stabilization consists of a nonlinear artificial diffusion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities fulfilling lower bounds. However, the first algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes. We report some numerical experiments to validate the theoretical results on blowup and nonblowup phenomena. In the blowup setting, we identify a locking phenomenon that relates the [Formula: see text]-norm to the [Formula: see text]-norm limiting the growth of the singularity when supported on a macroelement.
Publisher: Elsevier BV
Date: 04-2023
Publisher: Elsevier BV
Date: 04-2012
Publisher: Springer Science and Business Media LLC
Date: 11-07-2007
Publisher: Elsevier BV
Date: 11-2012
Publisher: Elsevier BV
Date: 09-2016
Publisher: Elsevier BV
Date: 04-2019
Publisher: Elsevier BV
Date: 09-2008
Publisher: Elsevier BV
Date: 07-2008
Publisher: Springer International Publishing
Date: 2017
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2016
DOI: 10.1137/15M1013511
Publisher: The Open Journal
Date: 26-08-2020
DOI: 10.21105/JOSS.02520
Publisher: Elsevier BV
Date: 12-2017
Publisher: Elsevier BV
Date: 04-2007
Publisher: Elsevier BV
Date: 09-2019
Publisher: Springer Science and Business Media LLC
Date: 18-09-2014
Publisher: Wiley
Date: 2008
DOI: 10.1002/FLD.1532
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2016
DOI: 10.1137/15M1045648
Publisher: Elsevier BV
Date: 03-2020
Publisher: Oxford University PressOxford
Date: 10-2009
DOI: 10.1093/ACPROF:OSO/9780199233854.003.0006
Abstract: We review some recent developments in the coupling of atomistic and continuum models based on the blending of the two models in an overlap, or bridge, subdomain. These coupling schemes resemble overlapping domain decomposition methods. However, their analysis and development is complicated by the non-local force model employed by the atomistic model. We present an abstract framework for atomistic-to-continuum (AtC) coupling methods and formulate precise mathematical notions of patch and consistency tests for the methods. The framework admits both force-based or energy-based coupling methods and allows us to identify four general classes of blending methods. We subject each class to patch and consistency tests and discuss important implementation issues such as: the enforcement of displacement continuity constraints in the bridge region internal vs. external blending the role of ghost forces, or forces that arise from coupling nonlocal and local models of force, and how they can be mitigated by blending methods.
Publisher: Elsevier BV
Date: 07-2022
Publisher: Elsevier BV
Date: 08-2013
Publisher: Begell House
Date: 2007
Publisher: Elsevier BV
Date: 10-2020
Publisher: Elsevier BV
Date: 06-2019
Publisher: Elsevier BV
Date: 2022
Publisher: Springer Science and Business Media LLC
Date: 13-10-2016
Publisher: Elsevier BV
Date: 09-2007
Publisher: Wiley
Date: 24-05-2019
DOI: 10.1002/NME.6085
Publisher: Elsevier BV
Date: 11-2023
Publisher: Elsevier BV
Date: 12-2018
Publisher: Elsevier BV
Date: 12-2018
Publisher: Elsevier BV
Date: 12-2015
Publisher: Elsevier BV
Date: 07-2022
Publisher: Springer Berlin Heidelberg
Date: 2008
Publisher: Elsevier BV
Date: 04-2015
Publisher: Elsevier BV
Date: 2024
Publisher: Elsevier BV
Date: 2020
Publisher: Elsevier BV
Date: 11-2009
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2018
DOI: 10.1137/18M1185624
Publisher: Elsevier BV
Date: 05-2010
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2010
DOI: 10.1137/090766681
Publisher: Elsevier BV
Date: 12-2022
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2006
DOI: 10.1137/050643532
Publisher: Elsevier BV
Date: 09-2020
Publisher: Springer Science and Business Media LLC
Date: 17-05-2023
DOI: 10.1007/S11831-023-09913-0
Abstract: This review paper discusses the developments in immersed or unfitted finite element methods over the past decade. The main focus is the analysis and the treatment of the adverse effects of small cut elements. We distinguish between adverse effects regarding the stability and adverse effects regarding the conditioning of the system, and we present an overview of the developed remedies. In particular, we provide a detailed explanation of Schwarz preconditioning, element aggregation, and the ghost penalty formulation. Furthermore, we outline the methodologies developed for quadrature and weak enforcement of Dirichlet conditions, and we discuss open questions and future research directions.
Publisher: Elsevier BV
Date: 12-2011
Publisher: Elsevier BV
Date: 02-2011
Publisher: Elsevier BV
Date: 06-2016
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2014
DOI: 10.1137/130931989
Publisher: Elsevier BV
Date: 10-2014
Publisher: Elsevier BV
Date: 2019
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2012
DOI: 10.1137/110835360
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2020
DOI: 10.1137/20M1328786
Publisher: Springer Science and Business Media LLC
Date: 27-07-2011
Publisher: Elsevier BV
Date: 06-2017
Publisher: Springer Science and Business Media LLC
Date: 07-11-2018
Publisher: Wiley
Date: 19-07-2013
DOI: 10.1002/NME.4541
Publisher: Begell House
Date: 2021
Publisher: Elsevier BV
Date: 11-2015
Publisher: Elsevier BV
Date: 03-2015
Publisher: Wiley
Date: 21-09-2015
DOI: 10.1002/NME.4987
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 06-2006
Publisher: Elsevier BV
Date: 07-2021
Publisher: Oxford University Press (OUP)
Date: 19-07-2013
Publisher: Springer Science and Business Media LLC
Date: 17-10-2016
Publisher: Wiley
Date: 2007
DOI: 10.1002/NME.1998
Publisher: Elsevier BV
Date: 07-2014
Publisher: Oxford University Press (OUP)
Date: 24-09-2013
Publisher: Springer Science and Business Media LLC
Date: 11-10-2017
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2014
DOI: 10.1137/130927206
Start Date: 10-2021
End Date: 10-2024
Amount: $475,000.00
Funder: Australian Research Council
View Funded ActivityStart Date: 08-2022
End Date: 08-2025
Amount: $396,000.00
Funder: Australian Research Council
View Funded Activity