Niall Bootland

Computational Mathematician

Niall Bootland is a member of the Computational Mathematics Group at the STFC Rutherford Appleton Laboratory. He completed his doctorate under Prof Andy Wathen at the University of Oxford in collaboration with the US Army Coastal and Hydraulics Laboratory. Here he worked on scalable two-phase flow solvers, in particular focusing on preconditioning for variable coefficient Navier–Stokes equations. Following this he worked with Prof Victorita Dolean at the University of Strathclyde as a research associate in scientific computing of wave scattering problems and applications. This work focused on domain decomposition methods for solving frequency domain wave propagation problems, such as those modelled by the heterogeneous Helmholtz or time-harmonic Maxwell equations.

His wider interests lie in computational methods for solving challenging problems rooted in applications, typically stemming from PDE models which are discretised by finite elements, and developing novel algorithms that are efficient and robust to model parameters. The focus of his work is primarily on the numerical linear algebra tools that are at the centre of effective computational simulations.

  • Numerical linear algebra
  • Preconditioning
  • Domain decomposition methods

ORCID iD: 0000-0002-3207-5395

Preprints:
  • N. Bootland, S. Borzooei, V. Dolean, and P.-H. Tournier, Numerical assessment of PML transmission conditions in a domain decomposition method for the Helmholtz equation, arXiv:2211.06859 (2022) link

Refereed articles:

  1. N. Bootland, V. Dolean, I.G. Graham, C. Ma, and R. Scheichl, Overlapping Schwarz methods with GenEO coarse spaces for indefinite and nonself-adjoint problems, IMA Journal of Numerical Analysis, (accepted) published online in advance (2022) link
  2. N. Bootland and V. Dolean, Can DtN and GenEO coarse spaces be sufficiently robust for heterogeneous Helmholtz problems?, Mathematical and Computational Applications, 27(3), 35 (2022) link
  3. N. Bootland, V. Dwarka, P. Jolivet, V. Dolean, and C. Vuik, Inexact subdomain solves using deflated GMRES for Helmholtz problems, In: S.C. Brenner et al. (Eds.) Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, Vol. 145. Springer, Cham, pp. 123–131 (2022) link
  4. N. Bootland, V. Dolean, I.G. Graham, C. Ma, and R. Scheichl, GenEO coarse spaces for heterogeneous indefinite elliptic problems, In: S.C. Brenner et al. (Eds.) Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, Vol. 145. Springer, Cham, pp. 115–122 (2022) link
  5. N. Bootland, V. Dolean, P. Jolivet, F. Nataf, S. Operto, and P.-H. Tournier, Several ways to achieve robustness when solving wave propagation problems, In: S.C. Brenner et al. (Eds.) Domain Decomposition Methods in Science and Engineering XXVI. Lecture Notes in Computational Science and Engineering, Vol. 145. Springer, Cham, pp. 15–26 (2022) link
  6. N. Bootland, V. Dolean, A. Kyriakis, and J. Pestana, Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices, Electronic Transactions on Numerical Analysis, 55, pp. 112–141 (2022) link
  7. N. Bootland, V. Dolean, P. Jolivet, and P.-H. Tournier, A comparison of coarse spaces for Helmholtz problems in the high frequency regime, Computers & Mathematics with Applications, 98, pp. 239–253 (2021) link
  8. N. Bootland and V. Dolean, On the Dirichlet-to-Neumann coarse space for solving the Helmholtz problem using domain decomposition, In: F.J. Vermolen and C. Vuik (Eds.) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, Vol. 139. Springer, Cham, pp. 175–184 (2021) link
  9. N. Bootland and A. Wathen, Multipreconditioning with application to two-phase incompressible Navier–Stokes flow, In: F.J. Vermolen and C. Vuik (Eds.) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, Vol. 139. Springer, Cham, pp. 165–173 (2021) link
  10. C.Z.W. Hassell Sweatman et al., Challenge from Transpower: Determining the effect of the aggregated behaviour of solar photovoltaic power generation and battery energy storage systems on grid exit point load in order to maintain an accurate load forecast, ANZIAM Journal, 60, pp. M1–M40 (2020) link
  11. H. Montanelli and N. Bootland, Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators, Mathematics and Computers in Simulation, 178, pp. 307–327 (2020) link
  12. N. Bootland, A. Bentley, C. Kees, and A. Wathen, Preconditioners for two-phase incompressible Navier–Stokes flow, SIAM Journal on Scientific Computing, 41(4), pp. B843–B869 (2019) link

Technical reports:

  1. N. Bootland, V. Dolean, F. Nataf, and P.-H. Tournier, Two-level DDM preconditioners for positive Maxwell equations, available on arXiv, arXiv:2012.02388 (2020) link
  2. A. Bentley, N. Bootland, A. Wathen, and C. Kees, Implementation details of the level set two-phase Navier–Stokes equations in Proteus, Tech. Report TR2017-10, Department of Mathematical Sciences, Clemson University (2017) link
  3. H. Batarfi, N. Bootland, I.I. San Juan, C. Please, M. Raffaelli, K. Stoyanova-Chokova, and A. Toshev, Modelling socio-historical dynamics, ESGI129, Mathematics in Industry Study Group Report (2017)
  4. N. Bootland et al., Automatic optimised design of umbilicals, ESGI116, Mathematics in Industry Study Group Report (2016) link
  5. D. Badziahin et al., Segmentation and scene content in moving images, ESGI107, Mathematics in Industry Study Group Report (2015) link
  6. N. Bootland, Blind source separation, InFoMM CDT Mini-Project Technical Report (and accompanying Lay Report), University of Oxford (2015) link
  7. N. Bootland, Block preconditioning for incompressible two-phase flow, InFoMM CDT Mini-Project Technical Report (and accompanying Lay Report), University of Oxford (2015) link

Theses:

  1. N. Bootland, Scalable two-phase flow solvers, Doctoral thesis, University of Oxford (2017) link
  2. N. Bootland, Exponential integrators for stiff PDEs, Master’s thesis, University of Oxford (2014)

  • Maple, MATLAB and FreeFem code used in the paper Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices [7] can be found here
  • The algorithms studied in the paper A comparison of coarse spaces for Helmholtz problems in the high frequency regime [6] are available in HPDDM and can be used in PETSc through the PCHPDDM preconditioner; see this paper
  • Chebfun code used in the paper Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators [2] is detailed here
  • MATLAB code that modifies the IFISS software package and is used in the paper Preconditioners for two-phase incompressible Navier–Stokes flow [1] can be found here
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