Niall Bootland

Computational Mathematician

Numerical Linear Algebra

Niall Bootland is a member of the Numerical Linear Algebra group within the Computational Mathematics theme 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
  • Solvers for wave propagation problems
  • Krylov methods

ORCiD: 0000-0002-3207-5395

Preprints:

  • N. Bootland and T. Rees, Multipreconditioning with directional sweeping methods for high-frequency Helmholtz problems, submitted (2024)
  • N. Bootland, V. Dolean, F. Nataf, and P.-H. Tournier, A robust and adaptive GenEO-type domain decomposition preconditioner for H(curl) problems in general non-convex three-dimensional geometries, available on arXiv, arXiv:2311.18783 (2023) link

Refereed articles:

  1. 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, In: Z. Dostál et al. (Eds.) Domain Decomposition Methods in Science and Engineering XXVII. Lecture Notes in Computational Science and Engineering, Vol. 149. Springer, Cham, pp. 445–453 (2024) link / pdf
  2. 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, 43(4), pp. 1899-1936 (2023) link / preprint
  3. 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 (open access)
  4. 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. 127–135 (2022) link / pdf
  5. 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. 117–125 (2022) link / pdf
  6. 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. 17–28 (2022) link / pdf
  7. 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 (open access)
  8. 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 / pdf
  9. 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 / preprint
  10. 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 / preprint
  11. 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 (open access)
  12. 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 / preprint
  13. 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 / preprint

Refereed technical reports:

  1. N. Bootland, T. Rees, and S. Thorne, A review of solution continuation techniques: methods and software, ExCALIBUR-NEPTUNE Report 2068625-TN-07 (2023) link
  2. H. Al Daas, N. Bootland, T. Rees, and S. Thorne, Time stepping techniques and preconditioning for hyperbolic and anisotropic elliptic problems: numerical results, ExCALIBUR-NEPTUNE Report 2068625-TN-04 (2023) link
  3. H. Al Daas, N. Bootland, T. Rees, and S. Thorne, A review of time stepping techniques and preconditioning for hyperbolic and anisotropic elliptic problems, ExCALIBUR-NEPTUNE Report 2068625-TN-03 (2023) 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 (2018) 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

I am not currently teaching any courses but my past experience is outlined below.

Outside of work, I currently teach the beginners' class at Oxford University Scottish Dance Society (OUSDS).

Department of Mathematics and Statistics, University of Strathclyde (2019–2022)
Class Tutor

  • MM111: Mathematics 1b
  • MM112: Mathematics 2b
  • MM205: Introduction To Newtonian Mechanics
  • MM406: Finite Element Methods For Boundary Value Problems And Approximation

Mathematical Institute, University of Oxford (2014–2018)
Teaching Assistant, Tutor, and Instructor

InFoMM CDT (DPhil) Course Instructor:

  •  Modelling, Analysis and Computation of Continuous Real-World Problems (MT 2016)

Tutor for visiting student tutorials:

  • Numerical Analysis (TT 2018 at Mansfield College)

Tutor for college tutorials:

  • Numerical Analysis (HT 2018 at Lincoln, Mansfield and St Hilda’s)

Consultation Sessions for undergraduate students:

  • Numerical Linear Algebra (TT 2017)

Class Tutor for undergraduate and MSc students:

  • Numerical Linear Algebra (MT 2016)

Teaching Assistant for undergraduate students:

  • Finite Element Methods for PDEs (HT 2016)
  • Nonlinear Systems (HT 2015)

Teaching Assistant for MSc students:

  • Numerical Linear Algebra (MT 2015)
  • Techniques of Applied Mathematics (MT 2014)
  • Supplementary Applied Mathematics (MT 2014)