Dr. Alex Bihlo

Department of Mathematics and Statistics

Memorial University of Newfoundland

Room HH-2008

St. John’s, NL, Canada A1C 5S7

1 709 864 8078

abihlo (at) mun [dot) ca

Research

My research interests mainly lie in the study of geometric properties of differential equations (in particular, symmetries and conservation laws) and the constructing of efficient numerical schemes preserving these properties. Concerning applications, I am primarily interested in the models of (geophysical) fluid mechanics although I have a growing interest in geophysical models as well.

Below you will find a list of my papers and some recent preprints. They are ordered by 'research field' although several papers would easily fit into more than one category.

Group analysis of differential equations

  • S. Opanasenko, A. Bihlo, R.O. Popovych and A. Sergyeyev, 2017. Extended symmetry analysis of isothermal no-slip drift flux model, arXiv:1705.09277.
  • R.O. Popovych and A. Bihlo, 2017. Inverse problem on conservation laws, arXiv:1705.03547.
  • A. Bihlo and R.O. Popovych, 2017. Group classification of linear evolution equations. J. Math. Anal. Appl. 448, 982-1005, arXiv:1605.09251.
  • A. Bihlo, E.M. Dos Santos Cardoso-Bihlo and R.O. Popovych, 2015. Algebraic method for finding equivalence groups. J. Phys.: Conf. Ser. 621, 012001 (17 pp), arXiv:1503.06487.
  • S. Szatmari and A. Bihlo, 2014. Symmetry analysis of a system of modified shallow-water equations. Commun. Nonlinear Sci. Numer. Simul. 19 (3), 530-537, arXiv:1212.5823.
  • A. Bihlo and G. Bluman, 2013. Conservative parameterization schemes. J. Math. Phys. 54, 083101 (24 pp), arXiv:1209.4279.
  • A. Bihlo, E.M. Dos Santos Cardoso-Bihlo and R.O. Popovych, 2012. Complete group classification of a class of nonlinear wave equations. J. Math. Phys. 53 (12), 123515, 32 pp, arXiv:1106.4801.
  • R.O. Popovych and A. Bihlo, 2012. Symmetry preserving parameterization schemes. J. Math. Phys. 53 (7), 073102, 36 pp, arXiv:1010.3010.
  • A. Bihlo and R.O. Popovych, 2012. Lie reduction and exact solutions of the vorticity equation on the rotating sphere. Phys. Lett. A 376 (14), 1179–1184, arXiv:1112.3019.
  • A. Bihlo and R.O. Popovych, 2011. Lie symmetry analysis and exact solutions of the quasi-geostrophic two-layer problem. J. Math. Phys. 52 (3), 033103, 24 pp, arXiv:1010.1542.
  • E.M. Dos Santos Cardoso-Bihlo, A. Bihlo and R.O. Popovych, 2011. Enhanced preliminary group classification of a class of generalized diffusion equations. Commun. Nonlinear Sci. Numer. Simul. 16 (9), 3622–3638, arXiv:1012.0297.
  • A. Bihlo and R.O. Popovych, 2011. Point symmetry group of the barotropic vorticity equation. In Proceedings of the 5th workshop “Group Analysis of Differential Equations & Integrable Systems”, 15–27, arXiv:1009.1523.
  • A. Bihlo and R.O. Popovych, 2009. Lie symmetries and exact solutions of the barotropic vorticity equation. J. Math. Phys. 50 (12), 123102, 12 pp, arXiv:0902.4099
  • A. Bihlo and R.O. Popovych, 2009. Symmetry analysis of barotropic potential vorticity equation. Commun. Theor. Phys. 52 (4), 697–700, arXiv:0811.3008.
  • A. Bihlo, 2009. Symmetries in atmospheric sciences. In Proceedings of the 4th workshop “Group Analysis of Differential Equations & Integrable Systems”, 6–12, arXiv:0902.4112.

Geometric numerical integration

  • R. Brecht, W. Bauer, A. Bihlo, F. Gay-Balmaz, S. MacLachlan, 2018. Variational integrator for the rotating shallow-water equations on the sphere, arXiv:1808.10507.
  • A. Bihlo and F. Valiquette, 2018. Symmetry-preserving finite element schemes: An introductory investigation, arXiv:1803.10058.
  • A. Wan, A. Bihlo and J.-C. Nave, 2017. Conservative methods for dynamical systems, SIAM J. Numer. Anal. 55 (5), 2255–2285, arXiv:1612.02417.
  • A. Bihlo and F. Valiquette, 2017. Symmetry-preserving numerical schemes, in Symmetries and Integrability of Difference Equations, 261–324, Springer, arXiv:1608.02557.
  • A. Wan, A. Bihlo and J.-C. Nave, 2016. The multiplier method to construct conservative finite difference schemes for ordinary and partial differential equations. SIAM J. Numer. Anal. 54 (1), 86–119, arXiv:1411.7720.
  • A. Bihlo, X. Coiteux-Roy and P. Winternitz, 2015. The Korteweg-de Vries equation and its symmetry-preserving discretization. J. Phys. A 48, 055201 (25 pp), arXiv:1409.4340.
  • A. Bihlo and J.-C. Nave, 2014. Convecting reference frames and invariant numerical models. J. Comput. Phys. 271, 656–663, arXiv:1301.5955.
  • A. Bihlo and J.-C. Nave, 2013. Invariant discretization schemes using evolution-projection techniques. SIGMA 9, 052, 23 pp, arXiv:1209.5028.
  • A. Bihlo, 2013. Invariant meshless discretization schemes. J. Phys. A: Math. Theor. 46 (6), 062001 (12 pp), arXiv:1210.2762.
  • A. Bihlo and R.O. Popovych, 2012. Invariant discretization schemes for the shallow-water equations. SIAM J. Sci. Comput. 34 (6), B810-B839, arXiv:1201.0498.

Geophysical fluid dynamics

  • B. Khouider, A. Bihlo, 2018. A new stochastic model for the regimes of stratocumulus phase transition: open cells, closed cells, and convective rolls, J. Geophys. Res. Atmos. (submitted).
  • R. Brecht, A. Bihlo, S. MacLachlan and J. Behrens, 2018. A well-balanced meshless tsunami propagation and inundation model, Adv. Water Resour. 115, 273-285, arXiv:1705.09831.
  • A. Bihlo and S. MacLachlan, 2018. Well-balanced mesh-based and meshless schemes for the shallow-water equations, Accepted in BIT Numer. Math., arXiv:1702.07749.
  • A. Bihlo., E.M. Dos Santos Cardoso-Bihlo and R.O. Popovych, 2015. Invariant and conservative parameterization schemes, in volume 2 of Parameterization of Atmospheric Convection, (R. S. Plant and J. I. Yano, Eds.), Imperial College Press, 483-524.
  • A. Bihlo, E.M. Dos Santos Cardoso-Bihlo and R.O. Popovych, 2014. Invariant parameterization and turbulence modeling on the beta-plane. Phys. D 269, 48-62, arXiv:1112.1917.
  • A. Bihlo and J. Staufer, 2011. Minimal atmospheric finite-mode models preserving symmetry and generalized Hamiltonian structures, Phys. D 240 (7), 599–606, arXiv:0909.1957.
  • A. Bihlo and R.O. Popovych, 2009. Symmetry justification of Lorenz’ maximum simplification. Nonlin. Dyn. 61 (1), 101–107, arXiv:0805.4061.
  • A. Bihlo, 2008. Rayleigh-Bénard Convection as a Nambu–metriplectic problem. J. Phys. A 41 (29), 292001 (6 pp), arXiv:0803.4458.

Domain decomposition

  • F. Donzelli, A. Bihlo, M. Kischinhevsky, C.G. Farquharson, 2017. Massively parallel stochastic solution of the geophysical gravity problem, arXiv:1709.07469.
  • A. Bihlo, C.G. Farquharson, R.D. Haynes, J.C. Loredo-Osti, 2017. Stochastic domain decomposition for the solution of the two-dimensional magnetotelluric problem. Computat. Geosci. 21 (1), 117-129, arXiv:1603.09311.
  • A. Bihlo, R.D. Haynes and E.J. Walsh, 2015. Stochastic domain decomposition for time dependent adaptive mesh generation. J. Math. Study 48 (2), 106-124, arXiv:1504.00084.
  • A. Bihlo and R.D. Haynes, 2014. Parallel stochastic methods for PDE based grid generation. Comput. Math. Appl. 68 (8), 804-820, arxiv:1310.3435.
  • A. Bihlo and R.D. Haynes, 2014. A stochastic domain decomposition method for time dependent mesh generation. Accepted in LNCSE., arxiv:1402.0266.

Theses

  • A. Bihlo, 2018. Geometric modeling in geophysical fluid dynamics. Habilitation thesis, University of Vienna (in preparation).
  • A. Bihlo, 2010. Symmetry methods in the atmospheric sciences. PhD thesis, University of Vienna, 165 pp. (Supervisors: Professor Dr. Michael Hantel, Professor Dr. Roman O. Popovych) (download)
  • A. Bihlo, 2007. Solving the vorticity equation with Lie groups. Master thesis, In Wiener Meteorologische Schriften, Vol. 6, facultas.wuv, Wien. (Supervisor: Professor Dr. Michael Hantel)

Talks

If you are interested in getting the slides of any of the talks listed below, just send me an email!

Invited talks

  • Geometry-preserving numerical modeling in geophysical fluid dynamics (CAIMS 2018, Toronto, June 2018)
  • A meshless tsunami propagation and inundation model (CAIMS 2018, Toronto, June 2018)
  • Symmetry-preserving discretization schemes (ASIDE, Montreal, June 2016)
  • Conservative discretization schemes (University of Vienna, May 2016)
  • Novel methods for geometric numerical integration (University of Saskatchewan, May 2015)
  • Geometry-preserving numerical modeling (Memorial University of Newfoundland, Oct 2014)
  • Conservative parameterization schemes (University of Vienna, Feb 2013)
  • Invariant discretization schemes (University of Vienna, Feb 2013)
  • Geometry-preserving modeling in meteorology (University of Reading, Feb 2013)
  • Invariant subgrid-scale closure schemes for turbulence modeling (2012 CMS Winter Meeting, Montréal, Dec 2012)
  • Invariant discretization schemes (2012 CMS Winter Meeting, Montréal, Dec 2012)
  • Invariant parameterization schemes and turbulence modeling (University of British Columbia, June 2012)
  • Invariant turbulence modeling, (Center for Turbulence Research, Stanford University, June 2012)
  • A tutorial on Hamiltonian mechanics (COST working group meeting, University of Munich, May 2011)
  • A method for constructing exact solutions of partial differential equations (University of Lisbon, Sept 2010)
  • Symmetry methods in dynamics meteorology (University of Frankfurt, Jan 2009)
  • Symmetrien und einige Anwendungen in der dynamischen Meteorologie (University of Bonn, July 2008)

Other presentations

  • Exactly conservative discretization schemes for dynamical systems (Memorial University of Newfoundland, April 2018)
  • Invariant discretization beyond finite differences (Memorial University of Newfoundland, March 2018)
  • A well-balanced meshless tsunami propagation and inundation model (University of British Columbia, Jan 2018)
  • Well-balanced mimetic mesh-based and meshless schemes for the shallow-water equations with bottom topography (2016 CMS Winter Meeting, Niagara Falls, Dec 2016)
  • Recent advancements in geometric numerical integration (University of British Columbia, Mar 2015)
  • Stochastic domain decomposition for parallel grid generation (University of British Columbia, Mar 2015)
  • Invariant and conservative numerical schemes: Theory and applications (University of British Columbia, Feb 2015)
  • Invariant discretization schemes (XXIInd International Conference on Integrable Systems and Quantum symmetries, Prague, Czech Republic, June 2014)
  • Grid generation using stochastic domain decomposition (University of Vienna, June 2014)
  • Parallel stochastic domain decomposition for PDE based grid adaptation (McGill University, Nov 2013)
  • Invariant discretization schemes (CAIMS 2013, Quebec City, Canada, June 2013)
  • Complete group classification of a class of nonlinear wave equations (2012 CMS Winter Meeting, Montréal, Dec 2012)
  • Invariant discretization of partial differential equations (McGill University, Nov 2012)
  • Invariant turbulence modeling (Conference "Symmetries of Differential Equations: Frames, Invariants and Applications", University of Minnesota, May 2012)
  • Invariant parameterization schemes (Conference "Symmetries of Differential Equations: Frames, Invariants and Applications", University of Minnesota, May 2012)
  • Invariant numerical schemes for the shallow-water equations (Centre de recherches mathématiques, Sept 2011)
  • Symmetry methods in the atmospheric sciences (University of Vienna, Dec 2010)
  • Symmetry preserving parameterization schemes (Fifth International Workshop on Group Analysis of Differential Equations and Integrable systems, Protaras, Cyprus, June 2010)
  • Symmetry preserving discretization schemes (EGU General Assembly, Vienna, May 2010)
  • Minimal atmospheric finite-mode models preserving symmetry and generalized Hamiltonian structures (University of Vienna, Dec 2009)
  • Der Nambu Kalkül in der dynamischen Meteorologie (3rd Austrian Meteorology Day, Graz, Nov 2009)
  • Symmetrien, Erhaltungssätze und Low-order Modelle in der dynamischen Meteorologie (University of Vienna, May 2009)
  • Symmetry methods in dynamics meteorology (EGU General Assembly, Vienna, April 2009)
  • Symmetry methods in dynamics meteorology (ACA 2008 conference, Hagenberg, Austria, July 2008)
  • Application of finite and infinite dimensional Nambu mechanics in dynamic meteorology (EGU General Assembly, Vienna, July 2008)
  • Nambu Mechanik. Vom Kreisel zum Chaos (FU Berlin, Dec 2007)
  • Can Lie groups improve weather forecasts? (University of Vienna, Dec 2006)

Conferences

  • CAIMS 2018, Annual Meeting of the Canadian Applied and Industrial Mathematics Society, Toronto, ON, Canada (4–7 June 2018)
  • CAIMS 2017, Annual Meeting of the Canadian Applied and Industrial Mathematics Society, Halifax, NS, Canada (17–21 July 2017)
  • Connections in Geometric Numerical Integration and Structure-Preserving Discretization, Banff International Research Station, Banff, AB, Canada (11–16 June 2017)
  • SIDE 12 - Symmetries and Integrability of Difference Equations, Sainte-Adèle, QC, Canada (3–9 July 2016)
  • ASIDE - Abecedarian of SIDE, Montréal, QC, Canada (27 June–1 July 2016)
  • Recent Developments in Adaptive Methods for PDEs, Collaborative Workshop and Short Course, St. John's, NL, Canada (17–22 Aug 2014)
  • XXIInd International Conference on Integrable Systems and Quantum symmetries (ISQS-22), Prague, Czech Republic (26–27 June 2014)
  • CAIMS 2013, Annual Meeting of the Canadian Applied and Industrial Mathematics Society, Quebec City, QC, Canada (16–20 June 2013)
  • Canadian Mathematical Society Winter Meeting, Montréal, QC, Canada (7 Dec–10 Dec 2012)
  • Symmetries of Differential Equations: Frames, Invariants and Applications, Minneapolis, USA (17–20 May 2012)
  • Workshop Balance, Boundaries and Mixing in the Climate Problem, Université de Montréal, Montréal, QC, Canada (28–30 Sept 2011)
  • Workshop of COST-Action ES0905 Basic concepts for convection parameterization in weather forecast and climate model, Cambridge, UK (22–25 March 2011)
  • Fifth International Workshop Group Analysis of Differential Equations and Integrable Systems, Protaras, Cyprus (6–10 June 2010)
  • European Geosciences Union – General Assembly, Vienna (5 May 2010)
  • Third Austrian Meteorology Day, Graz (6 Nov 2009)
  • Kickoff-Workshop Nambu Calculus, Vienna (15–19 June 2009)
  • European Geosciences Union – General Assembly, Vienna (23 April 2009)
  • Application of Computer Algebra (ACA) – RISC Summer 2008, Hagenberg, Austria (27–28 July 2008)
  • European Geosciences Union – General Assembly, Vienna (17 April 2008)

Short-term scientific visits

  • Department of Mathematics, University of British Columbia, Vancouver, BC, Canada (22 Jan–26 Jan 2018)
  • Department of Mathematics and Statistics, McGill University, Montréal, QC, Canada (15 Aug–19 Aug 2017)
  • Department of Mathematics, Imperial College London, London, UK (5 July–8 July 2017)
  • Faculty of Mathematics, University of Vienna, Vienna, Austria (10 April–10 May 2017)
  • Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada (16 Aug–26 Aug 2016)
  • Institute of Meteorology and Geophysics, University of Vienna, Vienna, Austria (10 May–4 June 2016)
  • Faculty of Mathematics, University of Vienna, Vienna, Austria (10 May–4 June 2016)
  • Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK, Canada (3–8 May 2015)
  • Centre de recherches mathématiques, Université de Montréal, Montréal, QC, Canada (19–26 July 2014)
  • Department of Mathematics, University of British Columbia, Vancouver, BC, Canada (3–31 Aug 2013)
  • Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, Canada (24 May–14 June 2013)
  • Department of Mathematics, University of British Columbia, Vancouver, BC, Canada (21 May–14 June 2012)
  • Centro de Matematica e Aplicacoes, Instituto Superior Tecnico, Lisbon, Portugal (Sep 2010)
  • Department of Meteorology, FU Berlin, Berlin, Germany (10–14 Dec 2007)

Teaching

Memorial University

  • CMSC 6920 Applied Scientific Programming (Winter 2017, Winter 2018)
  • MATH 3132 Numerical analysis I (Fall 2016, Fall 2018)
  • MATH 3202 Vector calculus (Fall 2017)
  • MATH 6201 Numerical methods for time-dependent differential equations (Winter 2016, Winter 2017)
  • MATH 6210 Numerical methods for differential equations (Fall 2018)
  • MATH 6261 Geometric numerical integration (Fall 2017)

McGill University

  • MATH 262 Intermediate calculus (Fall 2013)

University of Vienna

  • Geophysical fluid dynamics (Summer 2008, Summer 2016)
  • Lectures on selected topics of dynamical meteorology (Summer 2011)
  • Fluid dynamics (Summer 2009)
  • Numerical and mathematical methods in meteorology (Winter 2007, Winter 2009)

The Team

I am part of Memorial University's Centre for Numerical Analysis and Scientific Computing. We are always looking for MSc and PhD students to work on projects related to geometric numerical integration, adaptive methods for PDEs, multigrid methods and high-performance computing. If you have an interest in any of these fields, please send me an email.

Postdocs

  • Fabrizio Donzelli (2016-present)

PhD students

  • Rüdiger Brecht (2017-present, with S. MacLachlan)
  • Stanislav Opanasenko (2017-present)

MSc students

  • Lada Atamanchuk-Anhel (2017-present)
  • Nataliia Poltavets (2017-present)
  • Evan Kielley (2017-present, with J. Munroe and S. MacLachlan)
  • Oleksandr Abramov (2016-present, with R. Haynes)
  • Stanislav Opanasenko (2016-2017): Extended symmetry analysis of isothermal no-slip drift flux model
  • Rüdiger Brecht (2016-2017, with J. Behrens, University of Hamburg): Solution of the shallow-water equations with wetting and drying boundary conditions through RBF discretisation

Undergraduate students

  • Ben Morrison (2017, with S. MacLachlan): Parallelization of a meshless tsunami propagation model
  • Leah Genge (2016-2017, with R. Haynes): Parallel stochastic domain decomposition

A few current and past collaborators

About Me

I obtained my Magister der Naturwissenschaften (MSc equivalent) and PhD in meteorology from the University of Vienna, but I consider myself both an applied mathematician and a meteorologist (I actually learned how to do a weather forecast!). My research is frequently inspired by problems arising in geophysical fluid mechanics. I always try to stay grounded in applications but do not mind taking detours in more theoretical realms if necessary. Despite planning to stay in Austria, thanks to an unsuccessful project application right after I finished my PhD I had to come up with a new plan which led me to become a postdoc at the CRM in Montreal. Gradually falling in love with Canada, I moved around the whole country, with stops at McGill University, Memorial University and the University of British Columbia. Back at Memorial, I started a faculty postition and became a Canada Research Chair in November 2015.

Education

  • PhD (meteorology), University of Vienna (2010)
  • Magister der Naturwissenschaften (meteorology), University of Vienna (2007)

Experience

  • Tier II Canada Research Chair in Numerical Analysis and Scientific Computing, Department of Mathematics and Statistics, Memorial University of Newfoundland (Nov 2015 – present)
  • Assistant professor, Department of Mathematics and Statistics, Memorial University of Newfoundland (Nov 2015 – present)
  • Visiting professor, Institute of Meteorology and Geophysics, University of Vienna (May 2016)
  • Visiting postdoctoral fellow, Department of Mathematics, University of British Columbia (Jan 2015 – Oct 2015)
  • Postdoctoral fellow, Department of Mathematics and Statistics, Memorial University of Newfoundland (Jan 2014 – Oct 2015)
  • Postdoctoral fellow, Department of Mathematics and Statistics, McGill University (Aug 2013 – Dec 2013)
  • Visiting postdoctoral fellow, Department of Mathematics and Statistics, McGill University (June 2012 – July 2013)
  • Postdoctoral fellow, Centre de recherches mathématiques, Université de Montréal (Aug 2011 – July 2013)
  • Postdoctoral fellow, Faculty of Mathematics, University of Vienna (Jan 2011 – July 2011)
  • PhD student, Faculty of Mathematics, University of Vienna (Oct 2008 – Dec 2010)
  • Research assistant, Department of Meteorology and Geophysics, University of Vienna (Oct 2007 – Sept 2008)

Grants

  • NSERC Discovery Grant (2016-2021)
  • IgniteR&D project of the Research & Development Corporation of Newfoundland and Labrador (RDC) (2016-2018)
  • Canada Research Chair in Numerical Analysis and Scientific Computing (2015-2020)
  • Postdoctoral fellowship of the Pacific Institute for the Mathematical Sciences (2014-2016)
  • APART Fellowship of the Austrian Academy of Sciences (2014-2018)
  • Schrödinger Fellowship of the Austrian Science Fund (2011-2014)
  • DOC-Fellowship of the Austrian Academy of Sciences (2009-2010)

Awards

  • CAIMS-PIMS Early Career Award 2018
  • Würdigungspreis des Bundesministeriums für Wissenschaft und Forschung (Award of Excellence of the Austrian Ministry for Science and Research) 2011
  • Awarded the doctor’s degree Sub Auspiciis Praesidentis rei publicae (highest distinction in Austria) in 2011
  • Merit scholarships of the University of Vienna in 2005, 2006, 2007