Andrea Moiola unipv Home

Ricercatore (RTDB)
Dipartimento di Matematica "F. Casorati"
Università degli studi di Pavia
Via Ferrata 5, 27100 Pavia, Italy

Phone: +39 0382 985656
Room: E15
WoS ResearcherID: K-6182-2015
Scopus Author ID: 37049069900
Profilo Iris
Google Scholar profile
Curriculum Vitae (pdf)

Teaching Research interests Papers Preprints Collaborators Slides Links Conferences & events

Since July 2017 I am "ricercatore" (equivalent to lecturer/assistant professor) at the Department of Mathematics of the University of Pavia.

From March 2013 to June 2017 I was a "senior research fellow" at the Department of Mathematics and Statistics of the University of Reading, UK (permanent post).

From March 2012 to February 2013 I held a "Fellowship for prospective researchers" on "Computational wave propagation", funded by the Swiss National Science Foundation, based in Reading and supervised by Simon N. Chandler-Wilde.

From 2008 to 2011 I was a PhD student at the "Seminar for Applied Mathematics" (SAM) - ETH Zürich, under the supervision of Ralf Hiptmair and Ilaria Perugia.

Recent teaching:

Primavera 2019: Metodi Numerici Avanzati per le Equazioni alle Derivate Parziali.
Autunno 2018: Modellistica Numerica.
Autunno 2017: Modellistica Numerica.
Spring 2016&2017: Numerical Methods for Financial Engineering (Henley Business School/ICMA centre).
Autumn 2013-2016: Vector Calculus (University of Reading).

Research interests:

Computational electromagnetics and wave propagation

Numerical analysis, approximation of PDEs

Finite element methods, discontinuous Galerkin, non-polynomial and Trefftz methods

Approximation theory

Wavenumber-explicit analysis of time-harmonic boundary value problems, scattering theory

Sobolev spaces on rough (non-Lipschitz) domains, wave scattering by fractal screens

Boundary and volume integral equations, boundary element methods

Papers in refereed journals and book chapters:

  1. K. McCusker, C.D. Westbrook, A. Moiola
    Analysis of the internal electric fields of pristine ice crystals and aggregate snowflakes, and their effect on scattering,
    Journal of Quantitative Spectroscopy and Radiative Transfer (JQSRT), 230, June 2019, pp. 155-171, (link to journal), DOI: 10.1016/j.jqsrt.2019.04.019.

  2. A. Moiola, E.A. Spence,
    Acoustic transmission problems: wavenumber-explicit bounds and resonance-free regions,
    Math. Models Methods Appl. Sci. (M3AS), 29(02), 2019, pp. 317-354 (link to journal, preprint: arXiv:1702.00745), DOI: 10.1142/S0218202519500106.

  3. G.C. Diwan, A. Moiola, E.A. Spence,
    Can coercive formulations lead to fast and accurate solution of the Helmholtz equation?,
    J. Comput. Appl. Math., 352, 2019, pp. 110-131 (link to journal, preprint: arXiv:1806.05934), DOI: 10.1016/

  4. A. Moiola, I. Perugia,
    A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation,
    Numer. Math., 138(2) 2018, pp. 389-435 (link to journal, read online at this link, preprint: arXiv:1610.08002), DOI:10.1007/s00211-017-0910-x.

  5. S.N. Chandler-Wilde, D.P. Hewett, A. Moiola,
    Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens,
    Integr. Equat. Oper. Th., 87(2) 2017, pp. 179-224 (link to journal, read online at this link, preprint: arXiv:1607.01994), DOI:10.1007/s00020-017-2342-5.

  6. D.P. Hewett, A. Moiola,
    A note on properties of the restriction operator on Sobolev spaces,
    Journal of Applied Analysis, 23(1) 2017, pp. 1-8 (link to journal, preprint: arXiv:1607.01741), DOI:10.1515/jaa-2017-0001.

  7. D.P. Hewett, A. Moiola,
    On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space,
    Analysis and Applications, 15(5) 2017, pp. 731-770 (link to journal, preprint: arXiv:1507.02698), DOI:10.1142/S021953051650024X.

  8. R. Hiptmair, A. Moiola, I. Perugia,
    A survey of Trefftz methods for the Helmholtz equation.
    In: Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, Springer Lect. Notes Comput. Sci. Eng.,
    edited by G.R. Barrenechea, F. Brezzi, A. Cangiani, E.H. Georgoulis, 2016, pp. 237-278, (link to chapter, preprint: arXiv:1506.04521), DOI:10.1007/978-3-319-41640-3_8.

  9. F. Kretzschmar, A. Moiola, I. Perugia, S.M. Schnepp,
    A priori error analysis of space-time Trefftz discontinuous Galerkin methods for wave problems,
    IMA J. Numer. Anal., 36(4) 2016, pp. 1599-1635 (link to journal, preprint: arXiv:1501.05253), DOI: 10.1093/imanum/drv064.

  10. R. Hiptmair, A. Moiola, I. Perugia,
    Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version,
    Found. Comput. Math., 16(3) 2016, pp. 637-675 (link to journal, preprint: SAM Report 2013-31), DOI: 10.1007/s10208-015-9260-1.

  11. S.N. Chandler-Wilde, D.P. Hewett, A. Moiola,
    Interpolation of Hilbert and Sobolev spaces: Quantitative estimates and counterexamples,
    Mathematika, 61(2) 2015, pp. 414-443 (link to journal, preprint: arXiv:1404.3599), DOI:10.1112/S0025579314000278.

  12. A. Moiola, E.A. Spence,
    Is the Helmholtz equation really sign-indefinite?,
    Siam Review, 56(2) 2014, pp. 274-312 (paper, link to journal, link to preprint), DOI:10.1137/120901301.

  13. C.J. Howarth, P.N. Childs, A. Moiola,
    Implementation of an interior point source in the ultra weak variational formulation through source extraction,
    J. Comput. Appl. Math., 27 2014, pp. 295-306 (link to journal, link to preprint), DOI:10.1016/

  14. R. Hiptmair, A. Moiola, I. Perugia, Ch. Schwab,
    Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM,
    Math. Model. Numer. Anal. (M2AN), 48 (3) 2014, pp. 727-752 (link to journal, link to preprint), DOI:10.1051/m2an/2013137.

  15. R. Hiptmair, A. Moiola, I. Perugia,
    Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes,
    Appl. Numer. Math., 79 2014, pp. 79-91 (link to journal, link to preprint), DOI:10.1016/j.apnum.2012.12.004.

  16. A. Moiola,
    Plane wave approximation in linear elasticity,
    Appl. Anal., 92(6) 2013, pp. 1299-1307 (link to journal, link to preprint), DOI:10.1080/00036811.2012.671300.

  17. R. Hiptmair, A. Moiola, I. Perugia,
    Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations,
    Math. Comput., 82(281) 2013, pp. 247-268 (link to journal, link to preprint), DOI:10.1090/S0025-5718-2012-02627-5.

  18. R. Hiptmair, A. Moiola, I. Perugia,
    Stability results for the time-harmonic Maxwell equations with impedance boundary conditions,
    Math. Models Methods Appl. Sci. (M3AS), 21(11) 2011, pp. 2263-2287, (link to journal, link to preprint), DOI: 10.1142/S021820251100574X.

  19. A. Moiola, R. Hiptmair, I. Perugia,
    Plane wave approximation of homogeneous Helmholtz solutions,
    Z. Angew. Math. Phys., 62(5) 2011, pp. 809-837 (link to journal, link to preprint), DOI: 10.1007/s00033-011-0147-y.

  20. A. Moiola, R. Hiptmair, I. Perugia,
    Vekua theory for the Helmholtz operator,
    Z. Angew. Math. Phys., 62(5) 2011, pp. 779-807 (link to journal, link to preprint), DOI: 10.1007/s00033-011-0142-3.

  21. R. Hiptmair, A. Moiola, I. Perugia,
    Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version,
    Siam J. Numer. Anal., 49(1) 2011, pp. 264-284 (paper, link to journal, link to preprint), DOI: 10.1137/090761057.

(The accepted/published versions of some of the papers are available on the CentAUR repository at the University of Reading.)

Reports, preprints, thesis:

  1. [NEW!]   A. Caetano, D.P. Hewett, A. Moiola
    Density results for Sobolev, Besov and Triebel-Lizorkin spaces on rough sets,
    arXiv:1904.05420, 2019 (submitted).

  2. A. Gibbs, S.N. Chandler-Wilde, S. Langdon, A. Moiola
    A high frequency boundary element method for scattering by a class of multiple obstacles,
    arXiv:1903.04449, 2019 (submitted).

  3. A. Gibbs, S. Langdon, A. Moiola
    Numerically stable computation of embedding formulae for scattering by polygons,
    arXiv:1805.08988, 2018 (submitted).

  4. A. Moiola,
    Trefftz-discontinuous Galerkin methods for time-harmonic wave problems,
    PhD dissertation, Seminar for Applied Mathematics, ETH Zürich, 2011 (link to pdf, also available on the ETH e-collection), DOI: 10.3929/ethz-a-006698757.

People I work with:

A. Caetano, Universidade de Aveiro
S.N. Chandler-Wilde, University of Reading
P.N. Childs, Roxar
G.C. Diwan, UCL
A. Gibbs, KU Leuven
D.P. Hewett, UCL
R. Hiptmair, ETH Zürich
C.J. Howarth
F. Kretzschmar
S. Langdon, University of Reading
K. McCusker, Meteorology, University of Reading
I. Perugia, University of Vienna
S.M. Schnepp
Ch. Schwab, ETH Zürich
E.A. Spence, University of Bath
C.D. Westbrook, Meteorology, University of Reading


Explicit bounds for electromagnetic transmission problems, Mafelap, 17-21 June 2019
Acoustic and electromagnetic transmission problems: wavenumber-explicit bounds and resonance-free regions (+gifs), Roma, 14 May 2019
Scattering by fractal screens, WONAPDE, Concepción, 21-25 January 2019
Scattering by fractal screens: functional analysis and computation, Bologna, 20 June 2018
Space-time Trefftz discontinuous Galerkin methods for wave problems, RICAM, Linz, 7-11 November 2016
Sobolev spaces on non-Lipschitz sets with application to BIEs on fractal screens, ETH Zurich, 2 November 2016
Approximation by plane and spherical waves, LMS Durham Symposium, 10 July 2014
Plane wave DG methods: Exponential convergence of the hp-version, Oxford, 15 May 2014
Is the Helmholtz equation really sign-indefinite?, British Computational PDEs Colloquium: New Trends, Edinburgh, 24 January 2014

(gif) (gif) (gif) (gif) (gif) (gif) (gif)
The fields scattered by (pre)fractal sound-soft (Dirichlet) screens hit by acoustic time-harmonic plane waves.
The screens are: a Cantor dust, a Koch snoflake, a square snowflake, a Sierpinski carpet, a Sierpinski triangle, an "atomic" Sierpinski triangle, a Vicsek fractal.


Dipartimento di Matematica, Università di Pavia
Scientific Computing: Numerical Methods and Applications Group, Pavia
UniPv-USI International PhD program in Computational Mathematics and Decision Sciences
Joint PhD Program in Mathematics Pavia - Milano Bicocca - INdAM

Department of Mathematics and Statistics, University of Reading
Numerical Analysis and Computational Modelling Group, Reading
MPE CDT Centre of doctoral training Mathematics of Planet Earth, University of Reading and Imperial College London

Swiss national science foundation
SAM - Seminar for Applied Mathematics, ETH Zürich

I'm member of
SIAM, Society for Industrial and Applied Mathematics
GNCS, Gruppo Nazionale per il Calcolo Scientifico - INdAM

Useful online tools
List of American and British spelling differences
NCLAB, use online Octave, Python and much more
SHERPA/RoMEO, publisher's policies regarding the self-archiving of journal articles and pre/post-prints
Detexify, find LaTeX code for symbols

Conferences, workshops and seminars:

XXI Congresso UMI, Pavia, 2-7 September
Waves 2019, Vienna, 25-30 August
ICIAM, Valencia, 15-19 July
Zurich, 24-28 June
Mafelap 2019, Brunel University, London, 17-21 June
HOFEIM 2019, Pavia, 28-31 May
Roma, 13-16 May
TiciNUM, Pavia, 10 May
Computational mathematics, statistics and machine learning, Pavia, 7-9 May
Informal seminar at IMATI-CNR, Pavia, 12 April
Pontificia Universidad Católica de Chile, Santiago, 4-8 February
WONAPDE 2019, Universidad de Concepción, Chile, 21-25 January
University of Bath, 7-11 January
Seminar at Oldenburg University, 15 November
Carlos Jerez-Hanckes visiting Pavia, 23-25 October
Numerical Analysis of Complex PDE Models in the Sciences, ESI thematic programme, Vienna, 25 June-20 July
Seminar at the University of Bologna, 20 June
Reading, 4-8 June
Zurich, 29 May-1 June
Inverse Problems: Modeling and Simulation, Malta, 21-25 May
Reading, 23-27 April
Dave Hewett visiting Pavia, 16-19 April
Seminar at SBAI, Sapienza, Roma, 21 March
Euan Spence visiting Pavia, 12-16 February
IGA 2017, International Conference on Isogeometric Analysis, Pavia, 11-13 September
IperPV2017, the XVII Italian Meeting on Hyperbolic Equations, Pavia, 6-8 September
Equadiff 2017, Bratislava, 24-28 July
Poems, Polytopal Element Methods in Mathematics and Engineering, Milano, 5-7 July
7th meeting of the Reading-Bath-Cardiff network on generalised solutions for nonlinear PDE, Reading, 13 June
Workshop on Wave propagation in complex domains, UCL, 30 March
Oberwolfach workshop on Space-time Methods for Time-dependent Partial Differential Equations, 12-18 March
Mathematics in the Spirit of Joe Keller, Turing Gateway to Mathematics, Cambridge, 2-3 March
International Conference on Domain Decomposition methods, DD XXIV, Svalbard, 6-10 February
Space-Time Methods for PDEs, RICAM, Linz, 7-11 November
Seminar at SAM, ETH Zurich, 2 November
PDE seminar at Reading, 18 October
Mathematical and Computational Aspects of Maxwell's Equations, Durham, 11-21 July
Modern Topics in Nonlinear PDEs and Geometric Analysis, LMS-CMI Research School, 4-8 July
Seminar at Hamburg University of Technology, 24 June
Mafelap 2016, Brunel University, London, 14-17 June
ReaDG 2016:   Recent advances in discontinuous Galerkin methods, Reading, 13 June
Computational and Numerical Analysis of Transient Problems in Acoustics, Elasticity, and Electromagnetism, Banff International Research Station, 17-22 January
Seminar at Laboratoire Poems, ENSTA-INRIA-CNRS, Palaiseau, France, 18 November
New directions in numerical computation, Oxford, 25-28 August
Waves 2015, minisymposium on "Wave-based discretizations", Karlsruhe, 20-24 July
XXIV CEDYA / XIV CMA, special session on Computational Acoustics, Cadiz, 8-12 June
Seminar at the University of Durham, 29 April
Lions-Magenes days, Pavia, 13-14 April
Seminar at the University of Bath, 20 February
Boundary and finite element methods for high frequency scattering problems, Reading, 15-16 December
ReaDG:   Recent advances in discontinuous Galerkin methods, Reading, 11-12 September
Building Bridges: Connections and Challenges in Modern Approaches to Numerical PDEs, Durham, 8-16 July
3rd International Conference on Neural Field Theory, Reading, 16-18 June
CIME course on Computational Electromagnetism, Cetraro, 9-14 June
Computational mathematics and applications seminar, Oxford, 15 May
Seminar at the University of Vienna, 24 March
Recent Advances in Nonlinear PDEs and Calculus of Variations, Reading, 12-14 February
British Computational PDEs Colloquium: New Trends, ICMS, Edinburgh, 23-24 January
Analysis of Partial Differential Equations, symposium in honour of Professor Vladimir Maz'ya, Liverpool, 16-17 December
Numerical analysis and data assimilation research afternoon, Reading, 30 October
Seminar at the Brain Embodiment Lab, Reading, 25 September
From Spectral Gaps to Particle Filters workshop, Reading, 17-18 September
Data Assimilation and Inverse Problems summer school, Reading, 22-26 July
CNS 2013 Computational Neurosciences Meeting, Paris, 13-18 July
LMS-EPSRC short course on Modern Nonlinear PDE Methods in Fluid Dynamics, Reading, 8-12 July
NETT Neural Engineering summer school, Nottingham, 1-5 July
Mafelap 2013, Brunel University, London, 11-14 June
Waves 2013, Gammarth, Tunisia, 3-7 June
Meeting on Riemann-Hilbert problems and their applications, Reading, 29-30 May
Seminar at the Collège de France, Paris, 17 May
Oberwolfach workshop on Computational Electromagnetism and Acoustics, 20-26 January
SIAM-UKIE annual meeting, Reading, 8 January
Reading departmental analysis day, Reading, 19 October
Seminar at the University of Leicester, 18 October
InnoWave conference, Nottingham, 3-7 September
Zürich Summer School 2012 on A Posteriori Error Control and Adaptivity, Zürich, 20-24 August
Mathmondes 2012, French-British Network on Waves, Reading, 9-10 July
Conference in honour of Nancy Nichols' 70th birthday, Reading, 2-3 July
ESCO2012, 3rd European Seminar on Computing, Pilsen, Czech Republic, 25-29 June
ICMS Workshop on Boundary Value Problems for Linear Elliptic and Integrable PDEs, Edinburgh, 28 May-1 June
Second international conference on Neural Field Theory, Reading, 19-21 April
Seminar at the University of Strathclyde, Glasgow, 17 April
Numerical analysis postgraduate seminar day, Reading, 30 March
Seminar at the University of Bath, 23 March
Seminar at the University of Reading, 12 March
Workshop on Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment, RICAM Linz, Austria, 21-25 November
Colloquium on Analysis and numerics of partial differential equations, in memory of Enrico Magenes, Pavia, 2-4 November
Workshop on Advances in Computational Wave Propagation, University College London, 2-3 September
Pro*Doc summer retreat, Disentis, Switzerland, 17-19 August
Finite Element Fair/Rodeo/Circus, University of Chicago Center, Paris, 3-4 June
Swiss Numerics Colloquium, Università della Svizzera Italiana, Lugano, Switzerland, 6 May
SamHyp2011 - Numerical methods for hyperbolic equations, Zürich, 18-19 February
Workshop on Next Generation Numerical Methods for Computational Wave Propagation, Cambridge, 17-18 September
ESF conference on Highly Oscillatory Problems: From Theory to Applications, Isaac Newton Institute, Cambridge, 12-17 September
Zürich Summer School 2010 on Sparse Tensor Discretisations of High-Dimensional Problems, Zürich, 23-27 August
Pro*Doc summer retreat, Disentis, Switzerland, 18-21 August
ACE'10 6th Workshop on Advanced Computational Electromagnetics, ETH Zürich, 5-7 July
Workshop on Non-Standard Numerical Methods for PDE's, Pavia, 29 June-2 July
DSPDEs'10, joint SIAM/RSME-SCM-SEMA Meeting on Emerging Topics in Dynamical Systems and PDEs, Barcelona, 31 May-4 June
Swiss Numerics Colloquium, ETH Zürich, 16 April
Oberwolfach workshop on Computational Electromagnetism and Acoustics, 14-20 February
WONAPDE 2010, Universidad de Concepción, Chile, 11-15 January
Seminar at the Chinese University of Hong Kong, 9 September
Pro*Doc summer retreat, Disentis, Switzerland, 16-19 August
Mafelap 2009, Brunel University, London, 9-12 June
Swiss Numerics Colloquium, Basel, 24 April