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Dipartimento di Matematica "F. Casorati"
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| Teaching | Research | Papers | Preprints | Lecture notes | Collaborators | Slides | Links | Conferences & events |
ASTICE -
New PRIN grant: Advanced Space-TIme disCrEtization methods: theory, solvers and applications
Post-doctoral positions in Pavia, Milano Politecnico and Milano Bicocca coming soon (autumn/winter 2023), please get in touch if interested!
Team members:
Gabriele Ciaramella,
Carlo Marcati,
Lorenzo Mascotto,
Ilario Mazzieri,
Andrea Moiola
| Since July 2020 | Associate professor | Department of Mathematics, University of Pavia |
| July 2017 - June 2020 | Ricercatore (RTDB, equivalent to lecturer) | Department of Mathematics, University of Pavia |
| March 2013 - June 2017 | Senior research fellow (permanent post) | Department of Mathematics and Statistics, University of Reading |
| March 2012 - February 2013 | SNSF Fellowship | University of Reading, supervised by Simon N. Chandler-Wilde |
| Sept. 2008 - November 2011 | PhD student | SAM - ETH Zürich, supervised by Ralf Hiptmair and Ilaria Perugia |
Computational electromagnetics and wave propagation
Numerical analysis, approximation of PDEs
Finite element, discontinuous Galerkin, non-polynomial, Trefftz and quasi-Trefftz methods
Approximation theory, in particular by non-polynomial functions
Wavenumber-explicit analysis of time-harmonic boundary value problems, scattering theory
Sobolev spaces on rough (non-Lipschitz) domains, wave scattering by fractal obstacles
Boundary and volume integral equations, boundary element methods
Space-time discretisations of evolution PDEs
[NEW!]
T. Chaumont-Frelet, A. Moiola, E.A. Spence
Explicit bounds for the high-frequency time-harmonic Maxwell equations in heterogeneous media,
J. Math. Pure. Appl., 2023
(link to journal,
preprint: arXiv:2301.07092), DOI: 10.1016/j.matpur.2023.09.004.
S. Gómez, A. Moiola, I. Perugia, P. Stocker
On polynomial Trefftz spaces for the linear time-dependent Schrödinger equation,
Appl. Math. Lett., 146, 2023, 108824
(link to journal,
preprint: arXiv:2306.09571),
DOI: 10.1016/j.aml.2023.108824.
L.M. Imbert-Gérard, A. Moiola, P. Stocker
A space-time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients,
Math. Comput., 92(341), 2023, pp. 1211-1249
(link to journal,
preprint: arXiv:2011.04617),
DOI: 10.1090/mcom/3786.
(NGSTrefftz on GitHub, implemented by Paul Stocker.)
A. Gibbs, D.P. Hewett, A. Moiola
Numerical quadrature for singular integrals on fractals,
Numer. Algorithms, 92, 2023, pp. 2071-2124.
(open access link to journal,
preprint: arXiv:2112.11793),
DOI: 10.1007/s11075-022-01378-9.
(IFSintegrals on GitHub, implemented by Andrew Gibbs.)
R. Hiptmair, A. Moiola, E.A. Spence
Spurious quasi-resonances in boundary integral equations for the Helmholtz transmission problem,
SIAM J. Appl. Math., 82(4), 2022, pp. 1446-1469
(pdf file, link to journal,
preprint: arXiv:2109.08530),
DOI: 10.1137/21M1447052.
(Link to Matlab routine.)
S. Gómez, A. Moiola
A space-time Trefftz discontinuous Galerkin method for the linear Schrödinger equation,
SIAM J. Numer. Anal., 60(2), 2022, pp. 688-714 (pdf file,
link to journal,
preprint: arXiv:2106.04724), DOI: 10.1137/21M1426079.
A. Caetano, D.P. Hewett, A. Moiola
Density results for Sobolev, Besov and Triebel-Lizorkin spaces on rough sets,
J. Funct. Anal., 281(3), 2021, 109019
(link to journal,
preprint:arXiv:1904.05420),
DOI: 10.1016/j.jfa.2021.109019.
S.N. Chandler-Wilde, D.P. Hewett, A. Moiola, J. Besson
Boundary element methods for acoustic scattering by fractal screens,
Numer. Math.,
147, 2021, 785-837 (open-access link to journal,
preprint: arXiv:1909.05547),
DOI: 10.1007/s00211-021-01182-y.
P. Bansal, A. Moiola, I. Perugia, Ch. Schwab
Space-time discontinuous Galerkin approximation of acoustic waves with point singularities,
IMA J. Numer. Anal., 41(3), 2021, pp. 2056-2109,
(free-access link to journal,
preprint: arXiv:2002.11575),
DOI: 10.1093/imanum/draa088.
A. Gibbs, S.N. Chandler-Wilde, S. Langdon, A. Moiola
A high frequency boundary element method for scattering by a class of multiple obstacles,
IMA J. Numer. Anal., 41(2), 2021, pp. 1197-1225
(free-access link to journal,
preprint: arXiv:1903.04449),
DOI: 10.1093/imanum/draa025.
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.
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.
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/j.cam.2018.11.035.
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.
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.
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.
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.
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.
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.
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.
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.
Corrigendum: Mathematika, 68(4) 2022, pp. 1393-1400, DOI: 10.1112/mtk.12155.
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.
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/j.cam.2014.04.017.
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.
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.
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.
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.
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.
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.
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.
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.
[NEW!]
A.M. Caetano, S.N. Chandler-Wilde, X. Claeys, A. Gibbs, D.P. Hewett, A. Moiola
Integral equation methods for acoustic scattering by fractals,
arXiv:2309.02184, 2023.
(IFSintegrals on GitHub, implemented by Andrew Gibbs.)
S. Gómez, A. Moiola
A space-time DG method for the Schrödinger equation with variable potential,
arXiv:2306.05780, 2023.
A.M. Caetano, S.N. Chandler-Wilde, A. Gibbs, D.P. Hewett, A. Moiola
A Hausdorff-measure boundary element method for acoustic scattering by fractal screens,
arXiv:2212.06594, 2022.
(IFSintegrals on GitHub, implemented by Andrew Gibbs.)
S. Gómez, L. Mascotto, A. Moiola, I. Perugia
Space-time virtual elements for the heat equation,
arXiv:2212.05343, 2022.
E. Parolin, D. Huybrechs, A. Moiola
Stable approximation of Helmholtz solutions by evanescent plane waves,
arXiv:2202.05658, 2022.
(evanescent-plane-wave-approx on GitHub, implemented by Emile Parolin.)
A. Gibbs, S. Langdon, A. Moiola
Numerically stable computation of embedding formulae for scattering by polygons,
arXiv:1805.08988, 2018.
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.
Integral equation methods for acoustic scattering by fractals, UMI Pisa, 4-9 September 2023
A Hausdorff-measure BEM for acoustic scattering by fractal screens, Roma, 15-17 March 2023
Non-polynomial methods for the Helmholtz equation, Oberwolfach, 25-30 September 2022
A space–time quasi-Trefftz DG method for the wave equation with smooth coefficients, Waves 2022, ENSTA Paris, 24-29 July 2022
Stable approximation of Helmholtz solutions by evanescent plane waves,
One World Numerical Analysis, 21 February 2022
Space-time DG for the wave equation: quasi-Trefftz and sparse versions, Augsburg, 13-15 September 2021
Numerical approximation of acoustic scattering by fractal screens, UMI, Pavia, 2-7 September 2019
Boundary element methods for scattering by fractal screens, Waves, Vienna, 25-30 August 2019
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: 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
Dipartimento di Matematica, Università di Pavia
Scientific Computing: Numerical Methods and Applications Group, Pavia
IMATI - CNR (Istituto di Matematica Applicata e Tecnologie Informatiche), Pavia
International PhD program in Computational Mathematics, Learning, and Data Science
, Pavia - USI
Joint PhD Program in Mathematics, Pavia - Milano Bicocca - INdAM
Very informal seminars, UniPv + IMATI-CNR
Presidio della qualità di ateneo, Università di Pavia
Current and previous grants
2023-2025 PRIN grant:
ASTICE - Advanced Space-TIme disCrEtization methods: theory, solvers and applications (PI)
2023-2025 PRIN-PNRR grant: NOTES - Next generatiOn numerical Technologies for dEsign and Simulation
2019-2023 PRIN grant: NA_FROM-PDEs -
Numerical Analysis of Full and Reduced order Methods for Partial Differential Equations
2020-2022 CE4WE - Circular Economy for Water and Energy
2016-2018 EPSRC 1st: Discretisations of sign-definite formulations for the Helmholtz equation (PI)
2012-2013 SNSF fellowship:
Computational Wave Propagation (PI)
Previous affiliations
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
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
UMI, Unione Matematica Italiana
