Article

Caetano, A. M., Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, Claeys, X., Gibbs, A., Hewett, D. P. and Moiola, A. (2024) Integral equation methods for acoustic scattering by fractals. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. ISSN 1364-5021 doi: https://doi.org/10.1098/rspa.2023.0650 (In Press)

Caetano, A. M., Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, Gibbs, A., Hewett, D. P. and Moiola, A. (2024) A Hausdorff-measure boundary element method for acoustic scattering by fractal screens. Numerische Mathematik. ISSN 0945-3245 doi: https://doi.org/10.1007/s00211-024-01399-7

Gibbs, A., Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, Langdon, S. and Moiola, A. (2020) A high frequency boundary element method for scattering by a class of multiple obstacles. IMA Journal of Numerical Analysis, 41 (2). pp. 1197-1239. ISSN 1464-3642 doi: https://doi.org/10.1093/imanum/draa025

McCusker, K. ORCID: https://orcid.org/0000-0002-1886-5323, Westbrook, C. D. ORCID: https://orcid.org/0000-0002-2889-8815 and Moiola, A. (2019) 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, 230. pp. 155-171. ISSN 0022-4073 doi: https://doi.org/10.1016/j.jqsrt.2019.04.019

Moiola, A. and Perugia, I. (2018) A space–time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation. Numerische Mathematik, 138 (2). pp. 389-435. ISSN 0029-599X doi: https://doi.org/10.1007/s00211-017-0910-x

Hewett, D. and Moiola, A. (2017) On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space. Analysis and Applications, 15 (5). pp. 731-770. ISSN 1793-6861 doi: https://doi.org/10.1142/S021953051650024X

Hewett, D. P. and Moiola, A. (2017) A note on properties of the restriction operator on Sobolev spaces. Journal of Applied Analysis, 23 (1). pp. 1-8. ISSN 1425-6908 doi: https://doi.org/10.1515/jaa-2017-0001

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, Hewett, D. P. and Moiola, A. (2017) Sobolev spaces on non-Lipschitz subsets of Rn with application to boundary integral equations on fractal screens. Integral Equations and Operator Theory, 87 (2). pp. 179-224. ISSN 1420-8989 doi: https://doi.org/10.1007/s00020-017-2342-5

Kretzschmar, F., Moiola, A., Perugia, I. and Schnepp, S. M. (2016) A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems. IMA Journal of Numerical Analysis, 36 (4). pp. 1599-1635. ISSN 1464-3642 doi: https://doi.org/10.1093/imanum/drv064

Hiptmair, R., Moiola, A. and Perugia, I. (2016) Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version. Foundations of Computational Mathematics, 16 (3). pp. 637-675. ISSN 1615-3375 doi: https://doi.org/10.1007/s10208-015-9260-1

Chandler-Wilde, S. N. ORCID: https://orcid.org/0000-0003-0578-1283, Hewett, D. P. and Moiola, A. (2015) Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples. Mathematika, 61 (2). pp. 414-443. ISSN 0025-5793 doi: https://doi.org/10.1112/S0025579314000278

Moiola, A. and Spence, E. A. (2014) Is the Helmholtz equation really sign-indefinite? SIAM Review, 56 (2). pp. 274-312. ISSN 1095-7200 doi: https://doi.org/10.1137/120901301

Hiptmair, R., Moiola, A., Perugia, I. and Schwab, C. (2014) Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM. ESAIM: Mathematical Modelling and Numerical Analysis M2AN, 48 (3). pp. 727-752. ISSN 1290-3841 doi: https://doi.org/10.1051/m2an/2013137

Howarth, C. J., Childs, P. N. and Moiola, A. (2014) Implementation of an interior point source in the ultra weak variational formulation through source extraction. Journal of Computational and Applied Mathematics, 271. 295 - 306. ISSN 0377-0427 doi: https://doi.org/10.1016/j.cam.2014.04.017

Hiptmair, R., Moiola, A. and Perugia, I. (2013) Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations. Mathematics of Computation, 82 (281). pp. 247-268. ISSN 1088-6842 doi: https://doi.org/10.1090/S0025-5718-2012-02627-5

Moiola, A. (2013) Plane wave approximation in linear elasticity. Applicable Analysis, 92 (6). pp. 1299-1307. ISSN 0003-6811 doi: https://doi.org/10.1080/00036811.2012.671300

Hiptmair, R., Moiola, A. and Perugia, I. (2013) Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes. Applied Numerical Mathematics, 79. pp. 79-91. ISSN 0168-9274 doi: https://doi.org/10.1016/j.apnum.2012.12.004

Hiptmair, R., Moiola, A. and Perugia, I. (2011) Stability results for the time-harmonic Maxwell equations with impedance boundary conditions. Mathematical models and methods in applied Sciences (M3AS), 21 (11). pp. 2263-2287. ISSN 0218-2025 doi: https://doi.org/10.1142/S021820251100574X

Moiola, A., Hiptmair, R. and Perugia, I. (2011) Plane wave approximation of homogeneous Helmholtz solutions. Zeitschrift für angewandte Mathematik und Physik, 62 (5). pp. 809-837. ISSN 0044-2275 doi: https://doi.org/10.1007/s00033-011-0147-y

Hiptmair, R., Moiola, A. and Perugia, I. (2011) Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version. SIAM Journal on Numerical Analysis (SINUM), 49 (1). pp. 264-284. ISSN 0036-1429 doi: https://doi.org/10.1137/090761057

Moiola, A., Hiptmair, R. and Perugia, I. (2011) Vekua theory for the Helmholtz operator. Zeitschrift für Angewandte Mathematik und Physik, 62 (5). pp. 779-807. ISSN 0044-2275 doi: https://doi.org/10.1007/s00033-011-0142-3

Book or Report Section

Hiptmair, R., Moiola, A. and Perugia, I. (2016) A survey of Trefftz methods for the Helmholtz equation. In: Building bridges: connections and challenges in modern approaches to numerical PDEs. Lecture Notes in Computational Science and Engineering. Springer.