Publications
2024
Algorithm xxx: An improved recurrence method for the scaled complex error function
Thompson, I. (n.d.). Algorithm xxx: An improved recurrence method for the scaled complex error function. ACM Transactions on Mathematical Software. doi:10.1145/3688799
2022
Array scattering resonance in the context of Foldy’s approximation
Nethercote, M. A., Kisil, A. V., Thompson, I., & Assier, R. C. (2022). Array scattering resonance in the context of Foldy’s approximation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 478(2268). doi:10.1098/rspa.2022.0604
Energy Flux in Thin Plates
Thompson, I., & Fazakerley, G. (2022). Energy Flux in Thin Plates. QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 75(2). doi:10.1093/qjmam/hbac006
2021
Analysis of Series and Products. Part 2: The Trapezoidal Rule
Thompson, I., Davies, M., & Urbikain, M. K. (2021). Analysis of Series and Products. Part 2: The Trapezoidal Rule. American Mathematical Monthly. doi:10.1080/00029890.2021.1859323
Analysis of Series and Products. Part 1: The Euler-Maclaurin Formula
Thompson, I., Davies, M., & Urbikain, M. K. (2021). Analysis of Series and Products. Part 1: The Euler-Maclaurin Formula. American Mathematical Monthly.
2020
Diffraction by a rigid strip in a plate modelled by Mindlin theory
Thompson, I. (2020). Diffraction by a rigid strip in a plate modelled by Mindlin theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2243). doi:10.1098/rspa.2020.0648
2019
A direct method for Bloch wave excitation by scattering at the edge of a lattice. Part II: Finite size effects
Brougham, R., & Thompson, I. (2019). A direct method for Bloch wave excitation by scattering at the edge of a lattice. Part II: Finite size effects. Quarterly Journal of Mechanics and Applied Mathematics, 72(3), 387-414. doi:10.1093/qjmam/hbz010
2018
Elastic waves trapped above a cylindrical cavity
Linton, C., & Thompson, I. (2018). Elastic waves trapped above a cylindrical cavity. SIAM Journal on Applied Mathematics, 78(4), 2083-2104. doi:10.1137/17M1155296
A DIRECT METHOD FOR BLOCH WAVE EXCITATION BY SCATTERING AT THE EDGE OF A LATTICE. PART I: POINT SCATTERER PROBLEM
Thompson, I., & Brougham, R. I. (2018). A DIRECT METHOD FOR BLOCH WAVE EXCITATION BY SCATTERING AT THE EDGE OF A LATTICE. PART I: POINT SCATTERER PROBLEM. QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 71(1), 1-24. doi:10.1093/qjmam/hbx022
A direct method for Bloch wave excitation by scattering at the edge of a lattice. Part I: Point scatterer problem
Thompson, I., & brougham, R. (2018). A direct method for Bloch wave excitation by scattering at the edgeof a lattice. Part I: Point scatterer problem. Quarterly Journal of Mechanics and Applied Mathematics, 71(1), 1-24. doi:10.1093/qjmam/hbx022
2016
Understanding Maple
Thompson, I. (2016). Understanding Maple. Cambridge University Press. doi:10.1017/9781316809761
A note on quasiperiodic Green's functions for arrays
Brougham, R. I., & Thompson, I. (2016). A note on quasiperiodic Green's functions for arrays. JOURNAL OF ENGINEERING MATHEMATICS, 98(1), 39-48. doi:10.1007/s10665-015-9809-7
2014
Oblique Rayleigh wave scattering by a cylindrical cavity
Linton, C. M., & Thompson, I. (2015). Oblique Rayleigh wave scattering by a cylindrical cavity. Quarterly Journal of Mechanics and Applied Mathematics, 68(3), 235-261. doi:10.1093/qjmam/hbv006
Scattering by a semi-infinite lattice and the excitation of Bloch waves
Tymis, N., & Thompson, I. (2014). Scattering by a semi-infinite lattice and the excitation of Bloch waves. The Quarterly Journal of Mechanics and Applied Mathematics, 67(3), 469-503. doi:10.1093/qjmam/hbu014
2013
Algorithm 926: Incomplete Gamma Functions with Negative Arguments
Thompson, I. (2013). Algorithm 926: Incomplete Gamma Functions with Negative Arguments. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 39(2). doi:10.1145/2427023.2427031
Electromagnetic guided waves on linear arrays of spheres
Linton, C. M., Zalipaev, V., & Thompson, I. (2013). Electromagnetic guided waves on linear arrays of spheres. WAVE MOTION, 50(1), 29-40. doi:10.1016/j.wavemoti.2012.06.002
2012
A note on the real zeros of the incomplete gamma function
Thompson, I. (2012). A note on the real zeros of the incomplete gamma function. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 23(6), 445-453. doi:10.1080/10652469.2011.597391
2011
Low-Frequency Scattering by a Semi-Infinite Lattice of Cylinders
Tymis, N., & Thompson, I. (2011). Low-Frequency Scattering by a Semi-Infinite Lattice of Cylinders. QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 64(2), 171-195. doi:10.1093/qjmam/hbr001
2010
Acoustic Scattering by Random Configurations of Cylinders
Thompson, I., & Parnell, W. J. (2010). Acoustic Scattering by Random Configurations of Cylinders. In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III Vol. 1281 (pp. 1757-+). doi:10.1063/1.3498207
GUIDED SURFACE WAVES ON ONE- AND TWO-DIMENSIONAL ARRAYS OF SPHERES
Thompson, I., & Linton, C. M. (2010). GUIDED SURFACE WAVES ON ONE- AND TWO-DIMENSIONAL ARRAYS OF SPHERES. SIAM JOURNAL ON APPLIED MATHEMATICS, 70(8), 2975-2995. doi:10.1137/100787519
Euler-Maclaurin Summation and Schlomilch Series
Thompson, I., & Linton, C. M. (2010). Euler-Maclaurin Summation and Schlomilch Series. QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 63(1), 39-56. doi:10.1093/qjmam/hbp022
2009
One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation
Linton, C. M., & Thompson, I. (2009). One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation. JOURNAL OF COMPUTATIONAL PHYSICS, 228(6), 1815-1829. doi:10.1016/j.jcp.2008.11.013
2008
An interaction theory for scattering by defects in arrays
Thompson, I., & Linton, C. M. (2008). An interaction theory for scattering by defects in arrays. SIAM JOURNAL ON APPLIED MATHEMATICS, 68(6), 1783-1806. doi:10.1137/070703144
A new approximation method for scattering by long finite arrays
Thompson, I., Linton, C. M., & Porter, R. (n.d.). A new approximation method for scattering by long finite arrays. The Quarterly Journal of Mechanics and Applied Mathematics, 61(3), 333-352. doi:10.1093/qjmam/hbn006
2007
Scattering by a semi-infinite periodic array and the excitation of surface waves
Linton, C. M., Porter, R., & Thompson, I. (2007). Scattering by a semi-infinite periodic array and the excitation of surface waves. SIAM JOURNAL ON APPLIED MATHEMATICS, 67(5), 1233-1258. doi:10.1137/060672662
On the excitation of a closely spaced array by a line source
Thompson, I., & Linton, C. M. (2007). On the excitation of a closely spaced array by a line source. IMA JOURNAL OF APPLIED MATHEMATICS, 72(4), 476-497. doi:10.1093/imamat/hxm014
Diffraction of flexural waves by cracks in orthotropic thin elastic plates. Part II. Far field analysis
Thompson, I., & Abrahams, I. D. (2007). Diffraction of flexural waves by cracks in orthotropic thin elastic plates. Part II. Far field analysis. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 463(2082), 1615-1638. doi:10.1098/rspa.2007.1837
Resonant effects in scattering by periodic arrays
Linton, C. M., & Thompson, I. (2007). Resonant effects in scattering by periodic arrays. WAVE MOTION, 44(3), 165-175. doi:10.1016/j.wavemoti.2006.09.002
2006
An improved uniform approximation for diffraction integrals
Thompson, I. (2006). An improved uniform approximation for diffraction integrals. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 462(2069), 1341-1353. doi:10.1098/rspa.2005.1623
2005
Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I - Formal solution
Thompson, I., & Abrahams, I. D. (2005). Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I - Formal solution. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 461(2063), 3413-3436. doi:10.1098/rspa.2004.1418
Mode generation and diffraction at the aperture of a waveguide
Thompson, I., Tew, R., & Christopoulos, C. (2005). Mode generation and diffraction at the aperture of a waveguide. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 38(12), 2701-2713. doi:10.1088/0305-4470/38/12/012
2002
On the existence of flexural edge waves on thin orthotropic plates
Thompson, I., Abrahams, I. D., & Norris, A. N. (2002). On the existence of flexural edge waves on thin orthotropic plates. JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 112(5), 1756-1765. doi:10.1121/1.1506686