Papers by P. A. Martin in Refereed Journals


  1. Hypersingular integral equations over a disc: Convergence of a spectral method and connection with Tranter's method. (With L. Farina and V. PĂ©ron). Journal of Computational and Applied Mathematics 269 (2014) 118-131. doi
  2. A scaled mapping parabolic equation for sloping range-dependent environments. (With A.M. Metzler, D. Moran, J.M. Collis and W.L. Siegmann). Journal of the Acoustical Society of America 135 (2014) EL172-EL178. doi
  3. Time-domain BEM for 3-D transient elastodynamic problems with interacting rigid movable disc-shaped inclusions. (With V.V. Mykhas'kiv and O.I. Kalynyak). Computational Mechanics (2014) doi
  4. On the long-time limit of the Garvin-Alterman-Loewenthal solution for a buried blast load. (With E. Kausel). International Journal of Solids and Structures 51 (2014) 1516-1520. doi
  5. N masses on an infinite string and related one-dimensional scattering problems. Wave Motion 51 (2014) 296-307. doi
  6. Scattering from a large cylinder with an eccentrically embedded core: an orders-of-scattering approximation. (With A.J. Yuffa and J.A. Scales). Journal of Quantitative Spectroscopy and Radiative Transfer 133 (2014) 520-525. doi
  7. Propagation in one-dimensional crystals with positional and compositional disorder. (With A. Maurel). European Physical Journal B 86 (2013) 486 (10 pages). doi pdf
  8. Explicit energy calculation for a charged elliptical plate. Applied Mathematics Letters 26 (2013) 893-898. doi pdf pdf with addendum
  9. Fritz Joseph Ursell. (With I.D. Abrahams). Biographical Memoirs of Fellows of the Royal Society 59 (2013) 407-421. doi pdf bibliography
  10. Peter Waterman and T-matrix methods. (With M.I. Mishchenko). Journal of Quantitative Spectroscopy and Radiative Transfer 123 (2013) 2-7. doi pdf
  11. Singularities in auxetic bimaterials. (With M.M. Adam and J.R. Berger). Mechanics Research Communications 47 (2013) 102-105. doi pdf
  12. Two-dimensional acoustic scattering, conformal mapping, and the Rayleigh hypothesis. Journal of the Acoustical Society of America 132 (2012) 2184-2188. doi pdf
  13. Jet noise: sound generation by disc and cylinder sources. (With M.J. Carley). Proceedings of the Royal Society A 468 (2012) 3947-3964. doi pdf
  14. Maurice Jaswon and boundary element methods. Engineering Analysis with Boundary Elements 36 (2012) 1699-1704. doi pdf
  15. Generation of internal gravity waves by an oscillating horizontal elliptical plate. (With S.G. Llewellyn Smith). SIAM Journal on Applied Mathematics 72 (2012) 725-739. doi pdf
  16. Comment on "Elastic wave propagation in a solid layer with laser-induced point defects" [J. Appl. Phys. 110, 064906 (2011)]. Journal of Applied Physics 112 (2012) 056101 (2 pages). doi pdf
  17. Moshinsky's shutter problem: an initial-value problem for the Klein-Gordon equation. (With F.V. Kowalski). Applicable Analysis 91 (2012) 309-322. doi pdf
  18. Finding a source inside a sphere. (With N.L. Tsitsas). Inverse Problems 28 (2012) 015003 (11 pages) doi pdf
  19. Internal gravity waves, boundary integral equations and radiation conditions. (With S.G. Llewellyn Smith). Wave Motion 49 (2012) 427-444. doi pdf
  20. Generation of internal gravity waves by an oscillating horizontal disc. (With S.G. Llewellyn Smith). Proceedings of the Royal Society A 467 (2011) 3406-3423. doi pdf
  21. Scattering by defects in an exponentially graded layer and misuse of the method of images. International Journal of Solids and Structures 48 (2011) 2164-2166. doi pdf
  22. Multiple scattering by random configurations of circular cylinders: reflection, transmission, and effective interface conditions. Journal of the Acoustical Society of America 129 (2011) 1685-1695. doi pdf
  23. The horn-feed problem: sound waves in a tube joined to a cone, and related problems. Journal of Engineering Mathematics 71 (2011) 291-304. doi pdf
  24. Multiple scattering of flexural waves by random configurations of inclusions in thin plates. (With W.J. Parnell). Wave Motion 48 (2011) 161-175. doi pdf
  25. Estimating the dynamic effective mass density of random composites. (With A. Maurel and W.J. Parnell). Journal of the Acoustical Society of America 128 (2010) 571-577. doi pdf
  26. Waves around almost periodic arrangements of scatterers: Analysis of positional disorder. (With A. Maurel). Mathematical Methods in the Applied Sciences 33 (2010) 2215-2224. doi pdf
  27. Effective propagation in a one-dimensional perturbed periodic structure: comparison of several approaches. (With A. Maurel and V. Pagneux). Waves in Random and Complex Media 20 (2010) 634-655. doi pdf
  28. Harry Bateman: from Manchester to Manuscript Project. Mathematics Today 46 (2010) 82-85. pdf
  29. Scattering by a cavity in an exponentially graded half-space. Journal of Applied Mechanics 76 (2009) 031009 (4 pages). doi pdf
  30. Thermal grooving by surface diffusion: Mullins revisited and extended to multiple grooves. Quarterly of Applied Mathematics 67 (2009) 125-136. doi pdf
  31. On functions defined by sums of products of Bessel functions. Journal of Physics A: Mathematical and Theoretical 41 (2008) 015207 (8 pages). doi pdf
  32. Multiple scattering by random configurations of circular cylinders: weak scattering without closure assumptions. (With A. Maurel). Wave Motion 45 (2008) 865-880. doi pdf
  33. Calculating the near field of a line of sources using Mellin transforms. ANZIAM Journal 49 (2007) 99-109. doi pdf
  34. Analysis of moire data for near-interface cracks. (With K. Rozenburg, J.R. Berger and I. Reimanis). International Journal of Fracture 143 (2007) 207-217. doi pdf
  35. On the T-matrix for scattering by small obstacles. Journal of Computational and Applied Mathematics 204 (2007) 219-230. doi pdf
  36. Stress intensity factor computation using the method of fundamental solutions: mixed-mode problems. (With J.R. Berger and A. Karageorghis). International Journal for Numerical Methods in Engineering 69 (2007) 469-483. doi pdf
  37. Perturbed cracks in two dimensions: a reprise. International Journal of Fracture 140 (2006) 299-303. doi pdf
  38. Discrete scattering theory: Green's function for a square lattice. Wave Motion 43 (2006) 619-629. doi pdf
  39. Multiple scattering by multiple spheres: a new proof of the Lloyd-Berry formula. (With C.M. Linton). SIAM Journal on Applied Mathematics 66 (2006) 1649-1668. doi pdf
  40. Exact solution of some integral equations over a circular disc. Journal of Integral Equations and Applications 18 (2006) 39-58. doi pdf
  41. Fundamental solutions for steady-state heat transfer in an exponentially graded anisotropic material. (With J.R. Berger, V. Mantic and L.J. Gray). Zeitschrift fur Angewandte Mathematik und Physik (ZAMP) 56 (2005) 293-303. doi pdf
  42. On flexural waves in cylindrically anisotropic rods. International Journal of Solids and Structures 42 (2005) 2161-2179. doi pdf
  43. Acoustic waves in slender axisymmetric tubes. Journal of Sound and Vibration 286 (2005) 55-68. doi pdf
  44. Multiple scattering by random configurations of circular cylinders: second-order corrections for the effective wavenumber. (With C.M. Linton). Journal of the Acoustical Society of America 117 (2005) 3413-3423. doi pdf
  45. Waves in wood: axisymmetric waves in slender solids of revolution. Wave Motion 40 (2004) 387-398. doi pdf
  46. On Webster's horn equation and some generalizations. Journal of the Acoustical Society of America 116 (2004) 1381-1388. doi pdf
  47. Semi-infinite arrays of isotropic point scatterers: a unified approach. (With C.M. Linton). SIAM Journal on Applied Mathematics 64 (2004) 1035-1056. doi pdf
  48. Acoustic scattering by inhomogeneous obstacles. SIAM Journal on Applied Mathematics 64 (2003) 297-308. doi pdf
  49. On Green's function for a bimaterial elastic half-plane. International Journal of Solids and Structures 40 (2003) 2101-2119. doi pdf
  50. Waves in wood: axisymmetric guided waves along boreholes. (With J.R. Berger). Chinese Journal of Mechanics, Series A 19 (2003) 105-111. pdf
  51. On connections between boundary integral equations and T-matrix methods. Engineering Analysis with Boundary Elements 27 (2003) 771-777. doi pdf
  52. The method of fundamental solutions for scattering and radiation problems. (With G. Fairweather and A. Karageorghis). Engineering Analysis with Boundary Elements 27 (2003) 759-769. doi pdf
  53. On the scattering of point-generated electromagnetic waves by a perfectly conducting sphere, and related near-field inverse problems. (With C. Athanasiadis and I.G. Stratis). Zeitschrift fur angewandte Mathematik und Mechanik (ZAMM) 83 (2003) 129-136. doi pdf
  54. The added mass of potential flow past rigid plates. (With N.M.A. Nik Long). International Mathematical Journal 3 (2003) 785-794.
  55. Scattering relations for point sources: acoustic and electromagnetic waves. (With C. Athanasiadis, A. Spyropoulos and I.G. Stratis). Journal of Mathematical Physics 43 (2002) 5683-5697. doi pdf
  56. On mechanical waves along aluminum conductor steel reinforced (ACSR) power lines. (With J.R. Berger). Journal of Applied Mechanics 69 (2002) 740-748. doi pdf
  57. Multiple scattering and modified Green's functions. Journal of Mathematical Analysis and Applications 275 (2002) 642-656. doi pdf
  58. The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics. (With M. Destrade and T.C.T. Ting). Journal of the Mechanics and Physics of Solids 50 (2002) 1453-1468. doi pdf
  59. On Green's function for a three-dimensional exponentially graded elastic solid. (With J.D. Richardson, L.J. Gray and J.R. Berger). Proceedings of the Royal Society A 458 (2002) 1931-1947. doi pdf
  60. Acoustic scattering by inhomogeneous spheres. Journal of the Acoustical Society of America 111 (2002) 2013-2018. doi pdf
  61. A boundary element regularization method for the boundary determination in potential corrosion damage. (With D. Lesnic and J.R. Berger). Inverse Problems in Engineering 10 (2002) 163-182. doi pdf
  62. On functionally graded balls and cones. Journal of Engineering Mathematics 42 (2002) 133-142. doi pdf
  63. On spherical-wave scattering by a spherical scatterer and related near-field inverse problems. (With C. Athanasiadis and I.G. Stratis). IMA Journal of Applied Mathematics 66 (2001) 539-549. doi pdf
  64. On the diffraction of Poincare waves. Mathematical Methods in the Applied Sciences 24 (2001) 913-925. doi pdf
  65. Waves in wood: free vibrations of a wooden pole. (With J.R. Berger). Journal of the Mechanics and Physics of Solids 49 (2001) 1155-1178. doi pdf
  66. On wrinkled penny-shaped cracks. Journal of the Mechanics and Physics of Solids 49 (2001) 1481-1495. doi pdf
  67. The spherical-cap crack revisited. International Journal of Solids and Structures 38 (2001) 4759-4776. doi pdf
  68. G. R. Wickham: an appreciation. (With I.D. Abrahams and A.N. Norris). Wave Motion 33 (2001) 1-6. doi pdf
  69. Perturbed cracks in two dimensions: an integral-equation approach. International Journal of Fracture 104 (2000) 317-327. doi pdf
  70. Time-harmonic torsional waves in a composite cylinder with an imperfect interface. (With J.R. Berger and S.J. McCaffery). Journal of the Acoustical Society of America 107 (2000) 1161-1167. doi pdf
  71. Waves in rectangular inlet with reflecting or absorbing walls. (With R.A. Dalrymple and L. Li). Journal of Waterway, Port, Coastal, and Ocean Engineering 126 (2000) 288-296. doi pdf
  72. Inverting the Sachs-Wolfe formula: an inverse problem in early-Universe cosmology. (With A. Berera). Inverse Problems 15 (1999) 1393-1404. doi pdf
  73. Electromagnetic scattering by a homogeneous chiral obstacle: scattering relations and the far-field operator. (With C. Athanasiadis and I.G. Stratis). Mathematical Methods in the Applied Sciences 22 (1999) 1175-1188. doi pdf
  74. Electromagnetic scattering by a homogeneous chiral obstacle: boundary integral equations and low-chirality approximations. (With C. Athanasiadis and I.G. Stratis). SIAM Journal on Applied Mathematics 59 (1999) 1745-1762. doi pdf
  75. Reduction of free-edge stress intensities in anisotropic bimaterials. (With J.R. Berger and J.P. Lien). International Journal of Fracture 91 (1998) 165-177. doi pdf
  76. Multiple scattering and the Rehr-Albers-Fritzsche formula for the propagator matrix. Journal of Physics A: Mathematical and General 31 (1998) 8923-8932. doi pdf
  77. On the added mass of rippled discs. Journal of Engineering Mathematics 33 (1998) 421-435. doi pdf
  78. On potential flow past wrinkled discs. Proceedings of the Royal Society A 454 (1998) 2209-2221. doi pdf
  79. Some efficient boundary integral strategies for time-harmonic wave problems in an elastic halfspace. (With L. Pan and F. Rizzo). Computer Methods in Applied Mechanics and Engineering 164 (1998) 207-221. doi pdf
  80. Scattering of water waves by a submerged disc using a hypersingular integral equation. (With L. Farina). Applied Ocean Research 20 (1998) 121-134. doi pdf. Erratum: 21 (1999) 157-158. pdf
  81. On the derivation of boundary integral equations for scattering by an infinite two-dimensional rough surface. (With J.A. DeSanto). Journal of Mathematical Physics 39 (1998) 894-912. doi pdf
  82. Smoothness-relaxation strategies for singular and hypersingular integral equations. (With F.J. Rizzo and T.A. Cruse). International Journal for Numerical Methods in Engineering 42 (1998) 885-906. doi pdf
  83. Radiation of water waves by a heaving submerged horizontal disc. (With L. Farina). Journal of Fluid Mechanics 337 (1997) 365-379. doi pdf
  84. On the derivation of boundary integral equations for scattering by an infinite one-dimensional rough surface. (With J.A. DeSanto). Journal of the Acoustical Society of America 102 (1997) 67-77. doi pdf
  85. On angular-spectrum representations for scattering by infinite rough surfaces. (With J.A. DeSanto). Wave Motion 24 (1996) 421-433. doi pdf. Corrigendum 32 (2000) 385-386. doi pdf
  86. A general formulation for light scattering by dielectric bodies near a perfectly conducting surface. (With J.C. Chao, F.J. Rizzo, I. El-Shafiey, Y.J. Liu and L. Udpa). J. Optical Soc. Amer. A 13 (1996) 338-344. doi pdf
  87. Water waves incident on an infinitely long rectangular inlet. (With R.A. Dalrymple). Applied Ocean Research 18 (1996) 1-11. doi pdf
  88. Hypersingular integrals: how smooth must the density be? (With F.J. Rizzo). International Journal for Numerical Methods in Engineering 39 (1996) 687-704. doi pdf
  89. Mapping flat cracks onto penny-shaped cracks, with application to somewhat circular tensile cracks. Quarterly of Applied Mathematics 54 (1996) 663-675. pdf
  90. Mapping flat cracks onto penny-shaped cracks: shear loadings. Journal of the Mechanics and Physics of Solids 43 (1995) 275-294. doi pdf
  91. Partitioning, boundary integral equations, and exact Green's functions. (With F.J. Rizzo). International Journal for Numerical Methods in Engineering 38 (1995) 3483-3495. doi pdf
  92. Regularized integral equations and curvilinear boundary elements for electromagnetic wave scattering in three dimensions. (With J.C. Chao, Y.J. Liu, F.J. Rizzo and L. Udpa). IEEE Transactions on Antennas and Propagation AP-43 (1995) 1416-1422. doi pdf
  93. Asymptotic approximations for functions defined by series, with some applications to the theory of guided waves. IMA Journal of Applied Mathematics 54 (1995) 139-157. doi pdf
  94. Trapping of water waves by submerged plates using hypersingular integral equations. (With N.F. Parsons). Journal of Fluid Mechanics 284 (1995) 359-375. doi pdf
  95. Fluid-solid interaction: acoustic scattering by a smooth elastic body. (With C.J. Luke). SIAM Journal on Applied Mathematics 55 (1995) 904-922. doi pdf
  96. Spectral methods for forward-propagating water waves in conformally-mapped channels. (With J.T. Kirby and R.A. Dalrymple). Applied Ocean Research 16 (1994) 249-266. doi pdf
  97. Scattering of water waves by submerged curved plates and by surface-piercing flat plates. (With N.F. Parsons). Applied Ocean Research 16 (1994) 129-139. doi pdf
  98. On the propagation of water waves along a porous-walled channel. (With R.A. Dalrymple). Proceedings of the Royal Society A 444 (1994) 411-428. doi pdf
  99. On amphidromic points. (With R.A. Dalrymple). Proceedings of the Royal Society A 444 (1994) 91-104. doi pdf
  100. Karp's theorem in elastodynamic inverse scattering. (With G. Dassios). Inverse Problems 9 (1993) 97-111. doi pdf
  101. Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle. (With P. Ola). Proceedings of the Royal Society of Edinburgh 123A (1993) 185-208. pdf
  102. A normal crack in an elastic half-space with stress-free surface. (With L. Paivarinta and S. Rempel). Mathematical Methods in the Applied Sciences 16 (1993) 563-579. doi pdf
  103. Boundary integral equations for the scattering of elastic waves by elastic inclusions with thin interface layers. Journal of Nondestructive Evaluation 11 (1992) 167-174. doi pdf
  104. Scattering of water waves by submerged plates using hypersingular integral equations. (With N.F. Parsons). Applied Ocean Research 14 (1992) 313-321. doi pdf
  105. Tip behaviour for cracks in bonded inhomogeneous materials. Journal of Engineering Mathematics 26 (1992) 467-480. doi pdf
  106. Perfect boundary conditions for parabolic water-wave models. (With R.A. Dalrymple). Proceedings of the Royal Society A 437 (1992) 41-54. doi pdf
  107. Havelock wavemakers, Westergaard dams and the Rayleigh hypothesis. Journal of Engineering Mathematics 26 (1992) 267-280. doi pdf
  108. Exact solution of a simple hypersingular integral equation. Journal of Integral Equations and Applications 4 (1992) 197-204. doi pdf. Addendum: 5 (1993) 297.
  109. End-point behaviour of solutions to hypersingular integral equations. Proceedings of the Royal Society A 432 (1991) 301-320. doi pdf
  110. Reflection and transmission from porous structures under oblique wave attack. (With R.A. Dalrymple and M.A. Losada). Journal of Fluid Mechanics 224 (1991) 625-644. doi pdf
  111. Identification of irregular frequencies in simple direct integral-equation methods for scattering by homogeneous inclusions. Wave Motion 13 (1991) 185-192. doi pdf
  112. Wave diffraction through offshore breakwaters. (With R.A. Dalrymple). Journal of Waterway, Port, Coastal, and Ocean Engineering 116 (1990) 727-741. doi pdf
  113. On the scattering of elastic waves by an elastic inclusion in two dimensions. Quarterly Journal of Mechanics and Applied Mathematics 43 (1990) 275-291. doi pdf
  114. On hypersingular boundary integral equations for certain problems in mechanics. (With F.J. Rizzo and I.R. Gonsalves). Mechanics Research Communications 16 (1989) 65-71. doi pdf
  115. On boundary integral equations for crack problems. (With F.J. Rizzo). Proceedings of the Royal Society A 421 (1989) 341-355. doi pdf
  116. Scattering of long waves by cylindrical obstacles and gratings using matched asymptotic expansions. (With R.A. Dalrymple). Journal of Fluid Mechanics 188 (1988) 465-490. doi pdf
  117. On single integral equations for the transmission problem of acoustics. (With R.E. Kleinman). SIAM Journal on Applied Mathematics 48 (1988) 307-325. doi pdf
  118. Orthogonal polynomial solutions for elliptical cracks under shear loadings. Quarterly Journal of Mechanics and Applied Mathematics 39 (1986) 519-534. doi pdf
  119. Orthogonal polynomial solutions for pressurised elliptical cracks. Quarterly Journal of Mechanics and Applied Mathematics 39 (1986) 269-287. doi pdf
  120. Inverse scattering for geophysical problems. III. On the velocity-inversion problems of acoustics. (With A.G. Ramm). Proceedings of the Royal Society A 399 (1985) 153-166. doi pdf
  121. On the T-matrix for water-wave scattering problems. Wave Motion 7 (1985) 177-193. doi pdf
  122. Integral-equation methods for multiple-scattering problems II. Water waves. Quarterly Journal of Mechanics and Applied Mathematics 38 (1985) 119-133. doi pdf
  123. Integral-equation methods for multiple-scattering problems I. Acoustics. Quarterly Journal of Mechanics and Applied Mathematics 38 (1985) 105-118. doi pdf
  124. On the null-field equations for water-wave scattering problems. IMA Journal of Applied Mathematics 33 (1984) 55-69. doi
  125. Diffraction of elastic waves by a penny-shaped crack: analytical and numerical results. (With G.R. Wickham). Proceedings of the Royal Society A 390 (1983) 91-129. doi pdf
  126. The scattering of regular surface waves by a fixed, half-immersed, circular cylinder. (With A.G. Dixon). Applied Ocean Research 5 (1983) 13-23. doi pdf
  127. Acoustic scattering and radiation problems, and the null-field method. Wave Motion 4 (1982) 391-408. doi pdf
  128. The discontinuity in the elastostatic displacement vector across a penny-shaped crack under arbitrary loads. Journal of Elasticity 12 (1982) 201-218. doi pdf
  129. On the null-field equations for water-wave radiation problems. Journal of Fluid Mechanics 113 (1981) 315-332. doi pdf
  130. Diffraction of elastic waves by a penny-shaped crack. Proceedings of the Royal Society A 378 (1981) 263-285. doi pdf
  131. On the null-field equations for the exterior problems of acoustics. Quarterly Journal of Mechanics and Applied Mathematics 33 (1980) 385-396. doi pdf

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