Publications

Publications listed on Google Scholar

Journal Articles

  1. A.-S. Bonnet-Ben Dhia, C. Carvalho, L. Chesnel, P. Ciarlet Jr. Plasmonic cavity modes: black-hole phenomena captured by Perfectly Matched Layers, PROCEEDING of PIERS 2013 in Stockholm(2013), pp. 638-642.
  2. A.-S. Bonnet-Ben Dhia, C. Carvalho, L. Chesnel, P. Ciarlet Jr. On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients, Journal of Computational Physics, 322(2016), pp. 224-247. [Preprint]
  3. C. Carvalho, L. Chesnel, P. Ciarlet Jr. Eigenvalue problems with sign-changing coefficients, Compte Rendus Mathématiques, 355(2017), pp. 671-675. [Preprint]
  4. A.-S. Bonnet-Ben Dhia, C. Carvalho, P. Ciarlet Jr. Mesh requirements for the finite element approximation of problems with sign-changing coefficients, Numerische Mathematik, 138(2018), pp. 1-38. [Preprint]
  5. C. Carvalho, S. Khatri, A. D. Kim Asymptotic analysis for close evaluation for layer potentials, Journal of Computational Physics, 655(2018), pp. 327-341. [Preprint]
  6. P. Sakkaplangkul, V. Bokil, C. Carvalho A fully fourth order accurate energy stable FDTD method for Maxwell's equations in metamaterials, IEEE Journal on Multiscale and Multiphysics Computational Techniques, 4(2019), pp. 260-268. [Preprint]
  7. C. Carvalho, S. Khatri, A. D. Kim Asymptotic approximations for the close evaluation of double-layer potentials, SIAM Journal for Scientific Computing, 42(2020), pp. A504-A533. [Preprint]
  8. S. Khatri, A. D. Kim, R. Cortes, C. Carvalho Close evaluation for layer potentials in three dimensions, Journal of Computational Physics, 423(2020), pp. 109798. [Preprint]
  9. C. Carvalho, A. D. Kim, L. Lewis, Z. Moitier Quadrature by Parity Asymptotic eXpansions (QPAX) for scattering by high aspect ratio particles, SIAM Multiscale Modeling and Simulation, 19(2021), pp. 1857-1884. [Preprint] [Code]
  10. C. Carvalho Modified representations for the close evaluation problem, Mathematical and Computational Applications, 26(2021), pp. 69. [Paper] [Code]
  11. C. Carvalho, C. Ciarlet Jr., C. Scheid Limiting amplitude principle and resonances in plasmonic structures with corners: numerical investigation, Computer Methods in Applied Mechanics and Engineering, 388(2022), pp. 114207. [Paper]
  12. C. Carvalho, Z. Moitier Scattering resonances for unbounded transmission problems with sign-changing coefficient, IMA Journal of Applied Mathematics, 88(2023), pp. 215-257. [Paper] [Code]

Proceedings

  1. A.-S. Bonnet-Ben Dhia, C. Carvalho, L. Chesnel, P. Ciarlet Jr., X. Claeys Plasmonic cavity modes with sign-changing permittivity, WAVES, Tunis, 2013. [Preprint]
  2. A.-S. Bonnet-Ben Dhia, C. Carvalho, L. Chesnel, P. Ciarlet Jr., X. Claeys Plasmonic cavity modes: black-hole phenomena captured by Perfectly Matched Layers, PIERS, Stockholm, 2013. [Preprint]
  3. A.-S. Bonnet-Ben Dhia, C. Carvalho, P. Ciarlet Jr. Plasmonic waveguides: T-coercivity approach for Maxwell's equations, WAVES, Karlsruhe, 2015. [Preprint]
  4. A.-S. Bonnet-Ben Dhia, C. Carvalho, C. Chambeyron, L. Chesnel, P. Ciarlet Jr., A. Nicolet, F. Zolla Curious energy losses at corners of metallic inclusions, WAVES, Karlsruhe, 2015. [Preprint]
  5. C. Carvalho, S. Khatri, A. D. Kim Local analysis of near fields in acoustic scattering, WAVES, Minneapolis, 2017. [Preprint]
  6. C. Carvalho, A. D. Kim, Z. Moitier Quadrature by Parity Asymptotic eXpansions (QPAX) for light scattering by high aspect ratio plasmonic particle, WAVES, Palaiseau, 2022. [Preprint]
  7. C. Carvalho, A. D. Kim, C. McCullough Asymptotic analysis for sound-hard acoustic scattering by two closely-situated spheres, WAVES, Palaiseau, 2022. [Preprint]
  8. C. Carvalho, E. A. Cortes, C. Tsogka Boundary Integral Equation Methods for Optical Cloaking Models, WAVES, Palaiseau, 2022. [Preprint]
  9. C. Carvalho, A. D. Kim, B. Latham Capturing plasmonic behaviors in light scattering by spheres using finite element methods and asymptotic quadrature, WAVES, Palaiseau, 2022. [Preprint]
  10. M. Bussonnier, C. Carvalho Papyri: better documentation for the scientific ecosystem in Jupyter, Proceedings of the 21st Python in Science Conference (SciPy 2022), 2022, pp. 65-72. [Preprint]
  11. C. Carvalho, A. D. Kim, C. McCullough Close evaluation of layer potentials in 3D for the multiple scattering, WAVES, Berlin, 2024.
  12. C. Carvalho, S. Chaillat, E. A. Cortes, C. Tsogka Fast and accurate boundary integral equation methods for the multi-layer transmission problem, WAVES, Berlin, 2024.
  13. C. Carvalho, B. Latham Plane Wave DG Method for Solving Helmholtz Equation in Complex Media, WAVES, Berlin, 2024.

Ph.D. Thesis

Mathematical and numerical study of plasmonic structure with corners (2016)
[PDF] [Defense Slides]

Code Repositories

  1. Quadrature by Parity eXpansions for scattering (Python)
    DOI: 10.5281/zenodo.4692601
  2. Asymptotics for metamaterial cavities (Python)
    DOI: 10.5281/zenodo.4716362
  3. Subtraction techniques for the close evaluation problem (Matlab)
    DOI: 10.5281/zenodo.3934284
  4. Asymptotic methods for the close evaluation problem (Mathematica)

Talks

  1. Plasmonic cavity modes with sign changing permittivity, WAVES, Tunis, 2013.
  2. Plasmonic cavity modes: black-hole phenomena captured by Perfectly Matched Layers, PIERS, Stockholm, 2013.
  3. Revealing guided modes in a plasmonic waveguide using Perfectly Matched Layers at the corners, KOZWAVES, Newcastle, Australia, 2014.
  4. Leaky modes in a non dissipative plasmonic waveguide with a bounded cross section, OWTNM, Nice, 2014.
  5. Leaky modes in a plasmonic waveguide, Leaky Days, 2015.
  6. Plasmonic waveguide: T-coercivity approach for Maxwell's equations, WAVES, Karlsruhe, 2015.
  7. Mesh requirements for transmission problems with sign-changing coefficients, Université de Reims, Reims, 2015.
  8. Mathematical and numerical study of plasmonic structures with corners, UC Merced, Merced, 2016.
  9. Mathematical and numerical study of plasmonic structures with corners, Oregon State University, Corvallis, 2017.
  10. Multiscale modeling to capture near-fields in plasmonic structures with corners, UC Merced, Merced, 2017.
  11. Local analysis of near-fields in acoustic scattering, WAVES, Minneapolis, 2017.
  12. Mesh requirements for transmission problems with sign-changing coefficients, SIAM PD17, Baltimore, 2017.
  13. Close evaluation of layer potentials, IRMAR seminar, Rennes, 2018.
  14. Accurate evaluation of electromagnetic near-field in plasmonic structures, ICERM Workshop, Providence, 2018. [Video]
  15. Multiscale modeling to capture near-fields in plasmonic structures, SIAM Annual Meeting, Portland, 2018.
  16. The Singular Complement Method for scattering problems in plasmonic structures, PIERS, Toyama, 2018.
  17. Numerical methods for light scattering in plasmonic structures with corners, INRIA Sophia-Antipolis, Nice, 2018.
  18. Asymptotic approximations of near fields in scattering problems, Tulane University, New Orleans, 2018.
  19. Capturing near-fields in plasmonic structures with corners, BASCD, Livermore, 2018.
  20. Accurate evaluation of near-fields in plasmonic structures, Caltech, 2019.
  21. Accurate evaluation of near-fields in plasmonic structures, Delaware, 2019.
  22. Asymptotic approximations of near-fields in plasmonic structures, AMS Spring and Central and Western Sectional Meeting, Hawaii, 2019.
  23. Asymptotic approximations for transmission boundary-value problems in plasmonic structures, EMTS, San Diego, 2019.
  24. The Singular Complement Method for dielectric-metamaterial transmission problems, MAFELAP, London, 2019.
  25. How to accurately compute near-fields in plasmonic structures, Portland State University, 2019.
  26. Boundary integral methods for optical cloaking, Energy and the Environment seminar, UC Merced, 2019.
  27. Subtraction techniques for the close evaluation of layer potentials, Imaging and Sensing seminar, UC Merced, 2020.
  28. Close evaluation of layer potentials in three dimensions, FSU, 2020.
  29. Accurate evaluation of near-fields in plasmonic structures, Fresnel Institute, 2020.
  30. Limiting amplitude principle in plasmonic structures with corners, Energy and the Environment seminar, UC Merced, 2020. [Video]
  31. Accurate evaluation of near-fields in plasmonic structures, University of Nice, France, 2021.
  32. Subtraction techniques for the close evaluation of layer potentials, SIAM CSE, 2021.
  33. Accurate evaluation of near-fields in plasmonic structures, Institut Camille Jordan, France, 2022.
  34. On the use of Perfectly Matched Layers for light scattering problems in plasmonic structures, CIRM, Marseille, 2022.
  35. Quadrature by Parity Asymptotic eXpansions (QPAX) for light scattering by high aspect ratio particle, MMCS team day, France, 2022. [Conference Site]
  36. Quadrature by Parity Asymptotic eXpansions (QPAX) for light scattering by high aspect ratio plasmonic particle, WAVES, Palaiseau, 2022.
  37. Numerical methods for the close evaluation of layer potentials in three dimensions, UML-UNC Computational Math seminar, 2022.
  38. Quadrature by Parity Asymptotic eXpansions (QPAX) for light scattering by high aspect ratio plasmonic particle, SIAM CSE23, Amsterdam, 2023.
  39. Résonances de scattering pour cavités de métamatériaux, Journées EDP de l'IECL (cancelled), 2023.
  40. Numerical methods for the close evaluation of layer potentials in three dimensions, ANEDP seminar, Lille, 2023.
  41. Scattering instabilities for metamaterial cavities, NACONF23, Glasgow, 2023.
  42. Scattering instabilities for metamaterial cavities, GRD Ondes 2023, Marseille, 2023.
  43. Integral methods for the close evaluation problem, JO des poètes (60th anniversary conference, co-organizer), 2024. [Conference Site]

Outreach