Research Interests

These are some of my Research Interests:

• Inverse and Direct Scattering Problems.
• Numerical Analysis.
• Wave Propagation.
• Domain Decomposition.
• Fast Direct Solvers.
• Integral Equations.
• Neural Networks.

Software

These are the links to GitHub repositories to software that I contributed to:

• Inverse acoustic scattering solver for 2D problems.
• Inverse volume solver for 2D problems.

Publications

• C. Borges, L. Greengard, M.O’Neil, M. Rachh. On the construction of scattering matrices for irregular or elongated enclosures using Green’s representation formula. Journal of  Scientific Computing 102, 2 (2025).
• T. Askham, C. Borges. Reconstructing the shape and material parameters of dissipative obstacles using an impedance model. Inverse Problems 40.9 (2024): 095004.
• T. Askham, C. Borges, J. Hoskins, M. Rachh. Random walks in frequency and the reconstruction of obstacles with cavities from multi-frequency data. Journal of  Scientific Computing 98, 15 (2024).
• M. Zhou, J. Han, M. Rachh, C. Borges. A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem. Journal of Computational Physics 490 (2023): 112341.
• C. Borges, M. Rachh, L. Greengard. On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary.
  Inverse Problems 39.3 (2023): 035004.
• C. Borges, M. Rachh. Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization. Advances in Computational Mathematics 48.1 (2022): 1-32.
• C. Borges, J. Lai. Inverse scattering reconstruction of a three-dimensional sound-soft axis-symmetric impenetrable object. Inverse Problems, 36.10 (2020): 105005.
• C. Borges, G. Biros. A domain decomposition preconditioning for an inverse volume scattering problem, Inverse Problems, 36.3 (2020): 035016.
• C. Borges, G. Biros. Reconstruction of a compactly supported sound profile in the presence of a random background medium, Inverse Problems, 34.11 (2018): 115007.
• C. Borges, A. Gillman, L. Greengard. High-resolution inverse scattering in two dimensions using recursive linearization, SIAM J. Imaging Sciences, volume 10, no. 2, pp. 641-664, 2017.
• S. Ambikasaran, C. Borges, L. Imbert-Gerard, L. Greengard. Fast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimensions, SIAM J. Sci. Comput., 38(3), A1770–A1787.
• C. Borges, L. Greengard. Inverse obstacle scattering in two dimensions with multiple frequency data and multiple angles of incidence, SIAM J. Imaging Sciences, vol. 8, no. 1, pp. 280–298, 2015.
• C. Borges. A multifrequency method for the solution of the acoustic inverse scattering problem. Ph.D.dissertation, Worcester Polytechnic Institute, Worcester, MA, January 2013.
• C. Borges, M. Sarkis, C. Schaerer. Coarse grid correction operator splitting for parabolic partial differential equations. In proceedings: X Meeting in Computational Modeling, November 2007, Rio de Janeiro, Brazil.
• C. Borges. Coarse grid correction operator splitting for parabolic partial differential equations. M.Sc.Thesis, Institute of Pure and Applied Mathematics, Rio de Janeiro, Brazil, October 2007.