Source Reconstructions in PDE's, in particular, the Laplace and Helmholtz Equations.
Partial Differential Equations:
Control Theory, Semigroup Theory.
Numerical Analysis:
Meshless Methods, in particular, the Method of Fundamental Solutions, MFS, to solve Direct Problems on the boundary;
Fast Fourier Transform, FFT, to implement the Discrete Fourier Transform, DFT.
Papers:
Carlos J. S. Alves, Roberto Mamud, Nuno F. M. Martins, and Nilson C. Roberty, On inverse problems for characteristic sources in Helmholtz equations, Mathematical Problems in Engineering, 2017: https://www.hindawi.com/journals/mpe/2017/2472060/
Conference Participation (from 2016):
Poster Presentation:
ICMC Summer Meeting on Differential Equations - Inverse Source Reconstruction and Identification Problem in Elliptic Equations (2016), book of abstracts, 62;
Oral Presentation:
CNMAC - Congresso Nacional de Matemática Aplicada e Computacional - On the Reconstruction of Characteristic Sources in Helmholtz equations using the Method of Fundamental Solutions, 2016 ;