Durante el curso se trabajará sobre algunos aspectos discutidos en los siguiente libros y artículos que pondremos a disposición de las y los estudiantes:

[1]       Weinberger, Hans F., “A First Course in Partial Differential Equations: with Complex Variables and Transform Methods”, Dover Publications, 1995.

[2]       Guenther, Ronald B & Lee, John W., “Partial Differential Equations of Mathematical Physics and Integral Equations”, Dover Publications, 1988.

[3]       Shen, Jie & Tang, Tao & Wang, Li-Lian, “Spectral Methods”, Springer, 2011.

[4]       Trefethen, Lloyd N., “Spectral Methods in MATLAB”, SIAM, 2000.

[5]       “IFGF-accelerated integral equation solvers for acoustic scattering”, Edwin Jimenez, Christoph Bauinger, and Oscar P. Bruno. Submitted. Available at https://arxiv.org/abs/2112. 06316

[6]       “Bootstrap domain-of-dependence: bounds and time decay of solutions of the wave equation”, Thomas Anderson and Oscar P. Bruno. Submitted. Available at https://arxiv.org/pdf/ 2010.09002.pdf

[7]       “Direct/iterative hybrid solver for scattering by inhomogeneous media”, Oscar P. Bruno and Ambuj Pandey. SIAM Journal on Scientific Computing, to appear (2024)

[8]       “Massively Parallelized Interpolated Factored Green Function Method”, Christoph Bauinger and Oscar P. Bruno, Journal of Computational Physics 475, p. 111837, (2023).

[9]       “FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment”, Oscar P. Bruno, Jan S. Hesthaven, and Daniel V. Leibovici, Journal of Computational Physics X 15, p. 100110, (2022).

[10]    “Foundry-Fabricated Grating Coupler Demultiplexer Inverse-Designed via Fast Integral Methods”, Constantine Sideris, Aroutin Khachaturian, Alexander D. White, Oscar P. Bruno, Ali Hajimiri, Nature Communications Physics 5, 68 (2022).

[11]    “Vector potential based MHD solver for non-periodic flows using Fourier continuation expansions”, Mauro Fontana, Pablo D. Mininni, Oscar P. Bruno and P. Dmitruk, Computer Physics Communications 275, 108304, (2022).

[12]    “Parallel inverse-problem solver for time-domain optical tomography with perfect parallelscaling”, Enzo Gaggioli and Oscar P. Bruno, Journal of Quantitative Spectroscopy & Radiative Transfer 290, p. 108300, (2022).

[13]    “Interpolated Factored Green Function method for accelerated solution of scattering problems”, Christoph Bauinger and Oscar P. Bruno. Journal of Computational Physics 430, 110095 (2021)

[14]    “Skin effect in neutron transport theory”, Enzo L. Gaggioli, Darío M. Mitnik, and Oscar P. Bruno, Physical Review E 104, no. 3, pp. L032801–1–L032801–6, (2021).

[15]    “A Chebyshev-based rectangular-polar integral solver for scattering by general geometries de-scribed by non-overlapping patches”, Oscar P. Bruno and E. Garza. Journal of Computational Physics 421 109740 (2020)

[16]    “Ultrafast simulation and optimization of nanophotonic devices with integral equation methods”, Constantine Sideris, Emmanuel Garza, and Oscar P. Bruno. ACS Photonics 6, 3233— 3240 (2019)

[17]    “An FC-based spectral solver for elastodynamic problems in general three-dimensional domains”, F. Amlani and O. P. Bruno, Journal of Computational Physics 307, 333–354 (2016)

[18]    “A spectral FC solver for the compressible Navier-Stokes equations in general domains I: Explicit time-stepping”, N. Albin, O. P. Bruno, Journal of Computational Physics 230, 6248– 6270 (2011).

[19]    “High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements”, O. P. Bruno and M. Lyon, Journal of Computational Physics 229, 2009–2033 (2010).