@misc{10481/87627,
year = {2023},
month = {8},
url = {https://hdl.handle.net/10481/87627},
abstract = {We propose to use spline Gauss quadrature rules for solving boundary value problems (BVPs) using the Nyström method. When solving BVPs, one converts the corresponding partial differential equation inside a domain into the Fredholm integral equation of the second kind on the boundary in the sense of boundary integral equation (BIE). The Fredholm integral equation is then solved using the Nyström method, which involves the use of a particular quadrature rule, thus, converting the BIE problem to a linear system. We demonstrate this concept on the 2D Laplace problem over domains with smooth boundary as well as domains containing corners. We validate our approach on benchmark examples and the results indicate that, for a fixed number of quadrature points (i.e., the same computational effort), the spline Gauss quadratures return an approximation that is by one to two orders of magnitude more accurate compared to the solution obtained by traditional polynomial Gauss counterparts.},
organization = {This work has received funding from the Spanish Ministry of Science and Innovation projects with references PID2019-108111RB-I00 and PID2019-104488RB-I00, the “BCAM Severo Ochoa” accreditation of excellence CEX2021-001142-S/MICIN/AEI/10.13039/501100011033, and the Basque Government through the BERC 2022-2025 program. The third author is a member of the INdAM-GNCS Research group. The fourth author is a member of the IMAG, the Institute of Mathematics of the University of Granada.},
publisher = {Elsevier},
title = {Solving boundary value problems via the Nyström method using spline Gauss rules},
doi = {10.1016/j.camwa.2023.04.035},
author = {Hashemian, Ali and Sliusarenko, Hanna and Remogna, Sara and Barrera Rosillo, Domingo and Bartoň, Michael},
}