Document Type
Article
Publication Date
2020
DOI
10.1216/jie.2020.32.293
Publication Title
Journal of Integral Equations and Applications
Volume
32
Issue
3
Pages
293-324
Abstract
Evaluating the Newton potential is crucial for efficiently solving the boundary integral equation of the Dirichlet boundary value problem of the Poisson equation. In the context of the Fourier-Garlerkin method for solving the boundary integral equation, we propose a fast algorithm for evaluating Fourier coefficients of the Newton potential by using a sparse grid approximation. When the forcing function of the Poisson equation expressed in the polar coordinates has mth-order bounded mixed derivatives, the proposed algorithm achieves an accuracy of order πͺ(n-m log3 n), with requiring πͺ(n log2 n) number of arithmetics for the computation, where n is the number of quadrature points used in one coordinate direction. With the help of this algorithm, the boundary integral equation derived from the Poisson equation can be efficiently solved by a fast fully discrete Fourier-Garlerkin method.
Original Publication Citation
Guan, W., Jiang, Y., & Xu, Y. (2020). Computing the Newton potential in the boundary integral equation for the Dirichlet problem of the Poisson equation. Journal of Integral Equations and Applications, 32(3), 293-324. https://doi.org/10.1216/jie.2020.32.293
Repository Citation
Guan, Wenchao; Jiang, Ying; and Xu, Yuesheng, "Computing the Newton Potential in the Boundary Integral Equation for the Dirichlet Problem of the Poisson Equation" (2020). Mathematics & Statistics Faculty Publications. 180.
https://digitalcommons.odu.edu/mathstat_fac_pubs/180
Comments
Β© 2020 Rocky Mountain Mathematics Consortium.
Included with the kind written permission of the publisher.