2014/08/14 by Nilima Nigam, Nigam, Nilima, Mary-Catherine Kropinski +3 · 1 citation
Engineering · Mathematics · #35J25 and 45B05 #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1408.3183
openalex publication_date 2014/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An integral equation method for solving the Yukawa-Beltrami equation on a multiply-connected sub-manifold of the unit sphere is presented. A fundamental solution for the Yukawa-Beltrami operator is constructed. This fundamental solution can be represented by conical functions. Using a suitable representation formula, a Fredholm equation of the second kind with a compact integral operator needs to be solved. The discretization of this integral equation leads to a linear system whose condition number is bounded independent of the size of the system. Several numerical examples exploring the properties of this integral equation are presented.