Boundary integral equation analysis on the sphere

• Published in: Numerische Mathematik Vol. 128; no. 3; pp. 463 - 487
• Main Authors: Vico, Felipe, Greengard, Leslie, Gimbutas, Zydrunas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014
• Subjects: Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Numerical Analysis; Numerical and Computational Physics; Simulation; Theoretical; 78M05; 78A45; 65R20; 45B05; 31B10; 35Q61; 35Q60

We present a systematic analysis of the integral operators of potential theory that arise when solving the Helmholtz or Maxwell equations in the exterior (or interior) of a sphere in the frequency domain. After obtaining expressions for the signatures of layer potentials in the spherical harmonic or...