2007/02/17 by Alan Rufty, Rufty, Alan · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #31Bxx #35J99 #65D05 #65Nxx #Advanced Mathematical Modeling in Engineering #Computational Physics (physics.comp-ph) #Electromagnetic Scattering and Analysis #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geophysics (physics.geo-ph) #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.math-ph/0702063
openalex publication_date 2007/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article addresses the interpolation of harmonic functions over the interior of a ℝ3 unit sphere by linear combinations of fundamental-solution point-source basis functions, where all the sources are assumed to be outside the sphere. Since the source and field points are in different domains, the fundamental-solution basis functions are bounded and can be regarded as defining a new type of kernel space that is related to reproducing kernel Hilbert space (RKHS), but is different from it and which is labeled a Dirichlet integral dual-access collocation-kernel space (DIDACKS). DIDACKS theory has direct implications for the method of fundamental solutions (MFS) and some for the fast multipole method (FMM) and boundary element method (BEM).