Dirichlet integral point-source harmonic interpolation over ${\mathbb{R}}^3$ spherical interiors: DIDACKS II

Abstract

This article addresses the interpolation of harmonic functions over the interior of a ${\mathbb{R}}^3$ 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).

56 pages, no figures

References in corpus (3)

• Evenly distributed unitaries: on the structure of unitary designs
• Dirichlet integral dual-access collocation-kernel space analytic interpolation for unit disks: DIDACKS I
• A Dirichlet-integral based dual-access collocation-kernel approach to point-source gravity-field modleing

Cited by in corpus (4)

• Closed-form Dirichlet integral harmonic interpolation-fits for real n-dimensional and complex half-space: DIDACKS III
• A closed-form energy-minimization basis for gravity field source estimation: DIDACKS IV
• Uniqueness Theorems for Point Source Expansions: DIDACKS V
• Four Properties of Reproducing Kernel Hilbert Spaces