{"paper":{"title":"A Combination of Downward Continuation and Local Approximation for Harmonic Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian Gerhards","submitted_at":"2013-12-20T08:56:37Z","abstract_excerpt":"This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere $\\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available data on a sphere $\\Omega_r$ of radius $r<R$ (e.g., the spherical Earth's surface). The approximation is based on a two-step algorithm motivated by spherical multiscale expansions: First, a convolution with a scaling kernel $\\Phi_N$ deals with the downward continuation from $\\Omega_R$ to $\\Omega_r$, while in a second step, the result is locally refined by a convolution on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5856","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}