A D-N alternating algorithm for exterior 3-D problem with ellipsoidal artificial boundary

<abstract><p>In this study, based on a general ellipsoidal artificial boundary, we present a Dirichlet-Neumann (D-N) alternating algorithm for exterior three dimensional (3-D) Poisson problem. By using the series concerning the ellipsoidal harmonic functions, the exact artificial boundary condition is derived. The convergence analysis and the error estimation are carried out for the proposed algorithm. Finally, some numerical examples are given to show the effectiveness of this method.</p></abstract>

Introducing EGM2020

&lt;p&gt;The National Geospatial-Intelligence Agency [NGA], in conjunction with its U.S. and international partners, has completed its next Earth Gravitational Model (EGM2020), to replace EGM2008. The new &amp;#8216;Earth Gravitational Model 2020&amp;#8217; [EGM2020] will retain the same harmonic basis and resolution as EGM2008. As such, EGM2020 will be a ellipsoidal harmonic model up to degree (n) and order (m) 2159, but will be released as a spherical harmonic model to degree 2190 and order 2159. EGM2020 has benefited from new data sources and procedures. Updated satellite gravity information from the GOCE and GRACE mission, will better support the lower harmonics, globally. Multiple new acquisitions (terrestrial, airborne and shipborne) of gravimetric data over specific geographical areas (Antarctica, Greenland &amp;#8230;), will provide improved global coverage and resolution over the land, as well as for coastal and some ocean areas. Ongoing accumulation of satellite altimetry data as well as improvements in the treatment of this data, will better define the marine gravity field, most notably in polar and near-coastal regions. NGA and partners are evaluating different approaches for optimally combining the new GOCE/GRACE satellite gravity models with the terrestrial data. These include the latest methods employing a full covariance adjustment. NGA is also working to assess systematically the quality of its entire gravimetry database, towards correcting biases and other egregious errors where possible, and generating improved error models that will inform the final combination with the latest satellite gravity models. Outdated data gridding procedures have been replaced with improved approaches. For EGM2020, NGA intends to extract maximum value from the proprietary data that overlaps geographically with unrestricted data, whilst also making sure to respect and honor its proprietary agreements with its data-sharing partners.&lt;/p&gt;

Revisiting the Low-Frequency Dipolar Perturbation by an Impenetrable Ellipsoid in a Conductive Surrounding

This contribution deals with the scattering by a metallic ellipsoidal target, embedded in a homogeneous conductive medium, which is stimulated when a 3D time-harmonic magnetic dipole is operating at the low-frequency realm. The incident, the scattered, and the total three-dimensional electromagnetic fields, which satisfy Maxwell’s equations, yield low-frequency expansions in terms of positive integral powers of the complex-valued wave number of the exterior medium. We preserve the static Rayleigh approximation and the first three dynamic terms, while the additional terms of minor contribution are neglected. The Maxwell-type problem is transformed into intertwined potential-type boundary value problems with impenetrable boundary conditions, whereas the environment of a genuine ellipsoidal coordinate system provides the necessary setting for tackling such problems in anisotropic space. The fields are represented via nonaxisymmetric infinite series expansions in terms of harmonic eigenfunctions, affiliated with the ellipsoidal system, obtaining analytical closed-form solutions in a compact fashion. Until nowadays, such problems were attacked by using the very few ellipsoidal harmonics exhibiting an analytical form. In the present article, we address this issue by incorporating the full series expansion of the potentials and utilizing the entire subspace of ellipsoidal harmonic eigenfunctions.