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Fast and robust mesh generation on the sphere Application to coastal domains

Remacle, Jean-François, Jonathan Lambrechts

Proceedings, 25th International Meshing Roundtable, Elsevier, Science Direct, September 26-30 2016

INTERNATIONAL
MESHING
ROUNTABLE

25th International Meshing Roundtable
Washington DC, U.S.A.
September 26-30, 2016

Jean-François Remacle, Université catholique de Louvain, BE, jean-francois.remacle@uclouvain.be
Jonathan Lambrechts, Université catholique de Louvain, BE, jonathan.lambrechts@uclouvain.be

Abstract
This paper presents a fast an robust mesh generation procedure that is able to generate meshes of the earth system (ocean and continent) in matters of seconds. Our algorithm takes as input a standard shape-file i.e. geospatial vector data format for geographic information system (GIS) software. The input is initially coarsened in order to automatically remove unwanted channels that are under a desired resolution. A valid non-overlapping 1D mesh is then created on the sphere using the Euclidian coordinates system $x,y,z$. A modified Delaunay kernel is then proposed that enables to generate meshes on the sphere in a straightforward manner without parametrization. One of the main difficulty in dealing with geographical data is the over-sampled nature of coastline representations. We propose here an algorithm that automatically unrefines coastline data. Small features are automatically removed while always keeping a valid (non-overlapping) geometrical representation of the domain. A Delaunay refinement procedure is subsequently applied to the domain. The refinement scheme is also multi-threaded at a fine grain level, allowing to generate about a million points per second on 8 threads. Examples of meshes of the Baltic sea as well as of the global ocean are presented.

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