Research reports

Years: 2026 2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

CUBE: Cubed-Sphere Projection for Adaptive Mesh Generation in Spherical Coordinates

by F. Gatti

(Report number 2026-03)

Abstract
We present \texttt{CUBE}, an open-source Python framework for generating adaptive, non-singular meshes on the sphere using a cubed-sphere projection. The software maps spherical slices to Cartesian faces of an inscribed cube, avoiding the pole singularities inherent to latitude–longitude grids and producing quasi-uniform element sizes across the globe. A core feature of \texttt{CUBE} is error-driven spatial adaptation: the mesh is refined according to an estimator based on an approximation of the \(H^1\)-seminorm of the topography discretization error, which concentrates resolution where terrain gradients are large. The implementation leverages \texttt{numpy} and \texttt{scipy} for efficient array operations, integrates \texttt{gmsh} via its Python API for meshing, and supports standard geospatial input (e.g., GTOPO30 digital elevation models). \texttt{CUBE} is intended as an extensible tool to produce high-quality input meshes for atmospheric and geophysical models, improving accuracy while reducing computational cost through targeted refinement.

Keywords: cubed-sphere projection \sep unstructured meshes \sep adaptive mesh \sep finite elements

@Techreport{G26_1158,
  author = {F. Gatti},
  title = {CUBE: Cubed-Sphere Projection for Adaptive Mesh Generation in Spherical Coordinates},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2026-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2026/2026-03.pdf },
  year = {2026}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).