# One-parameter tetrahedral mesh generation for spheroids

## TL;DR

This paper presents a simple method for automatically generating tetrahedral meshes of spheroidal domains using a single integer parameter to control refinement, suitable for domains expressible in spherical coordinates.

## Contribution

It introduces a straightforward, parameter-dependent procedure for mesh generation of spheroidal domains, simplifying mesh refinement and element numbering.

## Key findings

- Meshes form a quasi-uniform family as refinement increases
- Method works well for domains with spherical coordinate representations
- Generated meshes are suitable for finite-element or finite-volume methods

## Abstract

This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes depend only on an integer parameter, whose value is associated with the degree of refinement. More specifically the procedure applies to the case where the boundary of a curved three-dimensional domain not so irregular can be expressed in spherical coordinates, with origin placed at a suitable location in its interior. An optimal numbering of mesh elements and nodes can be accomplished very easily. Several examples indicate that the generated meshes form a quasi-uniform family of partitions, as the corresponding value of the integer parameter increases, as long as the domain is not too distorted.