A handy tool for assessing tetrahedron-based finite-cell methods and for numerical simulations in spheroidal domains

Abstract

A straightforward procedure is presented for the generation of finite-cell meshes consisting of tetrahedrons for curved domains, whose boundary can be expressed in spherical coordinates with origin at a suitable location in its interior. Besides the equation of the boundary, the generation of the mesh depends only on an integer parameter, whose value is associated with its degree of refinement. Several examples indicate that the meshes of a given domain form a quasi-uniform family of partitions, as the value of the integer parameter increases. Mesh quality is optimal in the case of a ball but it remains quite correct as the shape of the domain moves away from perfect sphericity, with a gradual but in all natural downgrade. The procedure is a handy tool for an a priori order-checking of a new finite-cell method, as applied to a given type of boundary value problem posed in curved domains. A MATLAB code was developed to implement this tetrahedrization procedure for domains with three symmetry planes.