Work

A novel metric-based anisotropic mesh adaptation algorithm for 3D periodic domains

Year: 2025

Type: article

Abstract: We present a novel metric-based anisotropic mesh adaptation algorithm, named 3 DPAMA , to be employed for discretization of three-dimensional periodic domains. The proposed method – based on mathematically rigorous assumptions – utilizes established techniques for unconstrained anisotropic mesh adaptation and resorts to localized manipulations on the external boundary of the mesh. In particular, the scheme comprises four steps: (i) a non-periodic initial mesh adaptation, (ii) the splitting of the obtained volumetric grid into interior and exterior tessellations, (iii) minimal local operations to yield a periodic external surface, and (iv) the assembly of the final adapted grids. To demonstrate the robustness, efficacy, and flexibility of the proposed methodology, 3 DPAMA algorithm is employed in a continuous finite element setting to tackle test cases established in the literature as well as challenging scenarios that involve various periodic requirements, domain geometries, and isotropic and anisotropic metric fields. Finally, 3 DPAMA is employed in a practical use case where mesh adaptation is tightly coupled with the solution of a time-dependent partial differential equation.

Source: Mathematics and Computers in Simulation

DOI: 10.1016/j.matcom.2025.11.034

Authors: Giacomo Speroni, Nicola Ferro

Institutions: Politecnico di Milano, Ca' Foscari University of Venice

Language: English

Topic: Computational Geometry and Mesh Generation

Subfield: Computer Graphics and Computer-Aided Design

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,170

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Gruppo Nazionale per il Calcolo Scientifico