3D-1D coupling on non conforming meshes via three-field optimization based domain decomposition

TL;DR

This paper introduces a robust and flexible numerical method for simulating coupled 3D-1D elliptic equations, enabling independent meshing and accurate interface matching in complex geometries.

Contribution

It presents a novel three-field optimization-based domain decomposition approach for 3D-1D coupling on non-conforming meshes, improving flexibility and robustness.

Findings

Allows independent meshing of subdomains

Ensures accurate interface matching via functional minimization

Handles complex geometries effectively

Abstract

A new numerical approach is proposed for the simulation of coupled three-dimensional and one-dimensional elliptic equations (3D-1D coupling) arising from dimensionality reduction of 3D-3D problems with thin inclusions. The method is based on a well posed mathematical formulation and results in a numerical scheme with high robustness and flexibility in handling geometrical complexities. This is achieved by means of a three-field approach to split the 1D problems from the bulk 3D problem, and then resorting to the minimization of a properly designed functional to impose matching conditions at the interfaces. Thanks to the structure of the functional, the method allows the use of independent meshes for the various subdomains.