A Mollification Approach to Ramified Transport and Tree Shape Optimization

TL;DR

This paper introduces a mollification algorithm for numerically computing optimal irrigation patterns, providing regularization and convergence results, and applies it to optimize tree root and branch shapes.

Contribution

It develops a mollification-based regularization method for irrigation cost functionals and demonstrates its effectiveness in shape optimization problems.

Findings

Proved lower semicontinuity and Gamma-convergence of the mollified functional.

Successfully applied the method to optimize tree root and branch shapes.

Provided a regularized framework for numerical computation of irrigation patterns.

Abstract

The paper analyzes a mollification algorithm, for the numerical computation of optimal irrigation patterns. This provides a regularization of the standard irrigation cost functional, in a Lagrangian framework. Lower semicontinuity and Gamma-convergence results are proved. The technique is then applied to some numerical optimization problems, related to the optimal shape of tree roots and branches.