# Shape optimization of Stokesian peristaltic pumps using boundary integral methods

## TL;DR

This paper introduces a boundary integral method for optimizing the shape of peristaltic pumps that transport viscous fluids, enabling efficient shape updates without volume remeshing and demonstrating improved performance through numerical examples.

## Contribution

It develops a boundary integral approach for shape optimization of Stokesian peristaltic pumps, deriving shape derivatives and avoiding volume remeshing during optimization.

## Key findings

- Significant cost savings in shape optimization process.
- Effective boundary integral formulas for shape derivatives.
- Successful numerical demonstrations of optimized pump shapes.

## Abstract

This article presents a new boundary integral approach for finding optimal shapes of peristaltic pumps that transport a viscous fluid. Formulas for computing the shape derivatives of the standard cost functionals and constraints are derived. They involve evaluating physical variables (traction, pressure, etc.) on the boundary only. By emplyoing these formulas in conjuction with a boundary integral approach for solving forward and adjoint problems, we completely avoid the issue of volume remeshing when updating the pump shape as the optimization proceeds. This leads to significant cost savings and we demonstrate the performance on several numerical examples.