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This article presents a new boundary integral approach for finding optimalshapes of peristaltic pumps that transport a viscous fluid. Formulas forcomputing the shape derivatives of the standard cost functionals andconstraints are derived. They involve evaluating physical variables (traction,pressure, etc.) on the boundary only. By emplyoing these formulas in conjuctionwith a boundary integral approach for solving forward and adjoint problems, wecompletely avoid the issue of volume remeshing when updating the pump shape asthe optimization proceeds. This leads to significant cost savings and wedemonstrate the performance on several numerical examples.

Shape optimization of Stokesian peristaltic pumps using boundary integral methods