  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.
