Publications

2020

• Shape optimization of Stokesian peristaltic pumps using boundary integral methods
  
  • Bonnet Marc
  • Liu Ruowen
  • Veerapaneni Shravan
  Journal of Computational and Applied Mathematics, Elsevier, 2020, 46, pp.18. 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 employing these formulas in conjunction 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 (10.1007/s10444-020-09761-7)
  DOI : 10.1007/s10444-020-09761-7
• Spectral analysis of polygonal cavities containing a negative-index material
  
  • Hazard Christophe
  • Paolantoni Sandrine
  Annales Henri Lebesgue, UFR de Mathématiques - IRMAR, 2020, 3, pp.1161-1193. The purpose of this paper is to investigate the spectral effects of an interface between vacuum and a negative-index material (NIM), that is, a dispersive material whose electric permittivity and magnetic permeability become negative in some frequency range. We consider here an elementary situation, namely, 1) the simplest existing model of NIM : the non dissipative Drude model, for which negativity occurs at low frequencies; 2) a two-dimensional scalar model derived from the complete Maxwell’s equations; 3) the case of a simple bounded cavity: a polygonal domain partially filled with a portion of Drude material. Because of the frequency dispersion (the permittivity and permeability depend on the frequency), the spectral analysis of such a cavity is unusual since it yields a nonlinear eigenvalue problem. Thanks to the use of an additional unknown, we linearize the problem and we present a complete description of the spectrum. We show in particular that the interface between the NIM and vacuum is responsible for various resonance phenomena related to various components of an essential spectrum. (10.5802/ahl.58)
  DOI : 10.5802/ahl.58