Shape optimization of radiant enclosures with specular-diffuse surfaces by means of a random search and gradient minimization

Shape optimization as a tool to design biocatalytic microreactors

“…In the scientific literature several methods for optimization problems can be found. Random search is a simple gradient-free optimization method and it has been used and occasionally adopted for shape optimization in mechanical engineering [12,13].…”

Monte-Carlo and sensitivity transport models for domain deformation

“…When the geometric parameter creates a translation of the reflective boundary, other terms appear (not shown). See, for instance, the generalization of reflective sensitivity boundary conditions that have been done in [21] for deterministic method. The four other terms are very similar to the Dirac sources of configuration 2 : they translate in sensitivity terms the intensity discontinuity at the limit of modified boundary.…”

“…Several studies have addressed the question of finding shape derivatives for linear physical models through shape sensitivity analysis [24] . In the field of deterministic approach, [21] propose a generalization of the sensitivity models to the radiative transfer equation with specular and diffuse radiative boundary conditions in order to solve the shape optimization problems. In the present work, we extend the question of evaluating shape derivatives when using the Monte-Carlo method as a method of reference.…”