First Steps in the Space Separated Representation of Models Defined in Complex Domains

Abstract

Separated representations allow substituting the resolution of 3D models by a sequence of three one-dimensional problems [1]. This route is especially suitable when models are defined in hexahedral domains. When it is not the case, different possibilities exist. In a former work [2], we explored the route of immersing the domain into a hexahedral domain, and then use a kind of penalty method to solve the model whilst enforcing the boundary conditions. In the present work, we are analyzing two alternative routes. The first one consists of using an inverse technique in order to compute the boundary conditions on the border of the hexahedra in which the complex domain is immersed. The second one consists in solving the model in a regular domain for a number of geometrical parameters considered as extra-coordinates from which we could have access to the solution in any geometry resulting from a choice of those parameters.