Abstract Liouville’s equation on phase space in geometrical optics describes the evolution of an energy distribution through optical system, which is discontinuous across interfaces. The Galerkin spectral element method conservative and can achieve higher order convergence locally, making it a suitable for this equation. When dealing with interfaces space, non-local boundary conditions arise. B...

In recent years, the importance of economical considerations in the field of dam engineering has motivated many researchers to propose new methods for minimizing the cost of dames and in particular arch dams. This paper presents a method for shape optimization of double curvature arch dams corresponding to minimum construction cost while satisfying different constraints such as natural frequenc...

A powerful method to solve nonlinear first-order ordinary differential equations, which is based on a geometrical understanding of the corresponding dynamics of the so-called Lie systems, is developed. This method enables us not only to solve some of these equations, but also gives geometrical explanations for some, already known, ad hoc methods of dealing with such problems. MSC 2000: 34A26 (P...

Background: The design of intensity modulated radiation therapy (IMRT) plans is difficult and time-consuming. The retrieval of similar IMRT plans from the IMRT plan dataset can effectively improve the quality and efficiency of IMRT plans and automate the design of IMRT planning. However, the large IMRT plans datasets will bring inefficient retrieval result. Materials and Methods: An intensity-m...

This paper describes a method for suppressing spatial conflicts in cartographic generalization of isobathymetric lines. These lines are modeled by parametric curves. For that purpose, we review our preliminary works on the detection of intersections and examine the current methods used for line displacement. We focus on geometrical methods and on a cable network based method and propose a new s...

In this article we propose an original method for discrete surface smoothing. This method is based on a statistical estimation of the discrete tangent plane on the voxels of the discrete surface. A geometrical constraint is used to control the recognition of the tangent plane. The resulting surface representation allows us to get both smooth normal vectors of the surface and a smooth surface me...