Multithread parallelization of lepp-bisection algorithms

[EN]Longest edge (nested) algorithms for triangulation refinement in two dimensions are able to produce hierarchies of quality and nested irregular triangulations as needed both for adaptive finite element methods and for multigrid methods. They can be formulated in terms of the longest edge propagation path (Lepp) and terminal edge concepts, to refine the target triangles and some related neighbors. We discuss a parallel multithread algorithm, where every thread is in charge of refining a triangle t and its associated Lepp neighbors. The thread manages a changing Lepp(t) (ordered set of increasing triangles) both to find a last longest (terminal) edge and to refine the pair of triangles sharing this edge...

Some advances in open problems of isogeometric analysis

[EN]Isogeometric analysis (IGA) has arisen as an attempt to unify the fields of CAD and classical finite element methods. The main idea of IGA consists in using for analysis the same functions (splines) that are used in CAD representation of the geometry. The main advantage with respect to the traditional finite element method is a higher smoothness of the numerical solution and more accurate representation of the geometry. IGA seems to be a promising tool with wide range of applications in engineering. However, this relatively new technique have some open problems that require a solution. In this work we present our results and contributions to this issue…