Isogeometric analysis (IGA) has been recently introduced as a viable alternative to the standard, polynomial-based finite element analysis. One of the fundamental performance issues of the isogeometric analysis is the quadrature of individual components of the discretized governing differential equation. The capability of the isogeometric analysis to easily adopt basis functions implies that high order numerical quadrature schemes must be employed. This may become computationally prohibitive because the evaluation of the high degree basis functions and/or their derivatives at individual integration points is quite demanding. The situation tends to be critical in three-dimensional space where the total number of integration points can increase dramatically. The aim of this paper is to compare computational efficiency of several numerical quadrature concepts which are nowadays available in the isogeometric analysis. Their performance is asessed on the assembly of stifness matrix of B-spline based problems with special geometrical arrangement allowing to determine minimum number of integration points leading to exact results. and Článek zahrnuje seznam literatury a na str. 257-259 Appendix
In this paper, the algorithm for the discretization of 3D domains into tetrahedral boundary conforming meshes is presented. The algorithm is based on the Delaunay triangulation with special point ordering. The conformity of the resulting mesh with the initial triangulation of the domain boundary is ensured a priori thus the boundary recovery postprocessing step is eliminated. The constrained Delaunay triangulation of the boundary points is obtained using modified Watson's point insertion algorithm. The actual appearance of boundary faces in the final triangulation is achieved by the form of an oriented graph, of the violation of the empty-sphere property of all boundary faces. The cycle dependencies (closed loops in the graph) are eliminated by using the nodal perturbations, by classification of some of the violations as safe and (as the last resort) by forming a new tetrahedron using the advancing front technique. Once all the cyclic dependencies are eliminated, the point insertion process controlled by the dependency graph is started and the constrained Delaunay triangulation of the boundary points is built. In the next phase, additional points are inserted in the interior of the domain, while preserving the boundary constraints, to make the elements of appropriate size with aspect ratio close to one. The resulting mesh is then subjected to optimization in terms of the combination of Laplacian smoothing and topological transformations, in order to remove the potential slivers and to improve the overall mesh quality. and Obsahuje seznam literatury
Isogeometric analysis is a quickly emerging alternative ot the standard, polynomial-based finite element analysis. It is only the question of time, when it will be implemented into major software packages and will be intensively used by engineering community to the analysis of complex realistic problems. Computational demands of such analyses, that may likely exceed the capacity of a single computerk can be parallel processing requires usuall an appropriate decomposition of the investigated problem to the individual processing units. In the case of he isogeometric analysis, the decomposition corresponds to the spatial partitioning of the underlying spatial discretization. While there are several matured graphs-based decomposers which can be readily applied to the subdivison of finite element meshes, their use in the context of the isogeometric analysis is not straightforward because of a rather complicated construction of the graph corresponding to the computational isogeometric mesh. In this paper, a new technology for the construction of the dual graph of a two-dimensional NURBS-based (non-uniform rational B-spline) isogeometric mesh is introduced. This makes the partitioning of the isogeometric meshes for parallel processing accessible for the standard graph-based partitioning of the isogeometric meshes for parallel processing accessible for the standard graph-based partitioning approaches. and Obsahuje seznam literatury