The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski andŻochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Abstract. In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.
Abstract-In this paper, a method for calculating the importance factor of continuous features from a given set of patterns is presented. A real problem in many practical cases, like medical data, is to find which parts of patterns are crucial for correct classification. This leads to the need of preprocessing all data, which has influence on both time and accuracy of applied methods (when unimportant data hide those which are important). There are some methods that allow selection of important features for binary and sometimes discrete data or, after some preprocessing, continuous data. Very often however, such conversion is burdened with the risk of losing important data, which is a result of lack of knowledge of optimal discretization consequence. Proposed method allows to avoid that problem, because it is based on original, non-transformed continuous data. Two factors -concentration and diversity -are defined and are used to calculate the importance factor for each feature and pattern. Based on those factors e.g. unimportant features can be identified to decrease dimension of input data or ''bad'' patterns can be detected to improve classification. An example how proposed method can be used to improve decision tree is given as well.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.