Incorporating Topological Derivatives into Level Set Methods

نویسندگان

  • Martin Burger
  • Benjamin Hackl
چکیده

The aim of this paper is to investigate the use of topological derivatives in combination with the level set method for shape reconstruction and optimization problems. We propose a new approach generalizing the standard speed method, which is obtained by using a source term in the level set equation that depends on the topological derivative of the objective functional. The resulting approach can be interpreted as a generalized fixed-point iteration for the optimality system (with respect to topological and shape variations). Moreover, we apply the new approach for a simple model problem in shape reconstruction, where the topological derivative can be computed without additional effort. Finally, we present numerical tests related to this model problem, which demonstrate that the new method based on shape and topological derivative successfully reconstructs obstacles in situations where the standard level set approach fails.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Incorporating topological derivatives into shape derivatives based level set methods

Shape derivatives and topological derivatives have been incorporated into level set methods to investigate shape optimization problems. The shape derivative measures the sensitivity of boundary perturbations while the topological derivative measures the sensitivity of creating a small hole in the interior domain. The combination of these two derivatives yields an efficient algorithm which has m...

متن کامل

QSPR study on benzene derivatives to some physico-chemical properties by using topological indices

QSPR study on benzene derivatives have been made using recently introduced topological methodology. In this study the relationship between the Randic' (x'), Balaban (J), Szeged (Sz),Harary (H), Wiener (W), HyperWiener and Wiener Polarity (WP) to the thermal energy (Eth), heat capacity (CV) and entropy (S) of benzene derivatives is represented. Physicochemical properties are taken from the quant...

متن کامل

ISOGEOMETRIC TOPOLOGY OPTIMIZATION OF STRUCTURES USING LEVEL SET METHOD INCORPORATING SENSITIVITY ANALYSIS

This study focuses on the topology optimization of structures using a hybrid of level set method (LSM) incorporating sensitivity analysis and isogeometric analysis (IGA). First, the topology optimization problem is formulated using the LSM based on the shape gradient. The shape gradient easily handles boundary propagation with topological changes. In the LSM, the topological gradient method as ...

متن کامل

SOLVING MULTI CONSTRAINTS STRUCTURAL TOPOLOGY OPTIMIZATION PROBLEM WITH REFORMULATION OF LEVEL SET METHOD

Due to the favorable performance of structural topology optimization to create a proper understanding in the early stages of design, this issue is taken into consideration from the standpoint of research or industrial application in recent decades. Over the last three decades, several methods have been proposed for topology optimization. One of the methods that has been effectively used in stru...

متن کامل

The use of topological indices to predict thermodynamic properties of amino acids derivatives

In the present investigation the applicability of various topological indices are tested for the QSPR study on 80 amino acids derivatives. Relationship between the Randic' (1X), Balaban (J), Szeged (Sz), Harary (H), Wiener (W), Hyper-Wiener (WW) and Wiener Polarity (WP) indices to the thermodynamic Properties such as thermal energy Eth (J/mol) and heat capacity (CV J/mol. K) of amino acids is r...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003