Automated computation of topological derivatives with application to nonlinear elasticity and reaction–diffusion problems

نویسندگان

چکیده

While topological derivatives have proven useful in applications of topology optimization and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, particular the context nonlinear partial differential equation (PDE) constraints. We present a systematic yet formal approach for numerical computation large class PDE-constrained problems with respect to arbitrary inclusion shapes. Scalar vector-valued as well linear elliptic PDE constraints are considered two three space dimensions including elasticity model reaction–diffusion problems. The procedure follows Lagrangian computing derivatives. For where exact formula is known, numerically computed values show good coincidence. Moreover, by inserting into asymptotic expansion, we verify that obtained satisfy expected behavior also other, previously unknown indicating correctness procedure.

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Topological Derivatives in Plane Elasticity

We present a method for construction of the topological derivatives in plane elasticity. It is assumed that a hole is created in the subdomain of the elastic body which is filled out with isotropic material. The asymptotic analysis of elliptic boundary value problems in singularly perturbed geometrical domains is used in order to derive the asymptotics of the shape functionals depending on the ...

متن کامل

a comparison of teachers and supervisors, with respect to teacher efficacy and reflection

supervisors play an undeniable role in training teachers, before starting their professional experience by preparing them, at the initial years of their teaching by checking their work within the proper framework, and later on during their teaching by assessing their progress. but surprisingly, exploring their attributes, professional demands, and qualifications has remained a neglected theme i...

15 صفحه اول

construction and validation of translation metacognitive strategy questionnaire and its application to translation quality

like any other learning activity, translation is a problem solving activity which involves executing parallel cognitive processes. the ability to think about these higher processes, plan, organize, monitor and evaluate the most influential executive cognitive processes is what flavell (1975) called “metacognition” which encompasses raising awareness of mental processes as well as using effectiv...

Inequality Problems of Equilibrium Problems with Application

This paper aims at establishing the existence of results for a nonstandard equilibrium problems $(EP_{N})$. The solutions of this inequality are discussed in a subset $K$ (either bounded or unbounded) of a Banach spaces $X$. Moreover, we enhance the main results by application of some differential inclusion.

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

ژورنال

عنوان ژورنال: Computer Methods in Applied Mechanics and Engineering

سال: 2022

ISSN: ['0045-7825', '1879-2138']

DOI: https://doi.org/10.1016/j.cma.2022.115288