An Introduction to the Topological Derivative Method

DOI10.1007/978-3-030-36915-6zbMath1444.49001OpenAlexW3001596776MaRDI QIDQ5216827

Jan Sokolowski, Antonio André Novotny

Publication date: 20 February 2020

Published in: SpringerBriefs in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-36915-6

zbMATH Keywords

shape optimizationtopological derivativedomain truncation methodperturbed domaintopology design optimizationadjoint sensitivity methodasymptotic expansion of shape functional

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming (90-01) Theories of fracture and damage (74A45) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20) Variational methods for second-order elliptic equations (35J20) Shape theory in general topology (54C56) Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control (49-02) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis (65-01) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control (49-01) Sensitivity analysis for optimization problems on manifolds (49Q12)

Related Items (10)

High Order Topological Asymptotics: Reconciling Layer Potentials and Compound Asymptotic Expansions ⋮ Automated computation of topological derivatives with application to nonlinear elasticity and reaction-diffusion problems ⋮ Geometric aspects of shape optimization ⋮ Identification of an embedded tumor using the thermography process and the topological sensitivity analysis method ⋮ Emergence of elastostatic strain-gradient effects from topological optimization ⋮ Reconstruction of the source term in a time-fractional diffusion equation from partial domain measurement ⋮ Imaging of mass distributions from partial domain measurement ⋮ A phase field method based on multi-level correction for eigenvalue topology optimization ⋮ Topological Derivative of State-Constrained Objective Functions: A Direct Method ⋮ Topology design optimization of nanophotonic devices for energy concentration

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