Senior Researcher at the
National Laboratory for Scientific Computing

Antonio André Novotny

I am Senior Researcher at the National Laboratory for Scientific Computing, Petrópolis, Brazil. I have been trained as a mechanical engineer and applied mathematician. My field of specialization is topological asymptotic expansions of shape functionals with PDEs constraints in singularly perturbed geometrical domains. The main topic of current research is the theoretical development and application of the topological derivative method to shape and topology optimization, inverse problems, image processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena. CV Lattes: http://lattes.cnpq.br/8102993969523532

Books

An Introduction to the Topological Derivative Method

A.A. Novotny & J. Sokolowski. SpringerBriefs in Mathematics. Springer Nature, Switzerland, 2020. https://www.springer.com/gp/book/9783030369149

Applications of the Topological Derivative Method

A.A. Novotny, J. Sokolowski & A. Zochowski. Studies in Systems, Decision and Control Series. Springer Nature, Switzerland, 2019. https://www.springer.com/gp/book/9783030054311

Topological Derivatives in Shape Optimization

A.A. Novotny & J. Sokolowski. Interaction of Mechanics and Mathematics Series. Springer-Verlag, Berlin, Heidelberg, 2013. https://www.springer.com/gp/book/9783642352447

Análise de Sensibilidade Topológica: Teoria e Aplicações

A.A. Novotny & J. Sokolowski. Notas em Matemática Aplicada. SBMAC, 2014. https://arquivo.sbmac.org.br/arquivos/notas/livro_73.pdf

Papers

A new micro-seismic model for fault reconstruction in Reissner-Mindlin plates

A.A.M. da Silva and A.A. Novotny. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 45(10):536, 2023.

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Reconstruction of the source term in a time-fractional diffusion equation from partial domain measurement

M. Hrizi, A.A. Novotny & R. Prakash. Journal of Geometrical Analysis, 33:168, 2023.

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Emergence of elastostatic strain-gradient effects from topological optimization

V. Calisti, A. Lebée, A.A. Novotny & J. Sokolowski. European Journal of Mechanics, A/Solids, 100:104979, 2023.

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Reconstruction of pointwise sources in a time-fractional diffusion equation

M. Hrizi, M. Hassine & A.A. Novotny. Fractional Calculus and Applied Analysis Journal, 26(1):193-219, 2023.

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Imaging of mass distributions from partial domain measurement

M. Hrizi, A.A. Novotny & M. Hassine. Journal of inverse and ill-posed problems, 30(5):713-727, 2022.

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On the robustness of the topological derivative for Helmholtz problems and applications

G. Leugering, A.A. Novotny and J. Sokolowski. Control and Cybernetics, 51(2):227-248, 2022.

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A Hybrid Sequential Scheme for Brittle Hydraulic Fractures in Poroelastic Media

J.M.M. Luz Filho, M. Xavier, M.A. Murad & A.A. Novotny. International Journal for Multiscale Computational Engineering, 20(3):99-123, 2022.

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Aggregation and regularization schemes: a probabilistic point of view

A.J. Torii, J.R. de Faria & A.A. Novotny. Structural and Multidisciplinary Optimization, 65(3):76, 2022.

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Guest Editorial: On the topological derivative method and its applications in computational engineering

A.A. Novotny, S.M. Giusti, and S. Amstutz. Engineering Computations, 39(1):1-2, 2022.

Open access at https://doi.org/10.1108/EC-02-2022-759

Damage identification in plate structures based on the topological derivative method

A.A.M. da Silva & A.A. Novotny. Structural and Multidisciplinary Optimization, 65(1):7, 2022.

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Topology Design Optimization of Nanophotonic Devices for Energy Concentration

R. Mattoso, L.H. Gabrielli & A.A. Novotny. Applied Mathematical Modelling, 104:517-530, 2022.

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A Noniterative Reconstruction Method for Solving a Time-Fractional Inverse Source Problem from Partial Boundary Measurement

R. Prakash, M. Hrizi & A.A. Novotny. Inverse Problems, 38(1):015002, 2022.

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Sensitivity of the second order homogenized elasticity tensor to topological microstructural changes

V. Calisti, A. Lebée, A.A. Novotny & J. Sokolowski. Journal of Elasticity, 144:141-167, 2021.

Open access at https://doi.org/10.1007/s10659-021-09836-6

A priori error estimates for local reliability-based sensitivity analysis with Monte Carlo Simulation

A.J. Torii & A.A. Novotny, Reliability Engineering & System Safety, 213:107749, 2021.

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Topological Derivative-Based Topology Optimization of Plate Structures under Bending Effects

F. Carvalho, D. Ruscheinsky, S.M. Giusti, C. Anflor & A.A. Novotny. Structural and Multidisciplinary Optimization, 63(2):617-630, 2021.

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Topological Derivative-Based Topology Optimization of Structures Subject to Self-Weight Loading

A.A. Novotny, C.G. Lopes & R.B. Santos. Structural and Multidisciplinary Optimization, 63(4):1853-1861, 2021.

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Pollution sources reconstruction based on the topological derivative method

L. Fernandez, A.A. Novotny, R. Prakash & J. Sokolowski. Applied Mathematics & Optimization, 84:1493-1525, 2021

Open access at https://doi.org/10.1007/s00245-020-09685-0

On the Kohn-Vogelius Formulation for Solving an Inverse Source Problem

P. Menoret, M. Hrizi & A.A. Novotny. Inverse Problems in Science and Engineering, 29(1):56-72, 2021

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Topological asymptotic analysis of a diffusive-convective-reactive problem

D. Ruscheinsky, F. Carvalho, C. Anflor & A.A. Novotny. Engineering Computations, 38(1):477-500, 2021

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Pointwise Antennas Design in Hyperthermia Therapy

R. Mattoso & A.A. Novotny. Applied Mathematical Modelling, 89:89-104, 2021

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On the full-waveform inversion of seismic moment tensors

A.A.S. Amad, A.A. Novotny & B.B. Guzina. International Journal of Solids and Structures, 202(1):717-728, 2020

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Growth control of cracks under contact conditions based on the topological derivative of the Rice's integral

M. Xavier, A. A. Novotny & J. Sokolowski. Control and Cybernetics, 48(2):307-323, 2020

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Hydro-mechanical fracture modelling governed by topological derivatives

M. Xavier, N. Van Goethem & A. A. Novotny. Computer Methods in Applied Mechanics and Engineering, 365:112974, 2020

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Topology Design of Thermomechanical Actuators Combined with Heat Source Optimization

S.M. Giusti, Z. Mróz, A.A. Novotny & J. Sokolowski. Pure and Applied Functional Analysis, 4(4):825-848, 2019

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Relation Between Eshelbyan Mechanics and Topological Derivative Concept

M. Xavier, A. A. Novotny & J. Sokolowski. In: H. Altenbach & A. Öchsner (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg, 2019

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Optimization of the Electromagnetic Scattering Problem Based on the Topological Derivative Method

J.L. Pita Ruiz, A.A.S. Amad, L.H. Gabrielli & A.A. Novotny. Optics Express, 27(23):33586-33605, 2019

Open access at https://doi.org/10.1364/OE.27.033586

A Noniterative Reconstruction Method for the Inverse Potential Problem with Partial Boundary Measurements

L. Fernandez, A.A. Novotny & R. Prakash. Mathematical Methods in the Applied Sciences, 42(7):2256-2278, 2019

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Topological Derivatives of Shape Functionals. Part I: Theory in Singularly Perturbed Geometrical Domains

A.A. Novotny, J. Sokolowski & A. Zochowski. Journal of Optimization Theory and Applications, 180(2):341-373, 2019

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Topological Derivatives of Shape Functionals. Part II: First Order Method and Applications

A.A. Novotny, J. Sokolowski & A. Zochowski. Journal of Optimization Theory and Applications, 180(3):683-710, 2019

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Topological Derivatives of Shape Functionals. Part III: Second Order Method and Applications

A.A. Novotny, J. Sokolowski & A. Zochowski. Journal of Optimization Theory and Applications, 181(1):1-22, 2019

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Crack Growth Control Based on the Topological Derivative of the Rice’s Integral

M. Xavier, A. A. Novotny & J. Sokolowski. Journal of Elasticity, 134(2):175-191, 2019

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An Adjoint-Based Optimization Method for Gas Production in Shale Reservoirs

A.A. Novotny, M.A. Murad & S. Lima. Acta Geotechnica, 13(4): 833-852, 2018

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Topological Asymptotic Analysis of an Optimal Control Problem Modeled by a Coupled System

L. Fernandez, A.A. Novotny & R. Prakash. Asymptotic Analysis, 109(1-2):1-26, 2018

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Homogenized Couple Stress Model of Optimal Auxetic Structures Computed by Topology Optimization

J.F. Ganghoffer, I. Goda, A.A. Novotny, R. Rahouadj & J. Sokolowski. Journal of Applied Mathematics and Mechanics, 98(5):696-717, 2018

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A Noniterative Reconstruction Method for an Inverse Potential Problem Modeled by a Modified Helmholtz Equation

L. Fernandez, A.A. Novotny & R. Prakash. Numerical Functional Analysis and Optimization, 39(9):937-966, 2018

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Fast Solution of the Inverse Electromagnetic Casting Problem

T.J. Machado, A. Canelas, A.A. Novotny & J.R. Roche. Structural and Multidisciplinary Optimization, 57(6): 2447-2455, 2018

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A Simplified Model of Fracking Based on the Topological Derivative Concept

M. Xavier, N. Van Goethem & A. A. Novotny. International Journal of Solids and Structures, 139-140:211-223, 2018

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Reliability Based Topology Optimization of Structures under Stress Constraints

R.B Santos, A.J. Torii & A.A. Novotny. International Journal for Numerical Methods in Engineering, 114:660-674, 2018

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Design Optimization of Laminar Flow Machine Rotors Based on the Topological Derivative Concept

L.F.N. Sá, A.A. Novotny, J.S. Romero & E.C.N. Silva. Structural and Multidisciplinary Optimization, 56(5):1013–1026, 2017

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Asymptotic Analysis of Variational Inequalities with Applications to Optimum Design in Elasticity

C. G. Lopes, R. B. Santos, A. A. Novotny & J. Sokolowski. Asymptotic Analysis, 102 (3-4):227-242, 2017

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Topological Derivative-Based Topology Optimization of Structures Subject to Design-Dependent Hydrostatic Pressure Loading

M. Xavier & A.A. Novotny. Structural and Multidisciplinary Optimization, 56(1):47-57, 2017

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Structural weight minimization under stress constraints and multiple loading

R.B. dos Santos, C.G. Lopes & A.A. Novotny. Mechanics Research Communication, 81:44-50, 2017

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Topological Derivative-Based Fracture Modelling in Brittle Materials: A Phenomenological Approach

M. Xavier, E.A. Fancello, J.M.C. Farias, N. Van Goethem & A.A. Novotny. Engineering Fracture Mechanics, 179:13-27, 2017

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Obstacles Reconstruction from Partial Boundary Measurements Based on the Topological Derivative Concept

S.S. Rocha & A.A. Novotny. Structural and Multidisciplinary Optimization, 55(6):2131-2141, 2017

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Topology Design of Thermomechanical Actuators

S.M. Giusti, Z. Mróz, A.A. Novotny & J. Sokolowski. Structural and Multidisciplinary Optimization, 55(5):1575-1587, 2017

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A New One-Shot Pointwise Source Reconstruction Method

T.J. Machado, J.S. Angelo & A.A. Novotny. Mathematical Methods in the Applied Sciences, 40(5):1367-1381, 2017

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A New Non-Iterative Reconstruction Method for the Electrical Impedance Tomography Problem

A.D. Ferreira & A.A. Novotny. Inverse Problems, 33(3):035005, 2017

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A New Method for Topology Design of Electromagnetic Antennas in Hyperthermia Therapy

A.A.S. Amad, A.F.D. Loula & A.A. Novotny. Applied Mathematical Modelling, 42:209-222, 2017

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Topology Design of Compliant Mechanisms with Stress Constraints Based on the Topological Derivative Concept

C.G. Lopes & A.A. Novotny. Structural and Multidisciplinary Optimization, 54(4):737-746, 2016

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Topological Derivatives Applied to Fluid Flow Channel Design Optimization Problems

L. Sá, R. Amigo, A.A. Novotny & E.C.N. Silva. Structural and Multidisciplinary Optimization, 54(2):249-264, 2016

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Robust Compliance Topology Optimization Based on the Topological Derivative Concept

A.J. Torii, A.A. Novotny & R.B Santos. International Journal for Numerical Methods in Engineering, 106(11):889-903, 2016

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Topological Derivative Method for Electrical Impedance Tomography Problems

A. D. Ferreira, A. A. Novotny & J. Sokolowski. Informatyka Automatyka Pomiary, 6(2):4-8, 2016

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Energy Change to Insertion of Inclusions Associated with a Diffusive/Convective Steady-State Heat Conduction Problem

A.A. Novotny & V. Sales. Mathematical Methods in the Applied Sciences, 39(5):1233-1240, 2016

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Optimum Design of Flextensional Piezoelectric Actuators into Two Spatial Dimensions

R. Amigo, S.M. Giusti, A.A. Novotny, E.C.N. Silva & J. Sokolowski. SIAM Journal on Control and Optimization, 54(2):760-789, 2016

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A New Reconstruction Method for the Inverse Source Problem from Partial Boundary Measurements

A. Canelas, A. Laurain & A.A. Novotny. Inverse Problems, 31(7):075009, 2015

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Topological derivative-based topology optimization of structures subject to multiple load-cases

C.G. Lopes, R.B. Santos & A.A. Novotny. Latin American Journal of Solids and Structures, 12(5): 834-860, 2015

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Energy Change to Insertion of Inclusions Associated with the Reissner-Mindlin Plate Bending Model

V. Sales, A.A. Novotny & J. Muñoz-Rivera. International Journal of Solids and Structures, 59:132-139, 2015

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Design of bi-metallic devices based on the topological derivative concept

S.M. Giusti & A.A. Novotny. Mechanics Research Communications, 65:1-8, 2015

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Topology Design of Inductors in Electromagnetic Casting Using Level-Sets and Second Order Topological Derivatives

A. Canelas, A.A. Novotny & J.R. Roche. Structural and Multidisciplinary Optimization, 50(6):1151-1163, 2014

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Topology Design of Plates Considering Different Volume Control Methods

D.E. Campeão, S.M. Giusti & A.A. Novotny. Engineering Computations, 31(5):826-842, 2014

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Minimal Partitions and Image Classification Using a Gradient-Free Perimeter Approximation

S. Amstutz, A.A. Novotny & N. Van Goethem. Inverse Problems and Imaging, 8(2):361-387, 2014

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A New Reconstruction Method for the Inverse Potential Problem

A. Canelas, A. Laurain & A.A. Novotny. Journal of Computational Physics, 268:417-431, 2014

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Topological Sensitivity Analysis for Elliptic Differential Operators of Order 2m

S. Amstutz, A.A. Novotny & N. Van Goethem. Journal of Differential Equations, 256:1735-1770, 2014

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Sensitivity of a General Class of Shape Functional to Topological Changes

A.A. Novotny. Mechanics Research Communications, 51:1-7, 2013

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Strain Energy Change to the Insertion of Inclusions Associated to a Thermo-Mechanical Semi-Coupled System

S.M. Giusti, A.A. Novotny, J. Muñoz-Rivera & J. Esparta Rodriguez. International Journal of Solids and Structures, 50(9):1303-1313, 2013

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Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem

S.M. Giusti & A.A. Novotny. Mechanics Research Communications, 46:26-33, 2012

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Topological derivative-based topology optimization of structures subject to Drucker-Prager stress constraints

S. Amstutz, A.A. Novotny & E.A. de Souza Neto. Computer Methods in Applied Mechanics and Engineering, 233–236:123–136, 2012

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Second-Order Topological Expansion for Electrical Impedance Tomography

M. Hintermüller, A. Laurain & A.A. Novotny. Advances in Computational Mathematics, 36(2):235-265, 2012

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Topological Asymptotic Analysis of the Kirchhoff Plate Bending Problem

S. Amstutz & A.A. Novotny. ESAIM:COCV, Control, Optimisation and Calculus of Variations, 17(3):705-721, 2011

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On Shape Optimization for an Evolution Coupled System

G. Leugering, A.A. Novotny, G. Perla Menzala & J. Sokolowski. Applied Mathematics & Optimization, 64:441-466, 2011

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A New Method for Inverse Electromagnetic Casting Problems Based on the Topological Derivative

A. Canelas, A.A. Novotny & J.R. Roche. Journal of Computational Physics, 230:3570-3588, 2011

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Shape Sensitivity Analysis of a Quasi-Eletrostatic Piezoelectric System in Multilayered Media

G. Leugering, A.A. Novotny, G. Perla Menzala & J. Sokolowski. Mathematical Methods in the Applied Sciences, 33(17):2118–2131, 2010

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Crack Nucleation Sensitivity Analysis

N. Van Goethem & A.A. Novotny. Mathematical Methods in the Applied Sciences, 33(16):1978–1994, 2010

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Topological derivative for multi-scale linear elasticity models applied to the synthesis of microstructures

S. Amstutz, S.M. Giusti, A.A. Novotny & E.A. de Souza Neto. International Journal for Numerical Methods in Engineering, 84:733–756, 2010

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Topological Derivative-Based Optimization of Micro-Structures Considering Different Multi-Scale Models

E.A. de Souza Neto, S. Amstutz, S.M. Giusti & A.A. Novotny. Computer Modeling in Engineering and Sciences, 62(1):23-56, 2010

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Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions

S.M. Giusti, A.A. Novotny & E.A. de Souza Neto. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466:1703–1723, 2010

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Topological optimization of structures subject to von Mises stress constraints

S. Amstutz & A.A. Novotny. Structural and Multidisciplinary Optimization, 41(3):407–420, 2010

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Topological Sensitivity Analysis of a Multi-Scale Constitutive Model Considering a Cracked Microstructure

A.A. Novotny, J. Sokolowski & E.A. de Souza Neto. Mathematical Methods in the Applied Sciences, 33(5):676-686, 2010

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Topological Derivative for Steady-State Orthotropic Heat Diffusion Problem

S.M. Giusti, A.A. Novotny & J. Sokolowski. Structural and Multidisciplinary Optimization, 40(1):53-64, 2010

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Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions

A.M. Khludnev, A.A. Novotny, J. Sokolowski & A. Zochowski. Journal of the Mechanics and Physics of Solids, 57(10):1718-1732, 2009

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On the Second Order Topological Asymptotic Expansion

J. Rocha de Faria & A.A. Novotny. Structural and Multidisciplinary Optimization, 39(6):547–555, 2009

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On topological derivatives for elastic solids with uncertain input data

I. Hlavacek, A.A. Novotny, J. Sokolowski & A. Zochowski. Journal of Optimization Theory and Applications, 141(3):569-595, 2009

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First and Second Order Topological Sensitivity Analysis for Inclusions

J. Rocha de Faria, A.A. Novotny, R.A. Feijóo & E. Taroco. Inverse Problems in Science and Engineering, 17(5):665–679, 2009

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A Simple Method for Tomography Reconstruction

I. Larrabide, A.A. Novotny, R.A. Feijóo & R. de Souza Leão Lima. Inverse Problems in Science and Engineering, 17(3):365-380, 2009.

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Sensitivity of the Macroscopic Elasticity Tensor to Topological Microstructural Changes

S.M. Giusti, A.A. Novotny, E.A. de Souza Neto & R.A. Feijóo. Journal of the Mechanics and Physics of Solids, 57(3):555-570, 2009

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Sensitivity of the Macroscopic Thermal Conductivity Tensor to Topological Microstructural Changes

S.M. Giusti, A.A. Novotny, E.A. de Souza Neto & R.A. Feijóo. Computer Methods in Applied Mechanics and Engineering, 198(5-8):727-739, 2009

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Topological Sensitivity Analysis for Inclusions in Two-dimensional Linear Elasticity Problem

S.M. Giusti, A.A. Novotny & C. Padra. Engineering Analysis with Boundary Elements, 32(11):926-935, 2008

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Topological Derivative: A Tool for Image Processing

I. Larrabide, R.A. Feijóo, A.A. Novotny & E.A. Taroco. Computers & Structures, 86(13-14):1386-1403, 2008

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Second Order Topological Sensitivity Analysis

J. Rocha de Faria, A.A. Novotny, R.A. Feijóo, E. Taroco & C. Padra. International Journal of Solids and Structures, 44(14-15):4958-4977, 2007

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Topological Sensitivity Analysis for Three-dimensional Linear Elasticity Problem

A.A. Novotny, R.A. Feijóo, E. Taroco & C. Padra. Computer Methods in Applied Mechanics and Engineering, 196(41-44):4354-4364, 2007

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Topological Derivative for Linear Elastic Plate Bending Problems

A.A. Novotny, R.A. Feijóo, C. Padra & E. Taroco. Control and Cybernetics, 34(1):339-361, 2005

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Topological Sensitivity Analysis

A.A. Novotny, R.A. Feijóo, E. Taroco & C. Padra. Computer Methods in Applied Mechanics and Engineering, 192(7-8):803-829, 2003

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The Topological Derivative for the Poisson's Problem

R.A. Feijóo, A.A. Novotny, E. Taroco & C. Padra. Mathematical Models and Methods in Applied Sciences, 13(12):1825-1844, 2003

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A Fast hp Adaptive Finite Element Mesh Design

A.A. Novotny, J. Tomás Pereira, E.A. Fancello & C.S. Barcellos. Computer Methods in Applied Mechanics and Engineering, 190(1-2):133-148, 2000

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MatLab Codes

Compliance Topology Optimization

Computes the topological derivative and use it together with a level-set domain representation method in the context of structural compliance topology optimization design

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Synthesis of Compliant Mechanisms

Computes the topological derivative and use it together with a level-set domain representation method in the context of compliant mechanisms topology optimization design

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