Senior Researcher at the
National Laboratory for Scientific Computing

Antonio André Novotny

I am a 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, imaging 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. http://arquivo.sbmac.org.br/arquivos/notas/livro_73.pdf

Papers

Pointwise Antennas Design in Hyperthermia Therapy

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

Download file

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, 2020

Download file

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

P. Menoret, M. Hrizi & A.A. Novotny. Inverse Problems in Science and Engineering, 2020

Download file

Topological asymptotic analysis of a diffusive-convective-reactive problem

D. Ruscheinsky, F. Carvalho, C. Anflor & A.A. Novotny. Engineering Computations, 2020

Download file

Pollution sources reconstruction based on the topological derivative method

L. Fernandez, A.A. Novotny, R. Prakash & J. Sokolowski. Applied Mathematics & Optimization, 2020

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

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, 2020

Download file

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

Download file

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

Download file

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

Download file

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 accsess 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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

Topology Design of Thermomechanical Actuators

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

Download file

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

Download file

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

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

Topological Derivative Method for Electrical Impedance Tomography Problems

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

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

Download file

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

Download file

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

Download file

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

Download file

A New Reconstruction Method for the Inverse Potential Problem

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

Download file

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

Download file

Sensitivity of a General Class of Shape Functional to Topological Changes

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

Download file

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

Download file

Topological Derivative for an Anisotropic and Heterogeneous Heat Diffusion Problem

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

Download file

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

Download file

Second-Order Topological Expansion for Electrical Impedance Tomography

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

Crack Nucleation Sensitivity Analysis

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

Download file

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

Download file

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

Download file

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

Download file

Topological optimization of structures subject to von Mises stress constraints

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

Download file

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

Download file

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

Download file

On the Second Order Topological Asymptotic Expansion

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

Download file

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

Download file

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

Download file

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

Download file

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.

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file

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

Download file
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

Download file

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

Download file