Fabio Silva Botelho, PhD
Professor Adjunto, Departamento de Matemática
Universidade Federal de Santa Catarina - UFSC
Cálculo 1 – 2018-2 - Listas de exercícios -Resultados - REC
Cálculo 2 – 2018-2- Listas de exercícios -Resultados da P-3
Livros:
Functional Analysis and Applied Optimization in Banach Spaces, Springer 2014.
Real Analysis and Applications, Springer 2018.
This work is dedicated in memoriam to David Bohm and Jiddu Krishnamurti
Pre-prints – Physics
2. A Variational Formulation for the Relativistic Klein-Gordon Equation
Pre-prints-Applied Mathematics
Pre-print- On the solution of the Navier-Stokes system
0.1- arXiv:1907.02503 [pdf, ps, other]
math.OC
A numerical method for an inverse optimization problem through the generalized method of lines
Authors: Fabio Silva Botelho
Abstract: This article develops a solution for an inverse problem through the generalized method of lines. We consider a Laplace equation on a domain with internal and external boundaries with standard Dirichlet boundary conditions. Also, we specify a third non-homogeneous Newmann type boundary condition for the external boundary, and consider the problem of finding the optimal shape for the internal boundary such that all the prescribed boundary conditions are satisfied. The novelty here presented is the application of the generalized method of lines as a tool to compute a solution for such an inverse optimization problem. △ Less
Submitted 4 July, 2019; originally announced July 2019.
Comments: 7 pages
MSC Class: 49N45; 65N40
1.0-0arXiv:1907.00200 [pdf, ps, other]
math.OC
A duality principle and related numerical method for a class of shape optimization problems in elasticity
Authors: Fabio Botelho, Alexandre Molter
Abstract: In this article we develop a duality principle and concerning numerical method for a shape optimization problem in elasticity. We consider the problem of finding the optimal shape for an elastic solid which minimizes its structural inner energy resulting from the action of external loads to be specified. The main results are obtained through standard tools of convex analysis and duality theory. We emphasize our algorithm do not include a filter to process the results, so that the result obtained is indeed a critical point for the original optimization problem. Finally, in the last section, we present some numerical examples concerning applications of the theoretical results established. △ Less
Submitted 29 June, 2019; originally announced July 2019.
Comments: 7 pages
MSC Class: 49N15; 49Q10
1.0-arXiv:1906.07758 [pdf, ps, other]
math.OC
Duality suitable for a class of non-convex optimization problems
Authors: Fabio Botelho
Abstract: In this article we develop a duality principle suitable for a large class of problems in optimization. The main result is obtained through basic tools of convex analysis and duality theory. We establish a correct relation between the critical points of the primal and dual formulations and formally prove there is no duality gap between such formulations, in a local extremal context.
Submitted 18 June, 2019; originally announced June 2019.
Comments: 7 pages
MSC Class: 49N15
1. arXiv:1904.12379 [pdf, ps, other]
math.NA
On the generalized method of lines and its proximal explicit and hyper-finite difference approaches
Authors: Fabio Botelho
Abstract: This article firstly develops a proximal explicit approach for the generalized method of lines. In such a method, the domain of the PDE in question is discretized in lines and the equation solution is written on these lines as functions of the boundary conditions and domain shape. The main objective of introducing a proximal formulation is to minimize the solution error as a typical parameter… ▽ More
Submitted 7 May, 2019; v1 submitted 28 April, 2019; originally announced April 2019.
Comments: 18 pages, some typos corrected, a new result added
MSC Class: 65N40; 65N06
1.1. arXiv:1904.02286 [pdf, ps, other]
math.OC
A primal dual variational formulation and a multi-duality principle for a non-linear model of plates
Authors: Fabio Botelho
Submitted 18 April, 2019; v1 submitted 3 April, 2019; originally announced April 2019.
Comments: 20 pages, some typos corrected, a new result added
MSC Class: 49N15; 74P99
Artigos completos publicados em periódicos
1. Fabio Botelho, A note on Riemannian geometry and the relativistic quantum mechanics context. CIÊNCIA E NATURA, v. 40, p. 58, 2018.
2. Fabio Botelho.,A Variational Formulation for the Relativistic Klein-Gordon Equation. CIÊNCIA E NATURA, v. 40, p. 57, 2018.
4. Lucas dos Santos Fernandez, Alexandre Molter, Fabio Silva Botelho, Simultaneous topology optimization and proportional actuators localization. SeMA Journal, v. 23, p. --, 2016.
5. Fabio Botelho, On the Lagrange multiplier theorem in Banach spaces. Matemática Aplicada e Computacional (Cessou em 1997. Cont. ISSN 1807-0302 Computational & Applied Mathematics)^{ }, v. 32, p. 135-144, 2013.
6. Fabio Botelho. Existence of solution for the Ginzburg Landau system, a related optimal control problem and its computation by the generalized method of lines. Applied Mathematics and Computation^{ }, v. 218, p. 11976-11989, 2012.
7. Fabio Botelho, On duality principles for scalar and vectorial multi-well variational problems. Nonlinear Analysis^{ }, v. 75, p. 1904-1918, 2012.
8. Fabio Botelho, Dual Variational Formulations for a Non-linear Model of Plates. JOURNAL OF CONVEX ANALYSIS^{ }, v. 17, p. 131-158, 2010.