Publications

You can also find my articles on my Google Scholar profile. PhD thesis.

An inverse problem for estimating effective parameters in asymptotic elastodynamics with non-periodic roughness

Published in Book of Abstracts, The 17th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2026), 2026

We consider the problem of elastic wave propagation in a two-dimensional domain where part of the boundary is defined by a non-periodic rough perturbation. We assume that the maximum amplitude of this perturbation is small compared to the minimum wavelength. Standard discretization procedures in this context can be computationally intensive. Therefore, we seek an approximate model whose numerical complexity is robust with respect to this roughness. In this context, asymptotic expansions are well-known tools for providing effective models. Although a priori estimates exist for certain cases, most asymptotic models suffer from a modeling error proportional to the amplitude of the perturbation. In our work, we aim to reduce this modeling error by introducing a modification of the effective coefficients in the boundary condition. This modification is automatically adjusted by solving an inverse problem formulated as a minimization problem. In this minimization procedure, the data fidelity term is informed by synthetic data generated from a single run of the complete model. We il- lustrate our approach with two-dimensional numerical simulations.

Recommended citation: R. Zelada, A. Imperiale, and P. Moireau, “An inverse problem for estimating effective parameters in asymptotic elastodynamics with non-periodic roughness,” in Book of Abstracts, The 17th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2026), 2026.
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Shape Optimization with Ventcel Transmission Condition: Application to the Design of a Heat Exchanger

Published in SIAM Journal on Scientific Computing, 2026

This paper aims to optimize the shape of a fluid-to-fluid heat exchanger in order to maximize heat exchange under constraints of energy dissipation and volume. The novelty consists in taking into account the thin layer separating the two fluids by using Ventcel-type second-order transmission conditions. The physical model is then a weakly coupled problem between the steady-state Navier-Stokes equations for the dynamics of the two fluids dynamics and the convection-diffusion equation for the heat. We provide a shape sensitivity analysis and characterize the shape derivatives involved. Finally, we demonstrate the feasibility and effectiveness of the proposed method through 3D numerical simulations.

Recommended citation: Fabien Caubet, Carlos Conca, Marc Dambrine, Rodrigo Zelada. Shape Optimization with Ventcel Transmission Condition: Application to the Design of a Heat Exchanger, SIAM Journal on Scientific Computing, 48(2), 2026, pp. B113–B140.
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PhD thesis: Shape optimization for thin layers heat exchangers

Published in PhD thesis, University of Chile, University of Pau and Adour Countries, March, 2025

This thesis falls within two major areas of mathematics: numerical analysis of PDEs and shape/ topology optimization. We are interested in the optimal design of a heat exchanger. The aim is to consider the case of a two-fluid heat exchanger in a forced convection regime, in the case where the fluids are separated by a thin solid layer. Then, by addressing challenges arising from non-standard transmission conditions, this work contributes to advancing the theoretical and computational tools used to tackle coupled physical systems in shape optimization.

Recommended citation: R. Zelada. Shape optimization for thin layers heat exchangers. PhD thesis, University of Chile, University of Pau and Adour Countries, March 2025. Available at https://theses.fr/2025PAUU3006.
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How to insulate a pipe?

Published in Journal of Optimization Theory and Applications, 2025

This paper focuses on the problem of finding the optimal distribution of a thermal insulator around a pipe. We consider the framework of one fluid inside a pipe of thin width and surrounded by a thermal insulator. We use an asymptotic model to avoid dealing with the thin layer, leading to non-standard transmission conditions which involve discontinuities and second order tangential derivatives. We thus consider the shape optimization problem that aims to minimize the heat flux outside an insulator with a given volume. Then we characterize the shape derivative of the objective functional and perform 3D numerical simulations using the level set evolution method.

Recommended citation: F. Caubet, C. Conca, M. Dambrine, and R. Zelada. How to Insulate a Pipe? J. Optim. Theory Appl., 207(3):46, 2025.
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Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface

Published in ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 2025

The objective of this work is to study a diffusion equation with non-standard transmission conditions, which include discontinuities and the Ventcel boundary conditions at the interface. To handle jumps and means of the flux and test-functions, we use broken Sobolev spaces. We present a Nitsche finite element approach and compare it with a discontinuous Galerkin method. Consistency, stability and a priori error estimates are proven and numerically verified.

Recommended citation: D. Capatina, F. Caubet, M. Dambrine, and R. Zelada. Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface. ESAIM Math. Model. Numer. Anal., 59(2):999–1021, 2025.
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Shape optimization for a heat exchanger with a thin layer

Published in Monografías matemáticas "García de Galdeano", 2024

This paper focuses on a shape optimization method applied to fluid-to-fluid heat exchangers. We consider the framework of two fluids separated by a solid thin layer (the wall of the pipes) and we perform an asymptotic expansion in order to obtain an approximated model without thin layer. Due to this approximation, the multi-physics problem is reduced to a weak-coupled problem, between the steady-state Navier-Stokes equations for the two fluids dynamics and the convection-diffusion equation for the heat. The aim is then to optimize the shape of the heat exchanger in order to maximize the heat exchange and minimize the pressure drop. Thus, we characterize the shape derivative for the objective functional and perform numerical simulations in two dimensions.

Recommended citation: Caubet, F., Conca, C., Dambrine, M., & Zelada, R. (2024). Shape optimization for a heat exchanger with a thin layer. In Sixteenth International Conference Zaragoza-Pau on Mathematics and its Applications (Vol. 43, pp. 51-61).
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