Publications

Most of my publications should be indexed in my Google Scholar profile. As we all know, sometimes Google Scholar doesn’t update correctly, so I will try to keep the most recent version of my publications here as well (published articles, articles in press, and preprints). Additionally, many of my preprints can be consulted in arXiv.org and ResearchGate.

Journal articles

	Fantuzzi, G., and Fuentes, F. (2022). Convergent approximation of global minimzers of some polynomial integral functionals. [preprint soon]
	Fuentes, F., Goluskin, D., and Chernyshenko, S. (2022). Global stability of fluid flows despite transient growth of energy. Physical Review Letters, 128(204502). [preprint] [doi]
	Vaziri Astaneh, A., Fuentes, F., Mora, J., and Demkowicz, L. (2018). High-order polygonal discontinuous Petrov-Galerkin (PolyDPG) methods using ultraweak formulations. Computer Methods in Applied Mechanics and Engineering, 332:686-711. [preprint] [doi] [code]
	Keith, B., Petrides, S., Fuentes, F., and Demkowicz, L. (2017). Discrete least-squares finite element methods. Computer Methods in Applied Mechanics and Engineering, 327:226-255. [preprint] [doi]
	Fuentes, F., Demkowicz, L., and Wilder, A. (2017). Using a DPG method to validate DMA experimental calibration of viscoelastic materials. Computer Methods in Applied Mechanics and Engineering, 325:748-765. [preprint] [doi]
	Fuentes, F., Keith, B., Demkowicz, L., and Le Tallec, P. (2017). Coupled variational formulations of linear elasticity and the DPG methodology. Journal of Computational Physics, 348:715-731. [preprint] [doi]
	Keith, B., Fuentes, F., and Demkowicz, L. (2016). The DPG methodology applied to different variational formulations of linear elasticity. Computer Methods in Applied Mechanics and Engineering, 309:579-609. [preprint] [doi]
	Huang, D., Chernyshenko, S., Goulart, P., Lasagna, D., Tutty, O., and Fuentes, F. (2015). Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2183). [doi]
	Fuentes, F., Keith, B., Demkowicz, L., and Nagaraj, S. (2015). Orientation embedded high order shape functions for the exact sequence elements of all shapes. Computers & Mathematics with Applications, 70(4):353-458. [preprint] [doi] [code]

Conference articles

Bernal, L. M., Calo, V. M., Collier, N., Espinosa, G. A., Fuentes, F., and Mahecha, J. C. (2013). Isogeometric analysis of hyperelastic materials using PetIGA. Procedia Computer Science, 18:1604-1613. 2013 International Conference on Computational Science (ICCS). [doi] [code]

Conference Presentations

Here is a list of the latest talks and posters I’ve presented.

Talks

Rigorous global minimization of nonlinear integral functionals using finite element discretizations and polynomial optimization. Minimum Residual & Least-Squares Finite Element Methods Workshop. Pontificia Universidad Católica de Chile, Santiago, Chile, October, 2022.

Convergent approximations to global minima of integral functionals using polynomial optimization and finite element methods. Seminar. University of Victoria, Victoria, BC, Canada, July, 2022.

Convergent approximations to global minima of integral functionals using polynomial optimization and finite element methods. 15th World Congress in Computational Mechanics (WCCM). [Virtual] Yokohama, Japan, July, 2022.

Estabilidad global de fluidos regidos por las ecuaciones de Navier-Stokes. Coloquio de Facultad de Matemáticas. Pontificia Universidad Católica de Chile, Santiago, Chile, April, 2022.

Estabilidad global de flujo de Couette en 2D por encima del límite de estabilidad energético. Caleta Numérica: Seminario de Análisis Numérico y Matemática Aplicada. [Virtual] Pontificia Universidad Católica de Valparaiso, Valparaiso, Chile, August, 2021.

Convergent approximations to global minima of integral functionals using polynomial optimization and finite element methods. SIAM Conference on Applied Algebraic Geometry (SIAM AG). [Virtual] Houston, TX, USA, August, 2021.

Convergent approximations to global minima of integral functionals using polynomial optimization and finite element methods. 16th U.S. National Congress on Computational Mechanics (USNCCM). [Virtual] Chicago, IL, USA, July, 2021.

Global stability of 2D plane Couette flow despite transient growth of energy. International Conference on Spectral and High Order Methods (ICOSAHOM). [Virtual] Vienna, Austria, July, 2021.

Global stability of fluid flows despite transient growth of energy. Cornell Dynamics Seminar. Cornell University, Ithaca, NY, USA, March, 2020.

Using high-order DPG finite element methods to study form-wound medium-voltage coils. 15th U.S. National Congress on Computational Mechanics (USNCCM). Austin, TX, USA, August, 2019.

Global stability of 2D plane Couette flow beyond the energy stability limit. Workshop: Scientific Computing Across Scales: Extreme Events and Criticality in Fluid Mechanics. The Fields Institute for Research in Mathematical Sciences, University of Toronto, Toronto, ON, Canada, April, 2019.

Global stability of 2D plane Couette flow beyond the energy stability limit. AMS Sectional Meeting, Special Session on Analytical and Numerical Aspects of Turbulent Transport. University of Michigan, Ann Arbor, Ann Arbor, MI, USA, October, 2018.

Various applications of discontinuous Petrov-Galerkin (DPG) finite element methods. Scientific Computing and Numerics (SCAN) Seminar. Cornell University, Ithaca, NY, USA, August, 2018.

Various applications of discontinuous Petrov-Galerkin (DPG) finite element methods. PhD Dissertation Defense. The University of Texas at Austin, Austin, TX, USA, April, 2018.

Global stability of plane Couette flow beyond the energy stability limit. 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics. Denver, CO, USA, November, 2017.

Insulation integrity for power-dense, medium voltage, electric machinery (with Aleta Wilder). Office of Naval Research (ONR) Peer Review in Controls, Electromagnetism, and Power Electronics. Naval Postgraduate School, Monterey, CA, USA, November, 2017.

Discrete least-squares (DLS) and polygonal discontinuous Petrov-Galerkin (PolyDPG) finite element methods. Third Minimum Residual and Least Squares Finite Element Methods Workshop. Portland State University, Portland, OR, USA, October, 2017.

Global stability of 2D plane Couette flow beyond the energy stability limit. Texas Applied Mathematics and Engineering Symposium (TAMES). The University of Texas at Austin, Austin, TX, USA, September, 2017.

Global stability of two-dimensional plane Couette flow beyond the energy stability limit. 2017 Geophysical Fluid Dynamics Program. Woods Hole Oceanographic Institute (WHOI), Woods Hole, MA, USA, August, 2017.

Various applications of the DPG methodology. Oberwolfach Seminar: Discontinuous Petrov-Galerkin Methods. Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics), Oberwolfach, Germany, June, 2017.

Using discontinuous minimum residual methods to simulate DMA experiments in linear viscoelasticity. 2017 Finite Element Rodeo. University of Houston, Houston, TX, USA, March, 2017.

Using discontinuous minimum residual methods to validate DMA experimental calibration results in linear viscoelasticity. SIAM Conference on Computational Science and Engineering (CSE) 2017. Atlanta, GA, USA, February-March, 2017.

Minimum residual methods applied to linear thermoviscoelasticity. The Mathematics of Finite Elements and Applications (MAFELAP) 2016. Brunel University London, London, UK, June, 2016.

Minimum residual methods in linear thermoviscoelasticity. 2016 Finite Element Rodeo. Texas A&M University, College St., TX, USA, March, 2016.

The DPG methodology applied to various variational formulations of linear elasticity. Second Minimum Residual and Least Squares Finite Element Methods Workshop. Delft University of Technology, Delft, Netherlands, November, 2015.

High Order Shape Functions for Exact Sequence Elements of All Shapes. Part II. Pyramid. 13th U.S. National Congress on Computational Mechanics (USNCCM). San Diego, CA, USA, July, 2015.

High Order Shape Functions for Exact Sequence Elements of All Shapes. Part II. Pyramid. 2015 Finite Element Rodeo. Southern Methodist University, Dallas, TX, USA, February, 2015.

Posters

	Using discontinuous minimum residual methods to validate DMA experiments of viscoelastic materials. Workshop for Advances in Computational Sciences and Engineering (Oden 80 years). The University of Texas at Austin, Austin, TX, USA, March, 2017.
	Minimum residual methods in linear thermoviscoelasticity. Workshop for Advances in Mathematics for Finite Elements (Babuška 90 years). The University of Texas at Austin, Austin, TX, USA, March, 2016.
	Pyramid High Order Exact Sequence Shape Functions. Polytopal Element Methods in Mathematics and Engineering. Georgia Institute of Technology, Atlanta, GA, USA, October, 2015.
	Pyramid High Order Exact Sequence Shape Functions. Advanced Numerical Methods in the Mathematical Sciences. Texas A&M University, College St., TX, USA, May, 2015.
	Orientation Embedded Finite Element (FE) Shape Functions for the Exact Sequence Elements of All Shapes. Sixth International Workshop on High-Order Finite Element and Isogeometric Methods (HOFEIM). Frauenchiemsee Island, Germany, July, 2014.