Ricardo Ruiz Baier

School of Mathematics, Monash University
Office 315, 9 Rainforest Walk
Melbourne, VIC 3800, Australia
E-mail: Ricardo.RuizBaier@monash.edu
Phone: +61 3 9905 4485

SUPERVISED STUDENTS

I have had the privilege of supervising several outstanding young mathematicians
during their PhD and Master’s theses. I have also served as an advisor for
students undertaking semester or summer research projects.

Prospective students are warmly encouraged to contact me to discuss potential research opportunities.

PhD theses

12/2024-present, Sergio Carrasco.
Solvability results and numerical methods for contact problems with non-standard regularity
PhD thesis in Mathematics, Monash University, Australia
Co-directed with F. Chouly
08/2024-present, Abeer Alsohaim.
Numerical methods for mesoscale coupled models in biomechanics
PhD thesis in Mathematics, Monash University, Australia
Co-directed with S. Villa-Fuentes
01/2024-present, Siyad Rahman.
Theoretical and numerical analysis of multiphysics problems in thin structures
PhD thesis in Mathematics, Joint IITB-Monash Doctoral School, Australia-India
Co-directed with N. Nataraj
08/2023-present, Russel Demos.
Analysis of new formulations for nonlinearly coupled problems in continuum mechanics
PhD thesis in Mathematics, Monash University, Australia
Co-directed with Y. Bernard
05/2023-present, Andres E. Rubiano.
Analysis and novel discretisations for problems arising in large-strain poroelasticity
PhD thesis in Mathematics, Monash University, Australia
Co-directed with R. Khot
01/2022-present, Rishi Das.
Mathematical analysis and numerical methods for multiphysics problems in diffusion and viscoelasticity
PhD thesis in Mathematics, Joint IITB-Monash Doctoral School, Australia-India
Co-directed with H. Hutridurga and A.K. Pani
01/2022-present, Aamir Yousuf.
New numerical methods for coupled problems in thin geometries
PhD thesis in Mathematics, Joint IITB-Monash Doctoral School, Australia-India
Co-directed with N. Nataraj
11/2021-present, Utkarsh Rajput.
Mixed virtual element methods for coupled flow-transport problems
Doctoral thesis in Mathematics, Indian Institute of Space Science and Technology, India
Co-directed with S. Kumar
06/2021-09/2024, Ruben Caraballo.
Numerical analysis of vorticity formulations for fluid flow problems
Doctoral thesis in Mathematics, Universidad del Bío-Bío, Concepción, Chile
Co-directed with V. Anaya
01/2018-02/2020, Paul Méndez.
Numerical methods for the simulation of viscous flow and transport in porous media
Doctoral thesis in Applied Sciences with major in Mathematical Engineering, Universidad de Concepción, Chile
Co-directed with R. Bürger
08/2017-12/2019, Bryan Gomez-Vargas.
Mixed finite element methods for coupled diffusion problems in solid mechanics
Doctoral thesis in Applied Sciences with major in Mathematical Engineering, Universidad de Concepción, Chile
Co-directed with G.N. Gatica
04/2016-03/2019, Luis Miguel De Oliveira Vilaca.
Mechano-chemical patterning of the skin: A mathematical and statistical perspective
Doctoral thesis in Sciences with major in Physics of Biology, Université de Genève, Switzerland
Co-directed with B. Chopard and M.C. Milinkovitch
08/2014-12/2016, Mario Alvarez.
Mixed finite element methods for coupled problems in fluid mechanics
Doctoral thesis in Applied Sciences with major in Mathematical Engineering, Universidad de Concepción, Chile
Co-directed with G.N. Gatica

Honours and Master theses

08/2025-06/2026, Syed Syed Mudzhar.
MinRes methods for fully mixed poroelasticity
Master thesis in Mathematics, Monash University, Australia
08/2022-06/2023, Russel Demos.
Analysis of rotation-based formulations for continuum mechanics
Honours thesis in Mathematics, Monash University, Australia
03-11/2022, Chansophea In.
Fractal models and methods for flow in deformable porous media
Master thesis in Mathematics, Monash University, Australia
03-09/2019, Ningyuan Chen.
Computing numerical solutions for mechanochemical models of developmental growth
Master thesis in Mathematical Modelling and Scientific Computing, University of Oxford, UK
Co-directed with M. Taffetani
03-09/2019, Xiyao Li.
Augmented Lagrangian formulations for active cardiac mechanics using Kirchhoff stress
Master thesis in Mathematical Modelling and Scientific Computing, University of Oxford, UK
Co-directed with P.E. Farrell
03-09/2018, Adrienne Propp.
Computational modelling of cardiac electromechanics using stress-enhanced diffusion
Master thesis in Mathematical Modelling and Scientific Computing, University of Oxford, UK
01-09/2017, Zoa De Wijn.
Finite volume element approximation of three-field saddle-point problems
Master thesis in Mathematical Modelling and Scientific Computing, University of Oxford, UK
01-07/2013, Marie Dupraz.
Phenomenological and physiological approaches in the study of cardiac alternans:
Theoretical background, mathematical modeling and numerical simulations
Master thesis in Mathematics, École Polytechnique Fédérale de Lausanne, Switzerland
Co-directed with A. Quarteroni
01-07/2013, Luis Miguel De Oliveira Vilaca.
Mathematical modeling and numerical simulation of excitation-contraction phenomena in the heart
Master thesis in Molecular & Biological Chemistry, École Polytechnique Fédérale de Lausanne, Switzerland
Co-directed with A. Quarteroni
09/2010-07/2011, Davide Baroli.
Mathematical models and numerical methods for the mechanics of cardiac tissue
Master thesis in Mathematics, Università degli studi dell'Insubria, Italy
Co-directed with A. Quarteroni

Graduate and undergraduate projects

10/2021-06/2022, Claudio Correa.
A mixed finite element method based on Banach spaces for the coupled Poisson-Nernst-Plank/Stokes equations
Mathematical Engineering graduate thesis, Universidad de Concepción, Chile
Co-directed with G.N. Gatica
12/2021-02/2022, Kevin Dai.
Conditions for permeability deterioration in soft tissue
Summer research project. School of Mathematics, Monash University, Australia
12/2021-02/2022, Chrysovalantis Thomopoulos.
Hybrid continuum-discrete models for transport in rotational flows
Summer research project. School of Mathematics, Monash University, Australia
04/2019-07/2019, Matthew Shirley.
Modelling clogging mechanisms during silicon tapping
Research miniproject. Centre for Doctoral Training in Industrially Focused Mathematical Modelling, University of Oxford, UK
Co-directed with J.M. Oliver, C.P. Please, M. Moore
12/2018-04/2019, Francis Aznaran.
Augmented Lagrangian preconditioners for incompressible hyperelasticity
Research miniproject. Centre for Doctoral Training in PDEs, University of Oxford, UK
Co-directed with P.E. Farrell
06/2018-10/2018, Jennifer Dingwall.
Computing advection-reaction-diffusion dynamics interacting with poroelastic deforming structures
Summer research project. BA in Mathematics, University of Oxford, UK
06/2018-10/2018, Hyunyeon Kim.
Reaction-diffusion systems in deforming structures and models for tooth morphogenesis
Summer research project. BA in Mathematics, University of Oxford, UK
10/2017-03/2018, James Woodfield.
Numerical study of a class of interface problems in fluid mechanics
CCD dissertation. BA in Mathematics, University of Oxford, UK
10/2017-03/2018, Timothy Leach.
Anisotropic diffusion induced by stress in porous materials
BSP project. BA in Mathematics, University of Oxford, UK
06/2017-09/2017, James Woodfield.
Numerical approximation of a phase-change problem in natural convection
Summer research project. BA in Mathematics, University of Oxford, UK
01/2013-07/2013, Giacomo Rosilho de Souza.
An adaptive Rosenbrock method with applications in cardiac electrophysiology
Projet de semestre. Master in Mathematics, École Polytechnique Fédérale de Lausanne, Switzerland
Co-directed with S. Rossi
09/2012-01/2013, Marie Dupraz.
Modèles mathématiques et problèmes inverses pour l'activité électrique dans le coeur et les oreilletes
Projet de semestre. Master in Mathematics, École Polytechnique Fédérale de Lausanne, Switzerland
Co-directed with A. Quarteroni
01/2010-07/2010, Thimotée Pouchon.
Éstimateur à posteriori pour l'affinage de maillage dans la méthode des éléments finis
Projet de semestre. Bachelor en Mathématiques, École Polytechnique Fédérale de Lausanne, Switzerland
Co-directed with A. Quarteroni
09/2009-01/2010, Sabine Luisier.
On stabilized finite volume element methods for the transient Stokes problem
Projet de semestre. Bachelor en Mathématiques, École Polytechnique Fédérale de Lausanne, Switzerland
Co-directed with A. Quarteroni