The software that will help solve problems in geophysics: improved characterization and storage of CO2 in the Earth's subsurface

• The European Marie-Curie grant has allowed postdoctoral researcher Judit Muñoz to grow in the United States

Designing efficient, stable, and accurate numerical methods to solve wave propagation problems is the main objective of Judit Muñoz, who has been able to develop her project thanks to the Marie-Curie grants. The software they are working on simulates transient Partial Differential Equations (PDEs) using stable time integrators that support both classical and goal-oriented adaptive strategies. The ultimate goal of their work is to apply these new simulation methods to solve problems arising in geophysics, more specifically, these simulations will help to improve the characterization of the Earth's subsurface and their application to long-term CO2 storage.

EPDs are equations that describe physical processes that can be observed in nature, such as the propagation of waves or the movement of a fluid. The problem with these equations is that their solution is not known exactly, so they have to be simulated by computer. To solve these equations, the simulation methods must be very accurate and stable. Otherwise, the prediction will be wrong.

Looking to the future, the final stage of the fellowship is the application of the developed tools to industry, focusing on problems such as climate change, although for now most of the project's objectives are mainly academic. "In addition, during the fellowship," says Judit, "I will carry out outreach activities to transfer the results of the project to the scientific research public in our society".

"In the first year of this project we have met all the goals set out in the proposal," says the researcher. The work has resulted in several scientific articles, four of which have been published in Q1-indexed journals. According to the researcher, new related research topics have appeared and have been worked on thanks to Professor Demkowicz's group at UT Austin, with whom Judit Muñoz has acquired all the mathematical experience necessary to analyze and design new stabilized numerical methods for PDEs in the time domain.

In 2022, Muñoz Matute, thanks to the Marie-Curie grant, has participated in several dissemination activities, giving talks, such as at the Finite Element Rodeo (Dallas, USA), the ECCOMAS conference (Oslo, Norway), the ICCS conference(online) and the MinRes workshop (Santiago, Chile). In addition, she participated in the organization of a mini-symposium at the GACM Colloquium in Germany and gave two talks to students from two schools in the Basque Country to share her experience as a young researcher in the US. She explains that "in the last phase of the fellowship, I will return to Europe with the necessary experience to start a solid career as a researcher". This fellowship has allowed Muñoz Matute to work on a multidisciplinary research project and work at one of the best universities in the world in her field for a period of two years, learning from the best researchers in her field.

About Judit Muñoz

Judit Muñoz completed her PhD in October 2019 at the University of the Basque Country (UPV/EHU) under the supervision of Professor David Pardo and Elisabete Alberdi. She holds a Master's degree in Mathematical Modelling and Research, Statistics and Computing, and a Bachelor's degree in Mathematics from the same university.

During her PhD, she worked on numerical methods for transient partial differential equations (mainly on the advection-dominated diffusion equation, wave propagation problems, and Stokes flows), including finite element and finite difference methods, spatiotemporal variational formulations, goal-oriented adaptivity, error estimation, and residual minimization methods.

She is currently a postdoctoral researcher at BCAM in Professor David Pardo's Mathematical Design, Modelling, and Simulations (MATHDES) group. During the first two years of the Marie-Curie grant, she worked at the Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin with the group of Prof. Leszek Demkowicz.