Research

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My research focuses on the numerical analysis of time-dependent PDEs, with an emphasis on long-time stability and the development of efficient time-stepping schemes. I am particularly interested in applications to computational fluid dynamics, including the Navier-Stokes equations, as well as partitioned methods for coupled problems and data assimilation. I also have experience in adaptive mesh refinement techniques from my work at Lawrence Berkeley National Laboratory.

Papers

I. Barrio Sanchez, C. Trenchea, W.Pei, “Long-Time H1-Stability of the Cauchy One-Leg Theta-Method for the Navier-Stokes Equations”, 2024, Preprint, submitted for publication. [Link]

I. Barrio Sanchez, A. S. Almgren, J. B. Bell, M.T. Henry de Frahan, W. Zhang, “A new Re-redistribution Scheme for Weighted State Redistribution with Adaptive Mesh Refinement”, 2024, Journal of Computational Physics. [Link]

A. Naz, M. Lu, C. Broyles, I. Barrio Sanchez, “Competition of VEX Educational Robotics to Advance Girl’s Education (COVERAGE)”, June 2020, 2020 ASEE Virtual Annual Conference.[Link]

Talks

“Time-Stepping Methods for the Navier-Stokes Equations: Long-Time Stability, Nonlinear Coupling, and Data Assimilation.” PhD Overview Presentation, April 16, 2026.

“Overcoming Interface Challenges: Second-Order Partitioned Schemes for Heat Transfer.” 12th Graduate Student Conference, September 27, 2025. [Link]

“Second-order in time decoupled time stepping methods for heat transfer.” Recent Advances in Numerical PDEs, May 6, 2025. [Link]

“A new Re-redistribution Scheme for Weighted State Redistribution with Adaptive Mesh Refinement.” SIAM Conference on Computational Science and Engineering (CSE25), March 7, 2025. [Link]

“Long-term H¹-Stability of Cauchy's Method for the Navier-Stokes Equations.” The 42nd Southeastern-Atlantic Regional Conference on Differential Equations. November 9th, 2024. [SEARCDE 2024].

“Second-order partitioned algorithms with subiterations.” 11th Graduate Student Conference, Clemson University, April 20th, 2024. [Conference page].

“A new Re-redistribution Scheme for Weighted State Redistribution with Adaptive Mesh Refinement.” AWM Student Seminar, November 10, 2023. [Link]

“A new Re-redistribution Scheme for Weighted State Redistribution with Adaptive Mesh Refinement.” Computing Sciences Summer Program Poster Session, August 10, 2023.

“Competition of VEX Educational Robotics to Advance Girl’s Education (COVERAGE).” 2020 ASEE Virtual Annual Conference, Computers in Education Division Technical Session 10: STEM Outreach, June 2020.

Department of Mathematics

519 Thackeray Hall

Pittsburgh, PA 15260