List of Publications and Preprints

Neural Network Methods (my PhD work)

1. Z. Cai, A. Doktorova, R. D. Falgout, C. Herrera.
   Efficient Shallow Ritz Method for 1D Diffusion Problems.
   Computers & Mathematics with Applications (2025).
   Journal 2025
2. Z. Cai, A. Doktorova, R. D. Falgout, C. Herrera.
   Efficient Shallow Ritz Method for 1D Diffusion-Reaction Problems.
   SIAM Journal on Scientific Computing (2025).
   Journal 2025
3. Z. Cai, A. Doktorova, R. D. Falgout, C. Herrera.
   Convergence Analysis of Block Newton Methods for 1D Shallow Neural Network Approximation.
   Journal of Intelligent Algorithms and Scientific Computing (2026).
   Journal 2026
4. Z. Cai, C. Herrera.
   Structure-Guided Gauss-Newton Method: Linear Advection-Reaction Equation.
   Submitted.
   Preprint

Mixed Model and Mixed Precision Runge-Kutta Methods

1. S. Gottlieb, Z. J. Grant, C. Herrera.
   Mixed Precision Explicit Two-Derivative Runge–Kutta Methods.
   Pure and Applied Functional Analysis (2026). To appear.
   Journal 2026
2. J. Driscoll, S. Gottlieb, Z. J. Grant, C. Herrera, T. S. Kakumanu, M. H. Sawicki, M. Stephens.
   Stable Corrections for Perturbed Diagonally Implicit Runge–Kutta Methods.
   Submitted.
   Preprint
3. J. Driscoll, S. Gottlieb, Z. J. Grant, C. Herrera, T. S. Kakumanu, M. Stephens.
   Smooth Perturbations of Diagonally Implicit Runge–Kutta Methods.
   Spectral and High-Order Methods for Partial Differential Equations ICOSAHOM 2025 (2026). To appear.
   Journal 2026
4. C. Herrera, J. Driscoll, S. Gottlieb, Z. J. Grant, T. S. Kakumanu, A. Christlieb.
   Performance Evaluation of Stabilized Corrections for Mixed Precision Runge–Kutta Methods.
   IEEE High Performance Extreme Computing (2026). To appear.
   Refereed Conference Proceedings 2026

Virtual Element and Domain Decomposition Methods

1. J. G. Calvo, C. Herrera, F. A. Sequeira.
   An overlapping preconditioner for 2D virtual problems posed in H(rot) with irregular subdomains.
   In: Dostál, Z., et al. Domain Decomposition Methods in Science and Engineering XXVII. DD 2022. Lecture Notes in Computational Science and Engineering, vol 149. Cham: Springer Nature Switzerland (2024). 101-108.
   Refereed Conference Proceedings 2024
2. C. Herrera, R. Corrales-Barquero, J. Arroyo-Esquivel, J. G. Calvo.
   A numerical implementation for the high-order 2D virtual element method in MATLAB.
   Numerical Algorithms 92 (2023), 1707-1721.
   Journal 2023

Wastewater-Based Disease Surveillance

1. M. L. Daza-Torres, J. C. Montesinos-López, C. Herrera, Y. E. García, C. C. Naughton, H. N. Bischel, M. Nuño.
   Optimizing Spatial Distribution of Wastewater-Based Disease Surveillance to Advance Health Equity.
   Epidemics (2024). 49:100804.
   Journal 2024
2. J. C. Montesinos-López, M. L. Daza-Torres, Y. E. García, C. Herrera, C. W. Bess, H. N. Bischel, M. Nuño.
   Bayesian sequential approach to monitor COVID-19 variants through test positivity rate from wastewater.
   mSystems (2023). 8:e00018-23.
   Journal 2023

Epidemic Models

1. A. Serracín-Morales, C. Herrera-Garro, and F. Sanchez.
   Modeling the university drinking culture phenomenon.
   Technical Report