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).
  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).
  3. Z. Cai, A. Doktorova, R. D. Falgout, C. Herrera. Convergence Analysis of Block Newton Methods for 1D Shallow Neural Network Approximation. Submitted.

Mixed Model and Mixed Precision Runge-Kutta Methods

  1. S. Gottlieb, Z. Grant, C. Herrera. Mixed Precision Explicit Two-Derivative Runge–Kutta Methods. Submitted.

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.
  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.

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.
  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.

Epidemic Models

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