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Contact Information

Department of Computational and Applied Mathematics
6100 Main MS-134
Houston, Texas 77005-1827

Duncan Hall 3017

bryan.t.doyle (at) rice (dot) edu


Headshot of Bryan Doyle.

I am a fourth year PhD candidate in the Computational and Applied Math (CAAM) department at Rice University, and on track to graduate in May 2020. I am currently working with Dr. Beatrice Riviere on my dissertation topic: developing an efficient hybrid finite volume discontinuous Galerkin model for fluid flow in porous media. I have experience in discontinuous Galerkin and finite volume methods, and their implementation in high performance architectures. My specific interests lie in computational fluid dynamics, porous media flow, computational astrophysics, numerical methods for PDEs, machine learning, and high performance computing.

Example of dissertation work.
Example of my dissertation work. Two numerical methods are used simultaneously to simulate fluid flow: the discontinuous Galerkin method on the left half of the domain, and the finite volume method on the right.
Example of dissertation work.
Finite volume and discontinuous Galerkin method used simultaneously to simulate flow through heterogeneous media.

Research Interests

  • Computational fluid dynamics
  • Flow in porous media
  • Computational astrophysics
  • Numerical methods for PDEs
  • Machine learning
  • High performance computing

Professional Experience

  • Summer Intern: Lawrence Livermore National Labs
    • I assisted in the development of the Lab's general relativistic radiation magneto-hydrodynamics code to help improve shock capturing techniques for cosmological simulations. My responsibilities included reviewing recent topical literature, implementing new functionality into existing parallel high-performance computing framework, and documenting any change in performance or accuracy. (May 2019 - August 2019)
  • Summer Intern: TOTAL Research and Development Group
    • I assisted in the development of an oil reservoir simulator using discontinuous Galerkin approximation techniques. My work included the mathematical discretization of the system's governing equations, verifying that theoretical convergence rates were obtained, and producing results for common benchmark tests. (May 2017 - August 2017, May 2018 - August 2018)
  • Research Assistant: University of Colorado Aerospace Department
    • I assisted Dr. John Evans at the University of Colorado – Boulder in his research in the field of isogeometric analysis, which is a method of integrating finite element approximation schemes into CAD-based software designs. My work included designing tools and plugins for software packages used extensively by Dr. Evans and his research group. (May 2015 - August 2015)
  • Research Assistant: University of Colorado Aerospace Department
    • I assisted Dr. Dennis Akos at the University of Colorado - Boulder in his research and design of GPS tracking units by modifying, developing, and optimizing existing MatLab code to simulate both realistic and worst-case-scenario circumstances. This work included satellite acquisition, tracking, data decoding, and obtaining accurate position solutions in real-time. (May 2014 - May 2015)

Professional Service

  • Workshop Houston Math and Physics Tutor
    • I volunteered at local after-school workshop for high school students, where I assisted students with math and physics homework. (August 2018 - December 2018)
  • SIAM Treasurer
    • I worked with Rice University's local SIAM chapter as treasurer, where my responsibilities included tracking expenses for SIAM sponsored meetings, as well as ensuring our activities did not exceed the given budget. (August 2017 - August 2018)



  • Doyle, B., & Riviere, B. (2019). Numerical Error Quantification of Agent-based Models as Applied to Oil Reservoir Simulation. SPE Reservoir Simulation Conference. https://doi.org/10.2118/193935-MS