Dane Grundvig

Bio

I am currently a fifth year PhD student in the Department of Computational Applied Mathematics and Operations Research (CMOR) (formerly Computational and Applied Mathematics (CAAM)) at Rice University in Houston, TX. My PhD research is advised by Prof. Matthias Heinkenschloss and focuses on developing optimization algorithms for problems with inexact objective and constraint information with applications in reduced order modeling and shape optimization. I am currently a National Defense Science and Engineering Graduate (NDSEG) Fellow sponsored by the Army Research Office. See my updated CV.

Contact Info

• Email: dsg12@rice.edu

Education

• Ph.D., Computational and Applied Mathematics, Rice University, expected May 2025
• M.A., Computational and Applied Mathematics, Rice University, May 2023
• M.A., Mathematics, Brigham Young University, August 2020
• B.S., Mathematics with Applied and Computational Mathematics Emphasis, Minor in Economics, Brigham Young University, May 2018

Research Interests

• Reduced-order modeling
• Optimization
• PDE constrained optimization
• Optimization with Inexactness
• Numerical methods

Research and Work Experience

• Graduate Researcher - Department of Computational Applied Mathematics and Operations Research at Rice University, 2020-present
  • Optimization algorithms for problems with inexact objective and constraint information: Prof. Matthias Heinkenschloss)
• Graduate and Undergraduate Researcher - Department of Mathematics at Brigham Young University, 2016-2020
  • High-order finite difference methods for wave equations: Prof. Vianey Villamizar)
• Research Intern - National Security Agency, Summer 2018
  • Graph optimization, language modeling, n-gram techniques
• Programming Tutorial Developer, Brigham Young University, 2016-2018
  • Part of team that created two year long sequencce of programming tutorials on scientific computing in Python. Available at ACME

Publications and Preprints

• D. Grundvig, M. Heinkensclhoss Line-Search Based Optimization using Function Approximations with Tunable Accuracy. Submitted, under review

• D. Grundvig Line-Search Based Optimization using Function Approximations with Tunable Accuracy. Department of Computational Applied Mathematics and Operations Research, Rice University, (2023). https://hdl.handle.net/1911/115072

• V. Villamizar, T. Khajah, S. Acosta, D. Grundvig, J. Badger, O. Rojas High order local absorbing boundary conditions for acoustic and elastic scattering. Journal of the Acoustical Society of America, Vol. 148, pages 2451 (2020). https://doi.org/10.1121/1.5146764.

• V. Villamizar, D. Grundvig, O. Rojas, S. Acosta High order methods for acoustic scattering: Coupling farfield expansions ABC with deferred-correction methods. Wave Motion, Vol. 95, pages 102529 (2020). https://doi.org/10.1016/j.wavemoti.2020.102529.

• D. Grundvig High Order Numerical Methods for Problems in Wave Scattering. Department of Mathematics, Brigham Young University, (2020). http://hdl.lib.byu.edu/1877/etd11364

Talks and Presentations

• D. Grundvig, M. Heinkenschloss Line-search based optimization with online model reduction Presentation. Model Reduction and Surrogate Modeling, University of California San Diego, 2024

• D. Grundvig, M. Heinkenschloss Line-Search Based Optimization using Function Approximations with Tunable Accuracy Presentation. Modeling and Optimization: Theory and Applications, Lehigh University, 2024

• D. Grundvig Optimization with Inexactness: Line-Search Algorithms using Reduced Order Models Poster. 2024 National Defense Science and Engineering Graduate Fellowship Conference, New Orleans, 2024

• D. Grundvig, M. Heinkenschloss Line-Search Based Optimization Using Function Approximations with Tunable Accuracy Invited speaker. Department of Mathematics Colloquium, Brigham Young University, 2024

• D. Grundvig, M. Heinkenschloss Line-Search Methods for Unconstrained Optimization with Inexactness Arising from Reduced Order Models. Poster. SIAM Conference on Computational Science and Engineering, Eindhoven University of Technology, 2023

• D. Grundvig, M. Heinkenschloss Line Search Based Optimization Using Functions with Tunable Accuracy. Poster, SIAM Texas-Louisiana Section, University of Louisiana Lafayette, 2023

• D. Grundvig, M. Heinkenschloss Line-search methods for unconstrained optimization with inexactness arising from reduced order models. Presentation, SIAM Texas-Louisiana Section, University of Houston, 2022

• D. Grundvig, V. Villamizar Highly Accurate Equation Based Finite Difference Method Coupled with Farfield ABC for Acoustic Scattering. Presentation, SIAM Central States Section, Colorado State University, 2017

Honors and Awards

• National Defense Science and Engineering Graduate Fellowship, Mar. 2022,
  • Sponsoring Agency: Army Research Office.

Teaching

• Instructor, Computational Applied Mathematics & Operations Research Department, Rice University
  • Differential Equations in Science and Engineering, Summer 2024
• Instructor, Department of Mathematics, Brigham Young University
  • Essentials of Calculus, Fall 2018
  • Finite Mathematics, Summer 2019
  • Computational Linear Algebra, Winter-Spring 2020
• Teaching Assistant, Department of Computational and Applied Mathematics, Rice University
  • Differential Equations in Science and Engineering, Spring 2022
• Teaching Assistant, Department of Mathematics, Brigham Young University
  • Algorithm Design and Optimization, Fall 2019
  • Mathematical Analysis, Fall 2019
  • Algorithm Design and Optimization Lab, Fall 2017-Winter 2018

Service

• SIAM Student Chapter, Rice University
  • Treasurer, Aug. 2021 - Aug. 2022
• Graduate Student Advisory Committee, Rice University, Member, Sep. 2022 - May 2024