# Bradley M. Froehle

Ph.D., Mathematics

University of California, Berkeley

## Research

I’m currently working on high-order methods for solving fluid-structure interaction problems. The fluid, modeled using the compressible Navier-Stokes equations, is generally discretized usign a high-order discontinous Galerkin arbitrary Lagrangian Eulerian (DG-ALE) method. A variety of structures have been investigated including rigid airfoils, non-linear membranes, and thin hyperelastic structures.

Watch some videos:

## Teaching

**Math 228A**(Fall 2012; J. Strain)**Math 228A**(Fall 2010; P. Persson)**Math 228B**(Spring 2010; J. Sethian)**Math 1A (PDP)**(Fall 2009; R. Borcherds)**Math 1A**(Summer 2009)**ARE 298**(Spring 2009; L. Karp)**Math 1A**(Fall 2008; I. Agol)

## Codes & Python Utilities

- See my blog where I often describe Python tips and tricks.
- PyDistMesh is a simple Python code for generating unstructured triangular and tetrahedral meshes using
*signed distance functions*. It intends to have the same functionality as and similar interface to the MATLAB-based DistMesh. - PyMUMPS is a Python interface to MUMPS.
- rt2to3: Runtime (Python) 2to3 conversion (for developers)
- pydzipimport: Python zipimport with support for compiled extension modules
- Bitey Magic: IPython extension for Bitey. Sample Notebook.
- Proof of concept of using LLVM’s JIT to load Python extension modules.
- Slither is a tool for easily building static Python interpreters. This is necessary to ensure fast startup times when running on hundreds or thousands of cores.
- A SAT-based KenKen solver using the pycosat module.

## Papers & Presentations

### Journal Papers

- B. Froehle and P.-O. Persson,
**High-Order Accurate Fluid-Structure Simulation of a Tuning Fork**. To appear in Computers & Fluids.doi:10.1016/j.compfluid.2013.11.009 - B. Froehle and P.-O. Persson,
**A high-order discontinuous Galerkin method for fluid-structure interaction with efficient implicit-explicit time stepping**. To appear in Journal of Computational Physics.doi:10.1016/j.jcp.2014.03.034 - A. Boocher and B. Froehle,
**On generators of bounded ratios of minors for totally positive matrices**. Linear Algebra Appl.**428**(2008) pp. 1664-1684.doi:10.1016/j.laa.2007.10.011 arXiv:0804.3226 MR2388648

### Conference Papers

- B. Froehle and P.-O. Persson,
**A High-Order Implicit-Explicit Fluid-Structure Interaction Method for Flapping Flight**. Proc. of the 21st AIAA Computational Fluid Dynamics Conference, June 2013.doi:10.2514/6.2013-2690.

### Presentations

- 12th U.S. National Congress on Computational Mechanics, July 23, 2013.
**A High-Order Implicit-Explicit Discontinuous Galerkin Scheme for Fluid-Structure Interaction**. - High-Order Methods III, 21st AIAA Computational Fluid Dynamics Conference,

June 25, 2013.**A High-Order Implicit-Explicit Fluid-Structure Interaction Method for Flapping Flight**. - UC Berkeley / Lawrence Berkeley Laboratory: Applied Mathematics Seminar, April 3, 2013
**A High-Order Implicit–Explicit Discontinuous Galerkin Scheme for Fluid–Structure Interaction**. **Algorithms for precomputing fast Fourier transforms of the symmetric group**(with Marie Jameson and Michael Orrison) Poster presented at Joint Mathematics Meetings – January 2007, New Orleans, LA.*Undergraduate Student Poster Session Prize Winner*pdf Unfinished notes pdf

### Theses

**High-Order Discontinuous Galerkin Fluid-Structure Interaction Methods**Ph.D. thesis, Department of Mathematics, University of California, Berkeley, Sep 2013.**An Introduction to Combinatorial Garside Structures**Undergraduate senior thesis,Department of Mathematics, University of Minnesota, Twin Cities, May 2007. Presentation slides

### Miscellaneous

Other things which have my name on them, like talks I contributed to but did not give:

- F. Perez, M. Bussonnier, J. Frederic, B. Froehle, B. Granger, P. Ivanov, T. Kluyver, E. Patterson, B. Ragan-Kelley, and Z. Sailer, American Geophysical Union Fall Meeting; San Francisco, California; December 2013.
**IPython: components for interactive and parallel computing across disciplines**. - P. Marion, A. Ahmadia, and B. Froehle, SciPy 2013;Austin, Texas; June 2013.
**Import without a filesystem: scientific Python built-in with static linking and frozen modules**. (slides). - P.-O. Persson and B. Froehle, SIAM Conference on Computational Science and Engineering; Boston, Massachusetts; February, 2013.
**A High-Order Implicit-Explicit Discontinuous Galerkin****Scheme for Fluid-Structure Interaction**.

## Open Source Software Contributions

I have contributed code and bug fixes to numerous open source software projects including: IPython, Cython, matplotlib, CPython, Drupal, Apache, phpCAS, PHP, Octave, SymPy, Homebrew, Debian, MacPorts, CyanogenMod, HTML Purifier.

## Classes

### Spring 2010

- Research
- Valveless pumping — time periodic solutions and shape optimization.

- Math 203 – Asymptotic Analysis – L.C. Evans
- CS 267 – Applications of Parallel Computers – J. Demmel and K. Yelick

### Fall 2010

- Research
- Time periodic solutions of axially vibrating rubber bands.

- Engineering 266A – Finite Difference Methods for Fluid Dynamics – P. Colella

### Spring 2010

- Research
- Automated quadrature rules for prespecified families of functions
- High order methods for Landau-Lifschitz-Gilbert and similar equations

### Fall 2009

- Math 221 – Matrix Computations / Numerical Linear Algebra – J. Demmel
- Math 228A – Numerical Solutions of Differential Equations – P. Persson
- Math 303 – Professional Preparation
- Qualifying Exam – Syllabus – Passed on December 18, 2009

### Spring 2009

- Math 222B – Partial Differential Equations – L.C. Evans
- Math 228B – Numerical Solutions of Differential Equations – J. Strain
- Math 303 – Professional Preparation

### Fall 2008

- Math 261A – Lie Groups – M. Haiman
- Math 265 – Differential Topology – P. Teichner
- Math 300 – Teaching Workshop – P. Barrow
- Many Cheerful Facts

### Spring 2008

- Math 202B – Introduction to Topology and Analysis – M. Rieffel
- Math 215B – Algebraic Topology – R. Kirby
- Math 250 – Multilinear Algebra – D. Eisenbud
- Math 253 – Homological Algebra – P. Teichner
- Many Cheerful Facts

### Fall 2007

- Math 202A – Introduction to Topology and Analysis – J. Holmer
- Math 215A – Algebraic Topology – M. Hutchings
- Math 252 – Representation Theory – T.Y. Lam

## Other Activities

I was an officer in the Mathematics Graduate Student Association from 2008—2010.

I was the MGSA appointee to the department’s Computer Committee for the 2008-2009 school year. In Fall 2008 I surveyed other graduate students in the department and wrote a report outlining the status of the current computing infrastructure.

In 2008 I helped run Many Cheerful Facts, a series of weekly talks given by graduate students and aimed at a general mathematics audience.

I’m one of the delegates from the Mathematics Department to the Graduate Assembly, the graduate student government at University of California, Berkeley. I formerly chaired the Environmental Sustainability Committee and Technology Committee. I currently chair the Communications Committee.

In October 2009 I was appointed by Councilmember Jesse Arreguin (Berkeley, District 4) to the City of Berkeley Transportation Commission.

### Elsewhere on the Internet

Listed in no particular order:

## Education

- I received my Bachelor Science in Mathematics (summa cum laude) and Physics (high distinction) from the University of Minnesota in May 2007.
- Check out my CV or resume for more information.
- My Erdős number is currently 6. It should drop soon.