**Web application development**

One particular area I've been pushing relentlessly at lately (Spring 2018) is the development of skills necessary for web application development. There are many updates to come! Keep checking back - particularly at my main blog page - for current information on progress toward coding and deployment of my own projects (in addition to those already made and shared as part of online courses/bootcamps/etc.).

*Above: A screenshot of the YelpCamp application created as part of Colt Steele's Web Developer Bootcamp course given on udemy.com.*

**Population of my GitHub repository; exploration of new programming languages and analytical problems**

After setting up my GitHub repository, it sat mostly dormant for a while as I continued to work with code in private repositories of my own. I'm excited to continue populating the public repository with example code from my current and past projects so that curious readers/observers can take a closer look at my implementations and try the code out themselves.

Also, I've been educating myself lately about new (to me!) programming languages (Java, Python) and mathematical problems (machine learning, data science, etc.). I'll continue to update the public repository with new examples as they become available.

Also, I've been educating myself lately about new (to me!) programming languages (Java, Python) and mathematical problems (machine learning, data science, etc.). I'll continue to update the public repository with new examples as they become available.

**Creation of virtual reality environments for math visualization and education**

While teaching Calculus 3 (multivariable Calculus) courses during the past two years, and given my interest in interactive and emerging media, I thought it'd be fun to learn some 3D modeling and event scripting techniques to prototype an interactive VR environment for teaching some of the more visual (and volumetric!) concepts taught in the class.

A combination of Blender and Unreal Engine 4 have provided about as user-friendly and flexible a development environment as I could hope! The learning curve is still quite steep, but I've managed to construct a collection of several rather bare-bones activities tailored to key learning outcomes of Calculus 3 (for example, you can see an array of Riemann volumes in the screenshot above; these are used to approximate volume under/above curved surfaces). My goal is to further refine the environment seen above and to complete some simple interactive functionality for 4 specific activities associated with many Calc 3 curricula (integration (screenshot; foreground), quadric surface visualization (ex: the hyperboloid in the background), vector field visualization and manipulation, and slope/gradient evaluation and visualization).

A combination of Blender and Unreal Engine 4 have provided about as user-friendly and flexible a development environment as I could hope! The learning curve is still quite steep, but I've managed to construct a collection of several rather bare-bones activities tailored to key learning outcomes of Calculus 3 (for example, you can see an array of Riemann volumes in the screenshot above; these are used to approximate volume under/above curved surfaces). My goal is to further refine the environment seen above and to complete some simple interactive functionality for 4 specific activities associated with many Calc 3 curricula (integration (screenshot; foreground), quadric surface visualization (ex: the hyperboloid in the background), vector field visualization and manipulation, and slope/gradient evaluation and visualization).

*Above: several currently-hard-coded mathematical features/activities reside in a basic Unreal Engine 4-hosted virtual reality environment. Readers familiar with UE4's Virtual Reality template may recognize the light blue boxes in the top left of the screenshot.*

**Solving PDE/IVPs with RBF-FD in the presence of cornered interfaces**

Cornered interfaces presented a lingering problem for my radial basis function-generated finite difference (RBF-FD) work at the time of my Ph.D. dissertation. Since then, I've been working with Professor Greg Fasshauer (Department of Applied Mathematics and Statistics at the Colorado School of Mines) to accommodate such corners into our numerical methods. In the example data shown above, a triangular insulator poses a problem of cornered interfaces, and I've had some decent success lately (Spring 2018) with a new approach to handling the corners. Stay tuned for more updates!

**Electromagnetic wave simulation**

I've recently been participating in a fruitful cross-disciplinary collaboration with Professors Greg Fasshauer (Applied Mathematics and Statistics, Colorado School of Mines), Atef Elsherbeni (Electrical Engineering, Colorado School of Mines), and Mohammed Hadi (Electrical Engineering, Colorado School of Mines). We are exploring the use of RBF-FD to accurately model electromagnetic wave transport near conducting and dielectric materials.

We prepared a short presentation and paper for the 2018 International Applied Computational Electromagnetics Society (ACES) Symposium from March 24-29 in Denver, Colorado (http://aces-society.org/conference/Denver_2018/). We hope to soon expand the work into a full-length journal article.

We prepared a short presentation and paper for the 2018 International Applied Computational Electromagnetics Society (ACES) Symposium from March 24-29 in Denver, Colorado (http://aces-society.org/conference/Denver_2018/). We hope to soon expand the work into a full-length journal article.

*Above: A simulated electromagnetic wave front has begun near the bottom of the domain (y = 0) and traveled upward, encountering and bouncing off the perfectly conducting cylinder (dashed white circle) centered at (x = 0.5, y = 0.5). Analysis was conducted at the lower sampling point (smaller, solid white circle).*

**Ph.D. Dissertation**

My dissertation is available online in open access, but if you have trouble finding it, you can download it below. The top file is a copy with uncompressed images, and the bottom file is a slightly more compressed version for visitors with data caps or for easier viewing on mobile devices.

The dissertation explores options for accurate solution of wave and heat transport equations in scenarios where this transport occurs between different modeled materials. Traditional approaches often have a difficult time modeling such jumps in model parameters (density, wave speed, thermal diffusivity, etc.). The radial basis function-derived finite difference (RBF-FD) approaches investigated here incorporate such parameter changes accurately into the numerical solution.

The dissertation work was completed in the summer of 2016 under the generous help and guidance of Professor Bengt Fornberg (fornberg@colorado.edu) in the Department of Applied Mathematics at the University of Colorado, Boulder.

The dissertation explores options for accurate solution of wave and heat transport equations in scenarios where this transport occurs between different modeled materials. Traditional approaches often have a difficult time modeling such jumps in model parameters (density, wave speed, thermal diffusivity, etc.). The radial basis function-derived finite difference (RBF-FD) approaches investigated here incorporate such parameter changes accurately into the numerical solution.

The dissertation work was completed in the summer of 2016 under the generous help and guidance of Professor Bengt Fornberg (fornberg@colorado.edu) in the Department of Applied Mathematics at the University of Colorado, Boulder.

brad_martin_dissertation_final_draft__compressed_.pdf | |

File Size: | 7250 kb |

File Type: |

brad_martin_dissertation_final_draft.pdf | |

File Size: | 12739 kb |

File Type: |