Dr. Richard Barnard

(Old website of a former member, who has left MathCCES, see also list of former members)

MathCCES
RWTH Schinkelstr. 2
D-52062 Aachen
Germany

Office: 325 (Rogowski)
Phone: +49(0)241 80 98662
Email: (last name)@mathcces.rwth-aachen.de

CV available:cv.pdf

I recently finished a Latex package for the easy generation of scientific posters with Pascal Richter. It's available on CTAN: http://www.ctan.org/pkg/tikzposter

Research Interests:

* Nonsmooth Analysis
* Control Theory and Dynamical Systems
* PDE-Constrained Optimization
* Moment-based approximations
* Optimal Treatment Strategies in Radiotherapy

Upcoming Events:
* February 24-6, 2013: I will attend the final meeting of the DFG SPP 1253 meeting in Kloster Banz, Germany.

Short Biography:
09/81: Born in New Orleans, Louisiana
05/99: Graduated Brother Martin High School, New Orleans, Louisiana
08/99-05/03: Bachelor of Arts in Mathematics and English at University of Richmond
08/04-12/10: PhD in Mathematics at LSU (advisor: Peter Wolenski) (Thesis: Hamilton-Jacobi Theory for Optimal Control Problems on Stratified Domains)
10/10-present: Postdoctoral Research at RWTH Aachen

Publications:

1. Barnard, R., Frank, M., Herty, M., “Optimal Radiotherapy Treatment Planning Using Minimum Entropy Models”. Applied Mathematics and Computation Volume 219, Issue 5, 15 November 2012, Pages 2668–2679.
2. Barnard, R., Wolenski, P., “Flow Invariance on Stratified Domains”. Set-Valued and Variational Analysis, 2013, DOI:10.1007/s11228-013-0230-y. article
3. Barnard, R., “State Constrained Optimization with Partial Differential Equations via Generalized Gradients”. Submitted, preprint available on arXiv.
4. Barnard, R., Frank, M., Herty, M., “State-Constrained Optimization of PDEs via Infinite Penalization Methods”. To appear in Proceedings in Applied Mathematics and Mechanics
   
5. Herber, S.-C., Krycki, K., Barnard, R., Aures, A., Allelein, H.-J.“Sensitivity Analysis of a Multi-group Neutron Spectral Code.” Proceedings for Jahrestagung Kerntechnik (Annual Meeting on Nuclear Technology) 2012.
6. Krycki, K., Barnard, R., Herber, S., Frank, M., Allelein, H.-J. “Sensitivity analysis for the multigroup transport code TOTMOS”. In Preparation

Recent Talks:
* November 16, 2012 Lunch Seminar, MathCCES on “Sensitivity Analysis of the Multigroup Neutron Spectral Code TOTMOS”.
* October 11,2012 CELIA(Centre Lasers Intenses et Applications), University of Bourdeaux 1, Seminar Talk on “Optimal Treatment Planning in Radiotherapy”, in Bordeaux, France.
* October 5, 2012 AICES (RWTH) retreat in Monschau, Germany.
* September 3, 2012 Seminar week of the IGPM (RWTH) in Luxembourg.
* August 23, 2012 Invited Session on PDE Optimization in Medicine, 21st International Symposium on Mathematical Programming at TU Berlin, Germany. “Optimal radiotherapy treatment planning using minimum entropy models”.
* May 30, 2012 Minisymposium on optimal control in constrained domains, 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics in Vienna Austria. “Hamilton-Jacobi theory for the minimal time problem on stratified domains”.
* March 27, 2012 83rd Annual Meeting of GAMM in Darmstadt, Germany. “Optimization of PDEs with state constraints via Infinite Penalization methods”.

Supervised Student Projects
* Bachelor Thesis: Syrina Kausch, RWTH Aachen (Current, to be completed January 2013)
* UROP International Project at RWTH: Allison Betley, Washington University in St. Louis (Summer 2012) on “Computing Reachable Sets for Higher Dimensional Control Systems.”
* LSU MathCircle and later: Hira Khan and Joyce Ward on “A Geometric Perspective for an Oscillating Bead Problem” (Summer 2009-Spring2010).

Radiotherapy Results
One area of interest is in dose calculations using realistic data and physical modeling. Below are some videos generated with Edgar Olbrant and Martin Frank. Click images for the associated video
* Overview of test geometry.

* 3-D video using anaglyphs of particles accumulating and moving through body

* Comparison with Monte Carlo simulation using 15 MeV beam in same location

* Comparison of isosurfaces from M1 and Monte Carlo Simulations with 15 MeV beam

* Sample Optimization Step on 2-D section of water with Tumor (Large box) and Important Healthy Structure(Small Box). Dose calculation is on left, with current (unoptimized) source and resulting adjoint calculation on right.