Research Interests

My research focuses on the development of fast and accurate numerical methods for the efficient solution of deterministic and stochastic computational models. In particular, my interests include, but not limited, to Stochastic PDEs, Radial Basis Function Interpolation,  Regression, Hierarchical Basis.

Selected Publications

• Julio E. Castrillon-Candas, Jun Li, Victor Eijkhout, “A discrete adapted hierarchical basis solver for radial basis function interpolation”, BIT Numerical Mathematics, Springer, July 2012.
• S. D Heedene , K Amaratunga and J.E. Castrillon-Candas, “Generalized Hierarchical Bases: a Wavelet-Ritz-Galerkin Framework for Lagrangian FEM” , Engineering Computations, 22,1,15-37, 2005
• C. Bajaj, J. E. Castrillon-Candas, Vinay Siddavanahalli and Zaiqing Xu, “Compression of Macromolecular Structures and Properties”, Special Issue of Macromolecular Assemblies Highlighted, Structure, 13,3, 463-471, (2005)
• Julio E. Castrillon-Candas, Vinay K. Siddavanahalli, and Chandrajit Bajaj.“Nonequispaced Fourier Transforms for Protein-Protein Docking, ICES Technical Report 2005
• J. E. Castrillon-Candas and K. Amaratunga, ”Spatially Adapted Multiwavelets and Sparse Representation of Integral Operators on General Geometries”, SIAM Journal on Scientific Computing, 24,5, 1530-1566, 2003.
• J. E. Castrillon-Candas and K. Amaratunga, ”Fast Computation of Continuous Karhunen-Loeve Eigenfunctions using Wavelets”, IEEE Transactions on Signal Processing, 50, 1, 78-86, January 2002.
• K. Amaratunga and J. E. Castrillon-Candas: ”Surface Wavelets: A Multiresolution Signal Processing Tool for 3D Computational Modeling”. International Journal of Numerical Methods in Engineering, 52, 3, 239-271, September 2001.​

Patents

• ​Radar Terrain Navigation. Developed a novel (patent-pending) software for real-time Bayesian terrain navigation using a proprietary low-cost radar system.
  
•  Weather Radar Terrain Reconstruction. Developed a novel (patent-pending) Bayesian real-time reconstruction algorithm for terrain using data collected from a proprietary low-cost radar system.
  
• Prediction of human image search timings (patent-pending) based on an information theoretic model of the visual cortex.
  

Education Profile

• 2003-2005 ICES Postdoctoral Fellow. ICES (Formerly TICAM), University of Texas at Austin.
• 2001 Postdoc. Assoc, Intelligent Engineering Systems, Laboratory, Massachusetts Institute of Technology.
• 2001 PhD in Electrical Engineering and Computer Science, Massachusetts Institute of Technology.
• 1996 M.S. in Electrical Engineering and Computer Science, Massachusetts Institute of Technology
• 1992 Electrical Engineer, Instituto Tecnologico de Monterrey, Mexico

Professional Profile

• 2010-Present, Research Scientist II, King Abdullah University of Science and Technology. Thuwal, Saudi Arabia.
• 2006-2010, Research Scientist, Teledyne Scientific (Formerly Rockwell Scientific), Durham North Carolina)

Scientific and Professional Memberships

Society for Industrial and Applied Mathematics.
http://www.siam.org/

Awards

• 2012 SRI Center for Uncertainty Quantification in Science and Engineering. Participant, 4,100,000 USD.
• 2003 ICES Postdoctoral Fellowship

Affiliations

• Computer, Electrical and Mathematical Sciences and Engineering  (CEMSE)
• SRI Center for Uncertainty Quantification in Science and Engineering.
• Stochastic Numerics Research Group