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Scholarly Interest Report
         
Timothy C. Warburton
Professor
Professor of Computational and Applied Mathematics
 
e-mail:timwar@rice.edu
 
  • M.A. Mathematics (1993) Oxford University, UK
  • Ph.D. Applied Mathematics (1999) Brown University
  • Sc.M. Applied Mathematics (1994) Brown University
 
Primary Department
   Department of Computational and Applied Mathematics
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Websites
 nudg++: Nodal Unstructured Discontinuous Galerkin Book & Software
 Home Page
 
Research Areas
 Analysis of modern, high-order, unstructured, finite-element methods. Development of associated efficient algorithms, including parallel computational techniques, adaptivity, and advanced preconditioning methods for solving linear systems. Scientific computing applications for these methods including electromagnetics, acoustics and computational fluid dynamics in complex geometries. Simplification and introduction of these techniques to academic, defense and industrial environments. Development of artificial radiation boundary conditions for the time-domain Maxwell's equations. Architecturally tuned numerical algorithms, in particular GPGPU accelerated computing using CUDA and OPENCL.
 
Selected Publications
 Refereed articles
 

R. Gandham, D.S. Medina and T. Warburton "GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations." CICP (2014) In Revision

 
 

T. Warburton "A Low Storage Curvilinear Discontinuous Galerkin Method for Wave Problems." SIAM Journal on Scientific Computing, 35 (4) (2013) : A1987-A2012.

 
 Articles
 

Ali Karakus, T. Warburton, Haluk Aksel, Cuneyt Sert "Level set reinitialization for a high order adaptive discontinuous Galerkin method." International Journal of Numerical Methods for Heat and Fluid Flow (2014) Submitted

 
 

D.S. Medina, A. St-Cyr, and T. Warburton "OCCA: a unified approach to multi-threading languages." Technical Paper (2014)

 
 

David S. Medina, Amik St-Cyr, and Timothy Warburton "High-order finite differences on multithreaded architectures using OCCA." (arXiv.org) (2014)

 
 

Florian Kummer and T. Warburton "Patch-recovery filters for curvature in discontinuous Galerkin based level-set methods." Communications in Computational Physics (2014) Submitted

 
 

Jesse Chan and T. Warburton "A Comparison of High-Order Lagrange Interpolation Nodes for the Pyramid." SISC (2014) Submitted

 
 

Jesse Chan and T. Warburton "hp-finite element trace inequalities for the pyramid." CAMWA (2014) Submitted

 
 

S. Fahrenholtz, T. Moon, M. Franco, D. Medina, J. D. Hazle, R. J. Stafford, F. Maier, S. Danish, A. Gowda, A. Shetty, T. Warburton, and D. Fuentes "A Model Evaluation Study for Treatment Planning of Laser Induced Thermal Therapy." International Journal of Hyperthermia (2014) Submitted

 
 

Shelvean Kapita, Peter Monk, and T. Warburton "Residual based adaptivity and PWDG methods for the Helmholtz equation." SISC (2014) Submitted

 
 

D.S. Medina, A. St-Cyr, and T. Warburton "OCCA: a unified approach to multi-threading."  (2013) In Revision

 
 

R. Gandham, D.S. Medina and T. Warburton " GPU Accelerated Discontinuous Galerkin Methods for Shallow Water Equations."  (2013) In Revision

 
 

T. Warburton "Analysis of a Low Storage Curvilinear Discontinuous Galerkin Method for Wave Problems." SIAM Journal on Scientific Computing (2012) Submitted

 
 

Z.Gao, J.S. Hesthaven, T. Warburton "Efficient Absorbing Layers for Weakly Compressible Flows."  (2012) Submitted

 
 Book chapters
 

Andreas Kloeckner, Timothy Warburton and Jan S Hesthaven "High-Order Discontinuous Galerkin Methods by GPU Metaprogramming." GPU Solutions to Multi-scale Problems in Science and Engineering, Series: Springer Lecture Notes in Earth System Sciences 2013 (2013) : 353-374.

 
 

A. Klockner, T. Warburton and J.S. Hesthaven "High-Order DiscontinuousGalerkin Methods by GPU Metaprogramming." GPU Solutions to Multi-scale Problems in Science and Engineering (2011) : 353-374.In Press

 
 Refereed conference papers
 

Andreas Klockner (joint with Timothy Warburton & Jan S. Hesthaven) "Tools and Methods for Discontinuous Galerkin Solvers on Modern Computer Architectures." On The Theory and Applications of Discontinuous Galerkin Methods, MFO Technical Report 1208a (2012)

 
 

T. Warburton "Aspects of the a priori convergence analysis for the low storage curvilinear discontinuous Galerkin method." On the Theory and Applications of Discontinuous Galerkin Methods, MFO Technical Report 1208a (2012)

 
Presentations
 Invited Talks
 

Minisymposium Contributor.  "Accelerating High-order Methods." International Conference on Spectral and High-order Methods (ICOSAHOM), Salt Lake City, UT. (June 2014)

 
 

Invited Workshop Speaker.  "Accelerating Shallow Water Modeling." MA Hot Topics Workshop: Impact of Waves Along Coastlines, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN. (October 2014)

 
 

Invited Minisymposium Speaker.  "Low Storage Curvilinear Discontinuous Galerkin Methods." International Conference on Spectral and High-order Methods (ICOSAHOM), Salt Lake City, UT. (June 2014)

 
 

Invited Speaker.  "Many-core Algorithms for High-order Finite Element Methods: when
time to solution matters." Scientific Computing Around Louisiana (SCALA 2014), Louisiana State University, Baton Rouge, LA. (February 2014)

 
 

Invited Workshop Speaker.  "OCCA: A Unified Approach to Multi-Threading Languages." Algorithms and Abstractions for Assembly in PDE Codes, CSRI, Sandia National Lab, Albuquerque, NM. (Need Month 2014)

 
 

Invited Speaker.  "OCCA: A Unified Approach to Multi-Threading Languages." High Performance Computing Seminar, BP, Houston, TX. (Need Month 2014)

 
 

Invited Workshop Speaker.  "OCCA: A Unified Approach to Multi-Threading Languages." CESAR Handson Workshop, Argonne National Laboratory, Lemont, IL. (June 2014)

 
 

Invited workshop speaker.  "OCCA: An Extensible Portability Layer for Many-Core Programming." 43rd SPEEDUP Workshop on High-Performance Computing, University of Geneva, Geneva, Switzerland. (September 2014)

 
 

Invited Speaker.  "Tutorial: OCCA2, Hess Corporation." Hess Corporation, Houston, TX. (August, 2014)

 
 

Invited Seminar Speaker.  "DG | !(DG) ?." Hess corporation, Houston, TX. (April 2013)

 
 

Invited Minisymposium Speaker.  "Discontinuous Galerkin Methods on Many-core Architectures." Finite Elements in Flow Problems, special track of Advances in Computational Mechanics, San Diego, CA. (February 2013)

 
 

Invited Workshop Speaker.  "Discontinuous Galerkin Methods on Many-core Architectures." 2013 Oil & Gas High Performance Computing Workshop, Rice University, Houston, TX. (March 2013)

 
 

Invited Minisymposium Speaker.  "High-Order High-Throughput Numerical Methods for High-Contrast Seismic Imaging." SIAM Conference on Mathematical & Computational Issues in the Geosciences, Padova, Italy. (June 2013)

 
 

Invited Seminar Speaker.  "Many-core Algorithms for High-order Finite Element Methods: when time to solution matters." CSC Seminar, Mathematics Department, Simon Fraser University, Burnaby, BC. (September 2013)

 
 

Invited Seminar Speaker.  "Many-core Algorithms for High-order Finite Element Methods: when time to solution matters." SCAIM Seminar, Pacific Institute for the Mathematical Sciences, University of British Columbia, Vancouver, BC. (September 2013)

 
 

Invited Seminar Speaker.  "Many-core Algorithms for High-order Finite Element Methods: when time to solution matters." Scientific Computing Group Seminar, Division of Applied Mathematics, Brown University, Providence, RI. (December 2013)

 
 

Invited Colloquium Speaker.  "Many-core Algorithms for High-order Finite Element Methods: when time to solution matters." Mathematics Colloquium, Department of Mathematics, Florida State University, Tallahassee, FL. (November 2013)

 
 

Invited Minisymposium Speaker.  "The Low-storage Curvilinear Discontinuous Galerkin Method." Conference on the Mathematics of Finite Elements and Applications, Brunel University, Uxbridge, UK. (June 2013)

 
 

Invited Seminar Speaker.  "An Overview of Discontinuous Galerkin Methods." Shell Technology Center, Houston, TX. (June 2012)

 
 

Invited Speaker.  "CESAR: Nek and Many-core." Mathematics and Computer Science Division, Argonne National Laboratory, Chicago, IL. (January 2012)

 
 

Invited Seminar Speaker.  "Evaluating Discontinuous Galerkin Methods on Many-core Architectures." NASC Seminar, Courant Institute of Mathematical Sciences, New York University, New York, NY. (April, 2012)

 
 

Invited Speaker.  "GPU Accelerated Discontinuous Galerkin Methods." Workshop on Theory and Applications of Discontinuous Galerkin Methods, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany. (February 2012)

 
 

Invited Seminar Speaker.  "The Rice Advanced SCALable Simulation Project." Rice Space Physics Seminar, Physics Department, Rice University, Houston, TX. (November, 2012)

 
 Keynote Speaker
 

Keynote Speaker.  "Evaluating Discontinuous Galerkin Methods on Many-core Architectures." CADMOS Workshop on Large Scale Computing, EPFL, Lausanne, Switzerland. (September 2012)

 
 Posters
 

Presenter.  "ALMOND: Algebraic Multigrid on Numerous Devices." Rice Oil & Gas HPC Workshop, Rice University, Houston, TX. (2014) With Rajesh Gandham

 
 

Presenter.  "GPU Accelerated Lattice Boltzmann Method in Core Sample Analysis." Rice Oil & Gas HPC Workshop, Rice University, Houston, TX. With Frank Wang

 
 

Presenter.  "GPU Accelerated Numerical Methods for Tsunami Modeling." GPU Technology Conference, San Jose, CA. (2014) With Rajesh Gandham*, David Medina

 
 

Presenter.  "High Performance Discontinuous Galerkin Methods For Tsunami Modeling." IMA Hot Topics Workshop: Impact of Waves Along Coastlines, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN. (October 2014) With Rajesh Gandham and David Medina

 
 

Presenter.  "OCCA: A Unified Approach to Multi-Threading Languages." Algorithms and Abstractions for Assembly in PDE Codes, Sandia National Lab, Albuquerque, NM. (2014) With David Medina, Rajesh Gandham, and Amik St-Cyr

 
 

Presenter.  "OCCA: A Unified Approach to Multi-Threading Languages, joint with." Rice Oil & Gas HPC Workshop, Rice University, Houston, TX. (2014) With David Medina* and Amik St-Cyr

 
 

Presenter.  "Simulating Brain Cancer Laser Therapy with Spectral Elements on GPUs." OEDK Engineering Design Showcase, Rice University, Houston, TX. (2014) With Tim Moon, Michael Franco*, David Medina, and David Fuentes

 
 

Presenter.  "GPU Accelerated Numerical Methods for Tsunami Modeling." High-Performance Computing, Bengaluru, India. (2013) With Rajesh Gandham and David Medina

 
 

Presenter.  "High-order Numerical Methods for High-contrast Seismic Imaging." Rice 2013 Oil & Gas High Performance Computing Workshop, Houston, TX. (2013) With Rajesh Gandham, David Medina, and Amik St-Cyr

 
 Workshops
 

Invited Speaker.  "Many-core Algorithms for High-order Finite Element Methods: when time
to solution matters." Advances in Numerical Algorithms and High Performance Computing, University College London, London, UK. (April 2014)

 
 

Invited Speaker.  "OCCA: portability layer for many-core thread programming." 2014 Oil & Gas HPC Workshop, Rice University, Houston, TX. (March 2014)

 
 

Invited Instructor.  "Pan-American Advanced Engineering Institute advance-studies workshop on The science of predicting and understanding tsunamis, storm surges and tidal phenomena." Universidad Tecnica Federico Santa Maria, Valparaiso, Chile. (January 2013)

 
 

Invited Workshop Speaker.  "Portability Layer for GPUs: OCCA and GNek." Annual Review, Center for Exascale Simulation of Advanced Reactors, Argonne National Lab, Lemont, IL. (December 2013)

 
 

Invited Workshop Speaker.  "Portable many-core programming model and high-order finite element methods." Kick-off workshop for Advanced Air-Ocean-Land-Ice Global Coupled Prediction on Emerging Computational Architectures, Florida State University, Tallahassee, FL. (November 2013)

 
 

Invited Speaker.  "Evaluating Discontinuous Galerkin Methods on Many-core Architectures." Workshop on PDE Software Frameworks, Munster, Germany. (June 2012)

 
Editorial Positions
 Member of the Editorial Board, SIAM Journal on Scientific Computing. (2012 - 2013)

 Member of the Editorial Board, Computers and Mathematics with Applications. (2012 - 2012)

 Member of the Editorial Board, SIAM Journal on Scientific Computing. (2012 - 2012)

 Member of the Editorial Board, Computers and Mathematics with Applications. (2012 - 2013)

Supervised Theses & Dissertations
 A.J. Hergenroeder, M.A. Moment Matching and Modal Truncation for Linear Systems. (2012) (Co-Director)

 Yin Huang, M.A. Transparency Property of One Dimensional Acoustic Wave Equations. (2012) (Committee Member)

 Hong Liu, Ph.D Searching For FFLO States in Ultracold Polarized Fermi Gases: A Numerical Approach. (2012) (Committee Member)

 Nichole Stilwell, M.A. gNek: A GPU Accelerated Incompressible Navier Stokes Solver. (2013) (Thesis or Dissertation Director)

 Kenneth Davis, Ph.D. Instabilities in a Crystal Growth Melt Subjected to Alternating Magnetic Fields. (2013) (Committee Member)

 Jake Bruggemann, Physics Senior Thesis Computational Fluid Flow for Non-Newtonian Fluids Using Spectral Element Methods and GPUs. (2013) (Thesis or Dissertation Director)

 Jizhou Li, M.A. Locally Conservative Methods for Reservoir Flows. (Committee Member)