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Luke Olson

Research

Research history :: Ongoing projects :: Related interests

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Summary...

Areas of interest:	numerical analysis, scientific computing, high performance computing
Keywords:	numerical PDEs, finite elements, spectral elements, multigrid, iterative methods, GPUs, parallel

Research directions

Multigrid methods for high-order finite element (p-type) and spectral discretizations
Iterative methods and high-order discontinuous Galerkin methods
Efficient coarsening strategies in algebraic multigrid
Extending the robustness of algebraic multigrid
High-performance simulations
Multiscale/multiphysics/multidomain simulations
Applications in biochemistry, electrical, and mechanical engineering
Scientific computing on high-performance architectures

Group...

James Lai (PhD expected May 2012)

algebraic multigrid
least-squares and discontinuous least-squares finite element methods
conservation in Stokes flow
High-order hierarchical and interpolatory H(curl) finite elements
high-order preconditioning
[presentation] A Discontinuous Least-Squares Finite Element Method for Stokes Flow
[presentation] Algebraic Multigrid for High-Order H(curl) elements, 2011
[presentation] Algebraic multigrid for high-order hierarchical H(curl) elements. 11th Copper Mountain Conference on Iterative Methods.
SIAM Student Chapter at Illinois, Vice-President, 2010-2011

Steven Dalton (PhD expected 2014)

Cusp CUDA library
algebraic multigrd on the GPU

Group Affiliates...

Yuki Kimura (Chemical and Biomolecular Engineering)

cellular chemotaxis
neutrophil motility
bacteria motility

Group Alumni...

Jehanzeb Hameed Chaudhry PhD, 2011 (now at Colorado State University)

numerical methods for implicit solvation models
least-squares finite element methods for the Poisson-Boltzmann equation
finite element methods for the Poisson-Nerst-Planck
steric effects
error adaptivity, adjoint estimators

Jacob Schroder PhD, 2010 (now at Sandia National Laboratories)

PyAMG
evolution strength-of-connection
AMG to complex problems
contraint based AMG for non-symmetric problems
AMG for the indefinite Helmholtz problem
pure algebraic MG for high-order discontinuous Galerkin

Nathan Bell, PhD, 2008 (now at Nvidia)

scipy.sparse
PyAMG
discrete exterior calculus
k-form algebraic multigrid
exact sequence algebraic multigrid
hodge decomposisions

David Alber, PhD, 2007 (now at Microsoft)

Thesis: Efficient Setup Algorithms for Parallel Algebraic Multigrid
parallel algebraic multigrid methods
high performance computing
combinatorial scientific computing

Publications...

Jehanzeb Hameed Chaudhry, Eric C. Cyr, Kuo Liu, Thomas A. Manteuffel, Luke N. Olson, and Lei Tang. A goal-oriented approach to least-squares finite element methods. SIAM Journal on Numerical Analysis, 2011. in review. [ bib ]
Nathan Bell, Steven Dalton, and Luke N. Olson. Exposing fine-grained parallelism in algebraic multigrid methods. SIAM Journal on Scientific Computing, 2011. in review. [ bib ]
Jehanzeb Hameed Chaudhry, Jeffrey Comer, Aleksei Aksimentiev, and Luke N. Olson. A finite element method for modified Poisson-Nernst-Planck equations to determine ion flow though a nanopore. Journal of Computational Physics, 2011. in review. [ bib ]
James Lai and Multigrid for high-order interpolatory h(curl) conforming finite elements. Numerical Linear Algebra with Applications, 2011. in review. [ bib ]
Jehanzeb Hameed Chaudhry, Stephen D. Bond, and Luke N. Olson. A weighted adaptive least-squares finite element method for the Poisson-Boltzmann equation. Applied Mathematics and Computation, 2010. in review. [ bib ]
James Lai and Algebraic multigrid for high-order hierarchical h(curl) finite elements. SIAM Journal on Scientific Computing, 2011. to appear. [ bib ]
Luke N. Olson and Jacob B. Schroder. Components of a more robust multilevel solver for emerging architectures and complex applications. In SciDAC 2011, 2011. to appear. [ bib ]
Luke Olson, Hans Petter Langtangen, and Carol S. Woodward. Cse 2011: Siag/cse holds milestone meeting in reno. SIAM News, 44(5), June 2011. [ bib | http | pdf ]
Luke N. Olson and Jacob B. Schroder. Smoothed aggregation multigrid solvers for high-order discontinuous galerkin methods for elliptic problems. Journal of Computational Physics, 230(18):6959-6976, 2011. [ bib | doi | http | pdf ]
Luke N. Olson, Jacob B. Schroder, and Raymond S. Tuminaro. A general interpolation strategy for algebraic multigrid using energy minimization. SIAM Journal on Scientific Computing, 33(2):966-991, 2011. [ bib | doi | http | pdf ]
Pavel Bochev, James Lai, and A locally conservative, discontinuous least-squares finite element method for the stokes equations. International Journal for Numerical Methods in Fluids, 2011. [ bib | doi | http | pdf ]
J. Lai, P. Bochev, L. Olson, K. Peterson, D. Ridzal, and C. Siefert. A discontinuous velocity least squares finite element method for the stokes equations with improved mass conservation. In CSRI Summer Proceedings 2010, Sandia National Laboratory, December 2010. [ bib | pdf ]
Jehanzeb Chaudhry, Stephen Bond, and Finite element approximation to a finite-size modified Poisson-Boltzmann equation. Journal of Scientific Computing, 47:347-364, 2010. [ bib | doi | http | pdf ]
Hong Zhao, Amir H.G. Isfahani, Luke N. Olson, and Jonathan B. Freund. A spectral boundary integral method for flowing blood cells. Journal of Computational Physics, 229(10):3726-3744, 2010. [ bib | doi | http | pdf ]
Luke N. Olson and Jacob B. Schroder. Smoothed aggregation for Helmholtz problems. Numerical Linear Algebra with Applications, 17(2-3):361-386, 2010. [ bib | doi | http | pdf ]
D.M. Alber and L.N. Olson. Bucket-sorted independent sets for algebraic multigrid. Electronic Transactions on Numerical Analysis, 37:367 - 385, 2010. [ bib | .html | pdf ]
Stephen D. Bond, Jehanzeb Hameed Chaudhry, Eric C. Cyr, and Luke N. Olson. A first-order system least-squares finite element method for the Poisson-Boltzmann equation. Journal of Computational Chemistry, 31(8):1625-1635, 2010. [ bib | doi | http | pdf ]
Luke N. Olson, Jacob Schroder, and Raymond S. Tuminaro. A new perspective on strength measures in algebraic multigrid. Numerical Linear Algebra with Applications, 17(4):713-733, 2010. [ bib | doi | http | pdf ]
J. Schroder, R. Tuminaro, and L. Olson. Generalized strength of connection in algebraic multigrid. In CSRI Summer Proceedings 2007, Sandia National Laboratory, December 2007. [ bib | pdf ]
Nathan Bell and Luke N. Olson. Algebraic multigrid for k-form Laplacians. Numerical Linear Algebra with Applications, 15(2-3):165-185, 2008. [ bib | doi | http | pdf ]
Xi Lin, Luke Olson, and Jianming Jin. An interpolatory spectral element method using curl-conforming vector basis functions on tetrahedra. In Antennas and Propagation Society International Symposium, 2007 IEEE, pages 5095 -5098, June 2007. [ bib | doi | http | pdf ]
David M. Alber and Luke N. Olson. Parallel coarse-grid selection. Numerical Linear Algebra with Applications, 14(8):611-643, 2007. [ bib | doi | http | pdf ]
Algebraic multigrid preconditioning of high-order spectral elements for elliptic problems on a simplicial mesh. SIAM J. Sci. Comput., 29(5):2189-2209, 2007. [ bib | doi | http | pdf ]
J. S. Hesthaven, L. N. Olson, and L. C Wilcox. Developments in overlapping Schwarz preconditioning of high-order nodal discontinuous Galerkin discretizations. In Domain Decomposition Methods in Science and Engineering XVI, volume 55 of Lecture Notes in Computational Science and Engineering, pages 325-332. Springer Berlin Heidelberg, 2007. [ bib | doi | http | pdf ]
J. J. Heys, T. A. Manteuffel, S. F. McCormick, and L. N. Olson. Algebraic multigrid for higher-order finite elements. J. Comput. Phys., 204(2):520-532, 2005. [ bib | doi | http | pdf ]
H. de Sterck, Thomas A. Manteuffel, Stephen F. McCormick, and Numerical conservation properties of H(div)-conforming least-squares finite element methods for the Burgers equation. SIAM J. Sci. Comput., 26(5):1573-1597, 2005. [ bib | doi | http | pdf ]
H. de Sterck, Thomas A. Manteuffel, Stephen F. McCormick, and Least-squares finite element methods and algebraic multigrid solvers for linear hyperbolic PDEs. SIAM J. Sci. Comput., 26(1):31-54, 2004. [ bib | doi | http | pdf ]
L. N. Olson. A dual least-squares finite element method for hyperbolic pdes. In Eleventh Copper Mountain Conference On Multigrid Methods, 2003. (Best student paper). [ bib | pdf ]
L. N. Olson. Multilevel Least-Squares Finite Element Methods for Hyperbolic PDEs. PhD thesis, University of Colorado at Boulder, Department of Applied Mathematics, 2003. [ bib | pdf ]

Presentations...

Extending algebraic multigrid solvers: Next generation algorithms, applications, and architectures, July 2011. SciDAC 2011. [ pdf ]
Luke Olson and Jacob Schroder. Workshop: Pyamg tutorial, April 2011. Fifteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO. [ pdf ]
Algebraic multigrid on the gpu: Exposing fine-grained paallelism, April 2011. Fifteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO. [ pdf ]
Algebraic multigrid for problems in electromagnetics, July 2010. SIAM Annual Meeting, Pittsburgh, Pennsylvania.
Extending the robustness of algebraic multigrid, June 2010. Numerical Analysis Research Club Seminar, University of Washington.
Multigrid and scientific computing, June 2009. NSF Summer REU Program, Wabash College.
Algebraic multigrid for topological-based problems, April 2009. Computational and Applied Mathematics Seminar, Purdue University.
Advances in AMG for topological problems: A smoothed aggregation approach to k-form Laplacians, January 2008. Applied Mathematics Departmental Colloquium, University of Colorado at Boulder.
Algebraic multigrid (AMG) for high-order spectral elements, July 2007. 6th International Congress on Industrial and Applied Mathematics, Zurich, Switzerland. Minisymposium: Developments in algebraic multigrid methods for real-world applications.
Using algebraic multigrid (AMG) for high-order spectral elements, July 2007. Argonne National Laboratory, Argonne, IL.
Algebraic multigrid preconditioning for spectral elements: Strategies for unstructured, 3D, DG problems, April 2006. Ninth Copper Mountain Conference on Iterative Methods, Copper Mountain, CO.
A high-order mess, November 2005. Graduate Student Seminar, Department of Computer Science, University of Illinois at Urbana-Champaign.
Developments in multigrid for high-order spectral elements, November 2005. Computer Science Seminar, Department of Computer Science and Engineering, University of Minnesota.
Algebraic multigrid (amg) for higher-order methods, May 2005. 7th IMACS International Symposium on Iterative Methods in Scientific Computing,Toronto, ON.
Algebraic multigrid (amg) for higher-order methods, April 2005. Twelfth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO.
Overlapping Schwarz-type preconditioning and high-order elements, January 2005. 16th International Conference on Domain Decomposition Methods.
Preconditioning high-order discontinuous Galerkin discretizations of the Helmholtz equation, June 2004. International Conference On Spectral and High-Order Methods (ICOSAHOM) 2004, Brown University, Providence, RI.
Solution methods for high-order discontinuous Galerkin discretizations of the Helmholtz equation, April 2004. Eighth Copper Mountain Conference on Iterative Methods, Coper Mountain, CO.
Least-squares finite element methods:an overview of the methodology and extensions to hyperbolic conservation laws, October 2003. Scientific Computing and Numerical Analysis Seminar, Brown University, Providence, RI.
Least-squares finite element methods for hyperbolic PDEs, July 2003. International Council for Industrial and Applied Mathematics Conference, Sydney, AUS.
Least-squares finite element methods for linear hyperbolic PDEs: A study of AMG, April 2003. Eleventh Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO.
Least-squares finite element method for linear hyperbolic PDEs, February 2003. SIAM 2003 Computational Science and Engineering Conference, San Diego, CA.
de Rham cohomology and finite elements applied to hyperbolic PDEs, November 2002. Computational Mathematics Seminar, University of Colorado, Boulder, CO.
Developments in multilevel methods for time-dependent hyperbolic PDEs, April 2002. Seventh Copper Mountain Conference on Iterative Methods, Copper Mountain, CO.

Funded Projects...

AMG on the GPU (Nvidia Professor Partnership Program; PI: L Olson, equipment, 2010-2011)

algebraic multigrid methods optimized for GPU computing
hybrid approachs for mixed CPU-GPU computing
Cusp CUDA library

CAREER: Multilevel Discontinuous Least-Squares Finite Element Methods (NSF DMS 0746676, PI: L Olson, $400,000, 2007-2012)

discontinuous least-squares methods
high-order algebraic multigrid preconditioners
coupled flows: Stokes, convection-diffusion
cellular mechanics

Multiscale analysis of neutrophil chemotaxis and signal integration (NIH-NIGMS 5R01GM083601, PI: C V Rao, Co-PI: P Kennis, F Wang, L Olson, $1,436,288, 2007-2012)

mathematical methods for multiple scale simulation of coupled particle-continuum flow
cellular responses and chemotaxis
mechanisms for e coli motility
mechanisms for neutrophil motility
particle-in-cell type simulations