Luke Olson

Summary

Research Focus:
  • Multigrid methods
  • Sparse matrix computations
  • Finite element methods
  • High performance computing
  • Scalable solvers on GPUs, large-scale systems

Students

Natalie Beams
Natalie Beams (Mechanical Engineering)

N-body methods, finite elements, multigrid

Amanda Bienz
Amanda Bienz

reducing communication in sparse solvers, HPC, multigrid

Nathan Bowman
Nathan Bowman

locality, scalability, efficiency of sparse computations

Jon Calhoun

fault detection and recovery in numerical algorithms, multigrid

Erin Carrier
Erin Carrier

mesh refinement and optimization on GPUs

Scott High
Scott High

particle-in-cell methods, scalable algorithms

Erin Molloy
Erin Molloy

algebraic multigrid, graphs problems, high dimensional problems

Andrew Reisner
Andrew Reisner

structured solvers, electric field computations

Former Students

Publications

  • Bell, W. N., Dalton, S., Olson, L. N., High-throughput Sparse Matrix-Matrix Computations, ACM TOMS, 2014, to appear.
    BibTeX
  • Calhoun, Jon, Olson, Luke, Snir, Marc, FlipIt: An LLVM Based Fault Injector for HPC, Euro-Par 2014: Parallel Processing Workshops, Springer International Publishing, 8805 (2014).
    BibTeX   DOI: 10.1007/978-3-319-14325-5_47
  • Shaffer, Eric, Cheng, Zuofu, Yeh, Raine, Zagaris, George, Olson, Luke, Efficient GPU-based Optimization of Volume Meshes, Accelerating Computational Science and Engineering (CSE), IOS Press, 25 (2014).
    BibTeX   DOI: 10.3233/978-1-61499-381-0-285
  • Chaudhry, J., Cyr, E., Liu, K., Manteuffel, T., Olson, L., Tang, L., Enhancing Least-Squares Finite Element Methods Through a Quantity-of-Interest, SIAM Journal on Numerical Analysis, 52 (2014), 3085-3105.
    BibTeX   DOI: 10.1137/13090496X
  • MacLachlan, Scott P., Olson, Luke N., Theoretical bounds for algebraic multigrid performance: review and analysis, Numerical Linear Algebra with Applications, 21 (2014), 194-220.
    BibTeX   DOI: 10.1002/nla.1930
  • Byrne, Matthew B., Kimura, Yuki, Kapoor, Ashish, He, Yuan, Mattam, Kewin S., Hasan, Katherine M., Olson, Luke N., Wang, Fei, Kenis, Paul J. A., Rao, Christopher V., Oscillatory Behavior of Neutrophils under Opposing Chemoattractant Gradients Supports a Winner-Take-All Mechanism, PLoS ONE, 9 (2014), e85726.
    BibTeX
  • Chaudhry, Jehanzeb Hameed, Comer, Jeffrey, Aksimentiev, Aleksei, Olson, Luke N., A finite element method for modified Poisson-Nernst-Planck equations to determine ion flow though a nanopore, Communications in Computational Physics, 15 (2014), 93-125.
    BibTeX   DOI: 10.4208/cicp.101112.100413a
  • Bochev, Pavel, Lai, James, Olson, Luke, A non-conforming least-squares finite element method for incompressible fluid flow problems, International Journal for Numerical Methods in Fluids, 2012.
    BibTeX   DOI: 10.1002/fld.3748
  • Bell, N., Dalton, S., Olson, L., Exposing Fine-Grained Parallelism in Algebraic Multigrid Methods, SIAM Journal on Scientific Computing, 34 (2012), C123-C152.
    BibTeX   DOI: 10.1137/110838844
  • Bell, Nathan, Dalton, Steven, Olson, Luke, Exposing Fine-Grained Parallelism in Algebraic Multigrid Methods, NVR-2011-002, NVIDIA Corporation, June, 2011.
    BibTeX   URL
  • Chaudhry, Jehanzeb Hameed, Bond, Stephen D., Olson, Luke N., A weighted adaptive least-squares finite element method for the Poisson–Boltzmann equation, Applied Mathematics and Computation, 218 (2012), 4892-4902.
    BibTeX   DOI: 10.1016/j.amc.2011.10.054   URL
  • Lai, James H., Olson, Luke N., Algebraic Multigrid for High-Order Hierarchical H(curl) Finite Elements, SIAM Journal on Scientific Computing, 33 (2011), 2888-2902.
    BibTeX   DOI: 10.1137/100799095   URL
  • Olson, Luke N., Schroder, Jacob B., Components of a more robust multilevel solver for emerging architectures and complex applications, SciDAC 2011, Denver, CO, 2011.
    BibTeX   URL
  • Olson, Luke N., Schroder, Jacob B., Smoothed aggregation multigrid solvers for high-order discontinuous Galerkin methods for elliptic problems, Journal of Computational Physics, 230 (2011), 6959-6976.
    BibTeX   PDF   DOI: DOI: 10.1016/j.jcp.2011.05.009   URL
  • Olson, Luke, Langtangen, Hans Petter, Woodward, Carol S., CSE 2011: SIAG/CSE Holds Milestone Meeting in Reno, SIAM News, 44 (2011).
    BibTeX   URL
  • Olson, Luke N., Schroder, Jacob B., Tuminaro, Raymond S., A General Interpolation Strategy for Algebraic Multigrid Using Energy Minimization, SIAM Journal on Scientific Computing, 33 (2011), 966-991.
    BibTeX   PDF   DOI: 10.1137/100803031   URL
  • Bochev, Pavel, Lai, James, Olson, Luke, A locally conservative, discontinuous least-squares finite element method for the Stokes equations, International Journal for Numerical Methods in Fluids, 2011.
    BibTeX   PDF   DOI: 10.1002/fld.2536
  • Lai, J., Bochev, P., Olson, L., Peterson, K., Ridzal, D., Siefert, C., A Discontinuous Velocity Least Squares Finite Element Method for the Stokes Equations With Improved Mass Conservation, CSRI Summer Proceedings 2010, Sandia National Laboratory, 2010.
    BibTeX   PDF
  • Chaudhry, Jehanzeb, Bond, Stephen, Olson, Luke, Finite element approximation to a finite-size modified Poisson-Boltzmann equation, Journal of Scientific Computing, 47 (2010), 347-364.
    BibTeX   PDF   DOI: 10.1007/s10915-010-9441-7
  • Zhao, Hong, Isfahani, Amir H. G., Olson, Luke N., Freund, Jonathan B., A spectral boundary integral method for flowing blood cells, Journal of Computational Physics, 229 (2010), 3726-3744.
    BibTeX   PDF   DOI: 10.1016/j.jcp.2010.01.024
  • Olson, Luke N., Schroder, Jacob B., Smoothed aggregation for Helmholtz problems, Numerical Linear Algebra with Applications, 17 (2010), 361-386.
    BibTeX   PDF   DOI: 10.1002/nla.686
  • Alber, D.M., Olson, L.N., Bucket-Sorted Independent Sets for Algebraic Multigrid, Electronic Transactions on Numerical Analysis, 37 (2010), 367-385.
    BibTeX   PDF   URL
  • Bond, Stephen D., Chaudhry, Jehanzeb Hameed, Cyr, Eric C., Olson, Luke N., A First-Order Systems Least-Squares Finite Element Method for the Poisson-Boltzmann Equation, Journal of Computational Chemistry, 31 (2010), 1625-1635.
    BibTeX   PDF   DOI: 10.1002/jcc.21446
  • Olson, Luke N., Schroder, Jacob, Tuminaro, Raymond S., A new perspective on strength measures in algebraic multigrid, Numerical Linear Algebra with Applications, 17 (2010), 713-733.
    BibTeX   PDF   DOI: 10.1002/nla.669
  • Schroder, J., Tuminaro, R., Olson, L., Generalized Strength of Connection in Algebraic Multigrid, CSRI Summer Proceedings 2007, Sandia National Laboratory, 2007.
    BibTeX   PDF
  • Bell, Nathan, Olson, Luke N., Algebraic multigrid for k-form Laplacians, Numerical Linear Algebra with Applications, 15 (2008), 165-185.
    BibTeX   PDF   DOI: 10.1002/nla.577
  • Lin, Xi, Olson, Luke, Jin, Jianming, An interpolatory spectral element method using curl-conforming vector basis functions on tetrahedra, Antennas and Propagation Society International Symposium, 2007 IEEE, 2007.
    BibTeX   PDF   DOI: 10.1109/APS.2007.4396692
  • Alber, David M., Olson, Luke N., Parallel coarse-grid selection, Numerical Linear Algebra with Applications, 14 (2007), 611-643.
    BibTeX   PDF   DOI: 10.1002/nla.541
  • Olson, Luke, Algebraic multigrid preconditioning of high-order spectral elements for elliptic problems on a simplicial mesh, SIAM J. Sci. Comput., 29 (2007), 2189-2209.
    BibTeX   PDF   DOI: 10.1137/060663465
  • Hesthaven, J. S., Olson, L. N., Wilcox, L. C, Developments in Overlapping Schwarz Preconditioning of High-Order Nodal Discontinuous Galerkin Discretizations, Domain Decomposition Methods in Science and Engineering XVI, Springer Berlin Heidelberg, 55 (2007).
    BibTeX   PDF   DOI: 10.1007/978-3-540-34469-8_39
  • Heys, J. J., Manteuffel, T. A., McCormick, S. F., Olson, L. N., Algebraic multigrid for higher-order finite elements, J. Comput. Phys., 204 (2005), 520-532.
    BibTeX   PDF   DOI: 10.1016/j.jcp.2004.10.021
  • de Sterck, H., Manteuffel, Thomas A., McCormick, Stephen F., Olson, Luke, Numerical conservation properties of H(\rm div)-conforming least-squares finite element methods for the Burgers equation, SIAM J. Sci. Comput., 26 (2005), 1573-1597.
    BibTeX   PDF   DOI: 10.1137/S1064827503430758
  • de Sterck, H., Manteuffel, Thomas A., McCormick, Stephen F., Olson, Luke, Least-squares finite element methods and algebraic multigrid solvers for linear hyperbolic PDEs, SIAM J. Sci. Comput., 26 (2004), 31-54.
    BibTeX   PDF   DOI: 10.1137/S106482750240858X
  • Olson, L. N., A Dual Least-Squares Finite Element Method for Hyperbolic PDEs, Eleventh Copper Mountain Conference On Multigrid Methods, 2003, (Best student paper).
    BibTeX   PDF
  • Olson, L. N., Multilevel Least-Squares Finite Element Methods for Hyperbolic PDEs, University of Colorado at Boulder, Department of Applied Mathematics, 2003.
    BibTeX   PDF

Some Images

GPU Timings
GPU Timings: Timings for different components on a GPU.
Nanopore
Nanopore: Mesh for ion channel simulations.
Planewave
Planewave: Planewave used in a multigrid hierarchy for the Helmholtz scattering problem.
High-order aggregation
High-order aggregation: Aggregation of high-order nodes in a discontinuous Galerkin mesh.
Hole
Hole: A hole found in a sensor network problem (with multigrid).
Aggregates
Aggregates: Aggregates using Lloyd aggregations.
Hole
Hole: A hole found in a sensor network problem (with multigrid).
Aggregates
Aggregates: Just some aggregates generated by PyAMG.
Circular aggregates
Circular aggregates: Aggregates in a recirculating flow problem using the Evolution measure.
Long range
Long range: Long range connections in multigrid for high-order discontinuous galerkin discretizations.
Homology basis
Homology basis: One component of a homology basis for a rocker arm (solved with multigrid).
k-form aggregation
k-form aggregation: Edge aggregation for a Titan rocket mesh.
low-order DG
low-order DG: Elements in a low-order discontinuous Galerkin preconditioner.
Spurious modes
Spurious modes: Spurious modes in an H(div) least-squares formulation of a hyperbolic problem.
least-squares flow
least-squares flow: A circular hyperbolic flow using least-squares finite element methods.
High-order coarsening
High-order coarsening: Fine, coarse, and coarser levels of an algebraic heirarchy for high-order quadrilateral elemeents.
low order FE
low order FE: Graphical view of a low order FE preconditioner for a high-order SE.
Aggregation Close-up
Aggregation Close-up: A close up of aggregation of nodes using the Evolution Measure.
Aggregation
Aggregation: Aggregation of nodes using the classic measure.
Aggregation
Aggregation: Aggregation of nodes using the Evolution Measure.
High-order
High-order: High-order nodal locations on the corner, edges, faces, and interior of an element are highlighted.
Parallel Coarsening
Parallel Coarsening: Distributions of fine nodes in an algebraic multigrid method.
Parallel Coarsening
Parallel Coarsening: Coarse nodes and fine nodes in an algebraic multigrid heirarchy are shown. Processor boundaries stand out.
Parallel Coarsening
Parallel Coarsening: Communicaiton on processor boundaries for coarse nodes in an algebraic multigrid heirarchy are highlighted.