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
N-body methods, finite elements, multigrid
Amanda Bienz
Amanda Bienz
reducing communication in sparse solvers, HPC, multigrid
Jon Calhoun
Jon Calhoun
fault detection and recovery in numerical algorithms, multigrid
Scott High
Scott High
particle-in-cell methods, scalable algorithms
Pete Sentz
Pete Sentz
finite elements, reduced order modeling
Andrew Reisner
Andrew Reisner
structured solvers, electric field computations

Former Students

Publications

  • Manteuffel, Thomas A., Olson, Luke N., Schroder, Jacob B., Southworth, Ben S., A Root-Node Based Algebraic Multigrid Method, SIAM Journal on Scientific Computing, 2016, in review.
    
    @article{2016_MaOlScSo_rootnode,
              author = {Manteuffel, Thomas A. and Olson, Luke N. and Schroder, Jacob
                        B. and Southworth, Ben S.},
               title = {A Root-Node Based Algebraic Multigrid Method},
             journal = {SIAM Journal on Scientific Computing},
                year = {2016},
                note = {in review},
    }
                  
  • Dalton, Steven, Olson, Luke N., Merrill, Duane, Garland, Michael, Graph Partitioning on the GPU, PARCO15, IOS Press, 2015, in review.
    
    @inproceedings{2015_DaOlMiGa_partition,
              author = {Dalton, Steven and Olson, Luke N. and Merrill, Duane and
                        Garland, Michael},
               title = {Graph Partitioning on the GPU},
                year = {2015},
           booktitle = {{PARCO}15},
                note = {in review},
           publisher = {{IOS} Press},
    }
                  
  • Gropp, William, Olson, Luke N., Samfass, Philipp, Modeling MPI Communication Performance on SMP Nodes: Is It Time to Retire the Ping Pong Test, Proceedings of the 23rd European MPI Users' Group Meeting, New York, NY, USA, ACM, 2016.
      DOI: 10.1145/2966884.2966919   URL
    
    @inproceedings{2016_GrOlSa_pingpong,
              author = {Gropp, William and Olson, Luke N. and Samfass, Philipp},
               title = {Modeling {MPI} Communication Performance on {SMP} Nodes: Is
                        It Time to Retire the Ping Pong Test},
                year = {2016},
             address = {New York, NY, USA},
           booktitle = {Proceedings of the 23rd European MPI Users' Group Meeting},
               pages = {41--50},
           publisher = {ACM},
              series = {EuroMPI 2016},
    }
                  
  • Bienz, Amanda, Falgout, Robert D., Gropp, William, Olson, Luke N., Schroder, Jacob B., Reducing Parallel Communication in Algebraic Multigrid through Sparsification, SIAM Journal on Scientific Computing, 38 (2016), S332-S357.
      DOI: 10.1137/15M1026341
    
    @article{2016_BiFaGrOlSc,
              author = {Bienz, Amanda and Falgout, Robert D. and Gropp, William and
                        Olson, Luke N. and Schroder, Jacob B.},
               title = {Reducing Parallel Communication in Algebraic Multigrid
                        through Sparsification},
             journal = {SIAM Journal on Scientific Computing},
                year = {2016},
              volume = {38},
              number = {5},
               pages = {S332-S357},
    }
                  
  • Olson, Luke N., Encyclopedia of Applied and Computational Mathematics, Algebraic Multigrid Methods, Springer Berlin Heidelberg, 2015.
      PDF   DOI: 10.1007/978-3-540-70529-1
    
    @inbook{2015_Ol_encamg,
              author = {Olson, Luke N.},
               title = {Encyclopedia of Applied and Computational Mathematics},
                year = {2015},
             chapter = {Algebraic Multigrid Methods},
              editor = {Bj\"orn Engquist},
               pages = {977--981},
           publisher = {Springer Berlin Heidelberg},
    }
                  
  • Olson, Luke N., Encyclopedia of Applied and Computational Mathematics, Geometric Multigrid Methods, Springer Berlin Heidelberg, 2015.
      PDF   DOI: 10.1007/978-3-540-70529-1
    
    @inbook{2015_Ol_encmg,
              author = {Olson, Luke N.},
               title = {Encyclopedia of Applied and Computational Mathematics},
                year = {2015},
             chapter = {Geometric Multigrid Methods},
              editor = {Bj\"orn Engquist},
               pages = {981--987},
           publisher = {Springer Berlin Heidelberg},
    }
                  
  • Laguna, Ignacio, Schulz, Martin, Richards, David F., Calhoun, Jon, Olson, Luke, IPAS: Intelligent Protection Against Silent Output Corruption in Scientific Applications, Proceedings of the 2016 International Symposium on Code Generation and Optimization, New York, NY, USA, ACM, 2016.
      PDF   DOI: 10.1145/2854038.2854059   URL
    
    @inproceedings{2015_LaScRiCaOl_ipas,
              author = {Laguna, Ignacio and Schulz, Martin and Richards, David F.
                        and Calhoun, Jon and Olson, Luke},
               title = {IPAS: Intelligent Protection Against Silent Output
                        Corruption in Scientific Applications},
                year = {2016},
             address = {New York, NY, USA},
           booktitle = {Proceedings of the 2016 International Symposium on Code
                        Generation and Optimization},
               pages = {227--238},
           publisher = {ACM},
              series = {CGO 2016},
    }
                  
  • Calhoun, J., Snir, M., Olson, L., Garzaran, M., Understanding the Propagation of Error Due to a Silent Data Corruption in a Sparse Matrix Vector Multiply, 2015 IEEE International Conference on Cluster Computing, 2015, Best Poster Award.
      PDF   DOI: 10.1109/CLUSTER.2015.101
    
    @inproceedings{2015_CaSnOlGa,
              author = {Calhoun, J. and Snir, M. and Olson, L. and Garzaran, M.},
               title = {Understanding the Propagation of Error Due to a Silent Data
                        Corruption in a Sparse Matrix Vector Multiply},
                year = {2015},
           booktitle = {2015 IEEE International Conference on Cluster Computing},
               month = {Sept},
                note = {Best Poster Award},
               pages = {541-542},
    }
                  
  • Beams, Natalie N., Olson, Luke N., Freund, Jonathan B., A Finite Element Based P^3M Method for \N\-Body Problems, SIAM Journal on Scientific Computing, 38 (2016), A1538-A1560.
      PDF   DOI: 10.1137/15M1014644
    
    @article{2015_BeFrOl_fepppm,
              author = {Beams, Natalie N. and Olson, Luke N. and Freund, Jonathan
                        B.},
               title = {A Finite Element Based P$^3$M Method for \$N\$-Body
                        Problems},
             journal = {SIAM Journal on Scientific Computing},
                year = {2016},
              volume = {38},
              number = {3},
               pages = {A1538-A1560},
    }
                  
  • Dalton, S., Baxter, S., Merrill, D., Olson, L., Garland, M., Optimizing Sparse Matrix Operations on GPUs Using Merge Path, Parallel and Distributed Processing Symposium (IPDPS), 2015 IEEE International, 2015.
      PDF   DOI: 10.1109/IPDPS.2015.98
    
    @inproceedings{2015_DaBaMeOlGa_merge,
              author = {Dalton, S. and Baxter, S. and Merrill, D. and Olson, L. and
                        Garland, M.},
               title = {Optimizing Sparse Matrix Operations on GPUs Using Merge
                        Path},
                year = {2015},
           booktitle = {Parallel and Distributed Processing Symposium (IPDPS), 2015
                        IEEE International},
               month = {May},
               pages = {407-416},
    }
                  
  • Guo, Dahai, Gropp, William, Olson, Luke N, A Hybrid Format for Better Performance of Sparse Matrix-Vector Multiplication on a GPU, International Journal of High Performance Computing Applications, 2015.
      PDF   DOI: 10.1177/1094342015593156   URL
    
    @article{2015_GuGrOl_gpu,
              author = {Guo, Dahai and Gropp, William and Olson, Luke N},
               title = {A Hybrid Format for Better Performance of Sparse Matrix-
                        Vector Multiplication on a {GPU}},
             journal = {International Journal of High Performance Computing
                        Applications},
                year = {2015},
               month = {January},
    }
                  
  • Dalton, Steven, Olson, Luke, Bell, Nathan, Optimizing Sparse Matrix-Matrix Multiplication for the GPU, ACM Transactions on Mathematical Software, 41 (2015).
      PDF
    
    @article{2015_BeDaOl_SPMM,
              author = {Dalton, Steven and Olson, Luke and Bell, Nathan},
               title = {Optimizing Sparse Matrix-Matrix Multiplication for the
                        {GPU}},
             journal = {{ACM} Transactions on Mathematical Software},
                year = {2015},
              volume = {41},
              number = {4},
    }
                  
  • Beckwith, K., Veitzer, S., McCormick, S.F., Ruge, J.W., Olson, L.N., Calhoun, J.C., Fully-implicit ultrascale physics solvers and application to ion source modelling, Plasma Sciences (ICOPS) held with 2014 IEEE International Conference on High-Power Particle Beams (BEAMS), 2014 IEEE 41st International Conference on, 2014.
      PDF   DOI: 10.1109/PLASMA.2014.7012726
    
    @inproceedings{2015_BeMcOlVeRuCa_plasma,
              author = {Beckwith, K. and Veitzer, S. and McCormick, S.F. and Ruge,
                        J.W. and Olson, L.N. and Calhoun, J.C.},
               title = {Fully-implicit ultrascale physics solvers and application to
                        ion source modelling},
                year = {2014},
           booktitle = {Plasma Sciences (ICOPS) held with 2014 IEEE International
                        Conference on High-Power Particle Beams (BEAMS), 2014 IEEE
                        41st International Conference on},
               month = {May},
               pages = {1-8},
    }
                  
  • Calhoun, Jon, Olson, Luke N., Snir, Marc, Gropp, William D., Towards a More Fault Resilient Multigrid Solver, Proceedings of the High Performance Computing Symposium, San Diego, CA, USA, Society for Computer Simulation International, 2015.
      PDF
    
    @inproceedings{2015_CaOlSnGr_framg,
              author = {Calhoun, Jon and Olson, Luke N. and Snir, Marc and Gropp,
                        William D.},
               title = {Towards a More Fault Resilient Multigrid Solver},
                year = {2015},
             address = {San Diego, CA, USA},
           booktitle = {Proceedings of the High Performance Computing Symposium},
           publisher = {Society for Computer Simulation International},
              series = {HPC 15},
    }
                  
  • Cheng, Zuofu, Shaffer, Eric, Yeh, Raine, Zagaris, George, Olson, Luke, Efficient parallel optimization of volume meshes on heterogeneous computing systems, Engineering with Computers, 2015, 1-10.
      PDF   DOI: 10.1007/s00366-014-0393-7
    
    @article{2015_ChShYeZaOl_meshes,
              author = {Cheng, Zuofu and Shaffer, Eric and Yeh, Raine and Zagaris,
                        George and Olson, Luke},
               title = {Efficient parallel optimization of volume meshes on
                        heterogeneous computing systems},
             journal = {Engineering with Computers},
                year = {2015},
               pages = {1--10},
           publisher = {Springer London},
    }
                  
  • 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).
      PDF   DOI: 10.1007/978-3-319-14325-5_47
    
    @incollection{2014_CaOlSn_FlipIt,
              author = {Calhoun, Jon and Olson, Luke and Snir, Marc},
               title = {{FlipIt}: An {LLVM} Based Fault Injector for {HPC}},
                year = {2014},
           booktitle = {Euro-Par 2014: Parallel Processing Workshops},
              editor = {Lopes, Luis and Zilinskas, Julius and Costan, Alexandru and
                        Cascella, Roberto G. and Kecskemeti, Gabor and Jeannot,
                        Emmanuel and Cannataro, Mario and Ricci, Laura and Benkner,
                        Siegfried and Petit, Salvador and Scarano, Vittorio and
                        Gracia, Jose and Hunold, Sascha and Scott, Stephen L. and
                        Lankes, Stefan and Lengauer, Christian and Carretero, Jesus
                        and Breitbart, Jens and Alexander, Michael},
              volume = {8805},
               pages = {547-558},
           publisher = {Springer International Publishing},
              series = {Lecture Notes in Computer Science},
    }
                  
  • 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).
      DOI: 10.3233/978-1-61499-381-0-285
    
    @inproceedings{2014_Shetal_gpuvolumemesh,
              author = {Shaffer, Eric and Cheng, Zuofu and Yeh, Raine and Zagaris,
                        George and Olson, Luke},
               title = {Efficient GPU-based Optimization of Volume Meshes},
                year = {2014},
           booktitle = {Accelerating Computational Science and Engineering (CSE)},
              editor = {M. Bader and A. Bode and H.J. Bungartz and M. Gerndt and
                        G.R. Joubert and F. Peters},
              volume = {25},
               pages = {285--294},
           publisher = {IOS Press},
              series = {Advances in Parallel Computing},
    }
                  
  • 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.
      PDF   DOI: 10.1137/13090496X
    
    @article{2014_ChCyLiMaOlTa_goal,
              author = {Chaudhry, J. and Cyr, E. and Liu, K. and Manteuffel, T. and
                        Olson, L. and Tang, L.},
               title = {Enhancing Least-Squares Finite Element Methods Through a
                        Quantity-of-Interest},
             journal = {SIAM Journal on Numerical Analysis},
                year = {2014},
              volume = {52},
              number = {6},
               pages = {3085--3105},
    }
                  
  • MacLachlan, Scott P., Olson, Luke N., Theoretical bounds for algebraic multigrid performance: review and analysis, Numerical Linear Algebra with Applications, 21 (2014), 194-220.
      PDF   DOI: 10.1002/nla.1930
    
    @article{2014_MaOl_amgtheory,
              author = {MacLachlan, Scott P. and Olson, Luke N.},
               title = {Theoretical bounds for algebraic multigrid performance:
                        review and analysis},
             journal = {Numerical Linear Algebra with Applications},
                year = {2014},
              volume = {21},
              number = {2},
               pages = {194--220},
    }
                  
  • 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.
      PDF   DOI: 10.1371/journal.pone.0085726   URL
    
    @article{2014_Byetal_neutrophil,
              author = {Byrne, Matthew B. and Kimura, Yuki and Kapoor, Ashish and
                        He, Yuan and Mattam, Kewin S. and Hasan, Katherine M. and
                        Olson, Luke N. and Wang, Fei and Kenis, Paul J. A. and Rao,
                        Christopher V.},
               title = {Oscillatory Behavior of Neutrophils under Opposing
                        Chemoattractant Gradients Supports a Winner-Take-All
                        Mechanism},
             journal = {PLoS ONE},
                year = {2014},
               month = {01},
              volume = {9},
              number = {1},
               pages = {e85726},
           publisher = {Public Library of Science},
    }
                  
  • 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.
      PDF   DOI: 10.4208/cicp.101112.100413a   URL
    
    @article{2014_ChCoAkOl_mpnpe,
              author = {Chaudhry, Jehanzeb Hameed and Comer, Jeffrey and
                        Aksimentiev, Aleksei and Olson, Luke N.},
               title = {A finite element method for modified
                        {P}oisson-{N}ernst-{P}lanck equations
    to determine ion flow though a nanopore},
             journal = {Communications in Computational Physics},
                year = {2014},
              volume = {15},
               pages = {93--125},
    }
                  
  • 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, 375-402.
      PDF   DOI: 10.1002/fld.3748
    
    @article{2012_BoLaOl_disclsv,
              author = {Bochev, Pavel and Lai, James and Olson, Luke},
               title = {A non-conforming least-squares finite element method for
                        incompressible fluid flow problems},
             journal = {International Journal for Numerical Methods in Fluids},
                year = {2012},
               pages = {375--402},
           publisher = {John Wiley \& Sons, Ltd},
    }
                  
  • Bell, N., Dalton, S., Olson, L., Exposing Fine-Grained Parallelism in Algebraic Multigrid Methods, SIAM Journal on Scientific Computing, 34 (2012), C123-C152.
      PDF   DOI: 10.1137/110838844
    
    @article{2012_BeDaOl_amggpu,
              author = {Bell, N. and Dalton, S. and Olson, L.},
               title = {Exposing Fine-Grained Parallelism in Algebraic Multigrid
                        Methods},
             journal = {SIAM Journal on Scientific Computing},
                year = {2012},
              volume = {34},
              number = {4},
               pages = {C123--C152},
    }
                  
  • Bell, Nathan, Dalton, Steven, Olson, Luke, Exposing Fine-Grained Parallelism in Algebraic Multigrid Methods, NVR-2011-002, NVIDIA Corporation, June, 2011.
      PDF   URL
    
    @techreport{2011_BeDaOl_amggpu_tr,
              author = {Bell, Nathan and Dalton, Steven and Olson, Luke},
               title = {Exposing Fine-Grained Parallelism in Algebraic Multigrid
                        Methods},
                year = {2011},
         institution = {{NVIDIA} Corporation},
               month = {June},
              number = {NVR-2011-002},
    }
                  
  • 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.
      PDF   DOI: 10.1016/j.amc.2011.10.054   URL
    
    @article{2012_ChBoOl_rescaledpbe,
              author = {Chaudhry, Jehanzeb Hameed and Bond, Stephen D. and Olson,
                        Luke N.},
               title = {A weighted adaptive least-squares finite element method for
                        the Poisson-Boltzmann equation},
             journal = {Applied Mathematics and Computation},
                year = {2012},
              volume = {218},
              number = {9},
               pages = {4892--4902},
    }
                  
  • 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.
      PDF   DOI: 10.1137/100799095   URL
    
    @article{2011_LaOl_hierhocurl,
              author = {Lai, James H. and Olson, Luke N.},
               title = {Algebraic Multigrid for High-Order Hierarchical $H(curl)$
                        Finite Elements},
             journal = {SIAM Journal on Scientific Computing},
                year = {2011},
              volume = {33},
              number = {5},
               pages = {2888--2902},
           publisher = {SIAM},
    }
                  
  • Olson, Luke N., Schroder, Jacob B., Components of a more robust multilevel solver for emerging architectures and complex applications, SciDAC 2011, Denver, CO, 2011.
      PDF
    
    @inproceedings{2011_OlSc_scidac11,
              author = {Olson, Luke N. and Schroder, Jacob B.},
               title = {Components of a more robust multilevel solver for emerging
                        architectures and complex applications},
                year = {2011},
             address = {Denver, CO},
           booktitle = {SciDAC 2011},
               month = {July 10-14},
    }
                  
  • 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.
      PDF   DOI: 10.1016/j.jcp.2011.05.009   URL
    
    @article{2011_OlSc_hodg,
              author = {Olson, Luke N. and Schroder, Jacob B.},
               title = {Smoothed aggregation multigrid solvers for high-order
                        discontinuous Galerkin methods for elliptic problems},
             journal = {Journal of Computational Physics},
                year = {2011},
              volume = {230},
              number = {18},
               pages = {6959--6976},
    }
                  
  • Olson, Luke, Langtangen, Hans Petter, Woodward, Carol S., CSE 2011: SIAG/CSE Holds Milestone Meeting in Reno, SIAM News, 44 (2011).
      URL
    
    @article{2011_OlLaWo_csenews,
              author = {Olson, Luke and Langtangen, Hans Petter and Woodward, Carol
                        S.},
               title = {CSE 2011: SIAG/CSE Holds Milestone Meeting in Reno},
             journal = {SIAM News},
                year = {2011},
               month = {June},
              volume = {44},
              number = {5},
    }
                  
  • 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.
      PDF   DOI: 10.1137/100803031   URL
    
    @article{2011_OlScTu_energymin,
              author = {Olson, Luke N. and Schroder, Jacob B. and Tuminaro, Raymond
                        S.},
               title = {A General Interpolation Strategy for Algebraic Multigrid
                        Using Energy Minimization},
             journal = {SIAM Journal on Scientific Computing},
                year = {2011},
              volume = {33},
              number = {2},
               pages = {966--991},
           publisher = {SIAM},
    }
                  
  • 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, 782–-804.
      PDF   DOI: 10.1002/fld.2536
    
    @article{2011_BoLaOl_discls,
              author = {Bochev, Pavel and Lai, James and Olson, Luke},
               title = {A locally conservative, discontinuous least-squares finite
                        element method for the Stokes equations},
             journal = {International Journal for Numerical Methods in Fluids},
                year = {2011},
               pages = {782–-804},
           publisher = {John Wiley \& Sons, Ltd.},
    }
                  
  • 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.
      PDF
    
    @inproceedings{2010_LaBoOlPeRiSi_disclsproceed,
              author = {Lai, J. and Bochev, P. and Olson, L. and Peterson, K. and
                        Ridzal, D. and Siefert, C.},
               title = {A Discontinuous Velocity Least Squares Finite Element Method
                        for the Stokes Equations With Improved Mass Conservation},
                year = {2010},
           booktitle = {CSRI Summer Proceedings 2010, Sandia National Laboratory},
               month = {December},
    }
                  
  • 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.
      PDF   DOI: 10.1007/s10915-010-9441-7
    
    @article{2010_ChBoOl_mpbe,
              author = {Chaudhry, Jehanzeb and Bond, Stephen and Olson, Luke},
               title = {Finite element approximation to a finite-size modified
                        {P}oisson--{B}oltzmann equation},
             journal = {Journal of Scientific Computing},
                year = {2010},
              volume = {47},
               pages = {347--364},
           publisher = {Springer Netherlands},
    }
                  
  • 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.
      PDF   DOI: 10.1016/j.jcp.2010.01.024
    
    @article{2010_ZhIsOlFr_blood,
              author = {Zhao, Hong and Isfahani, Amir H. G. and Olson, Luke N. and
                        Freund, Jonathan B.},
               title = {A spectral boundary integral method for flowing blood
                        cells},
             journal = {Journal of Computational Physics},
                year = {2010},
              volume = {229},
              number = {10},
               pages = {3726--3744},
    }
                  
  • Olson, Luke N., Schroder, Jacob B., Smoothed aggregation for Helmholtz problems, Numerical Linear Algebra with Applications, 17 (2010), 361-386.
      PDF   DOI: 10.1002/nla.686
    
    @article{2010_OlSc_helmsa,
              author = {Olson, Luke N. and Schroder, Jacob B.},
               title = {Smoothed aggregation for {H}elmholtz problems},
             journal = {Numerical Linear Algebra with Applications},
                year = {2010},
              volume = {17},
              number = {2--3},
               pages = {361--386},
           publisher = {John Wiley \& Sons, Ltd.},
    }
                  
  • Alber, D.M., Olson, L.N., Coarsening Invariance and Bucket-Sorted Independent Sets for Algebraic Multigrid, Electronic Transactions on Numerical Analysis, 37 (2010), 367-385.
      PDF   URL
    
    @article{2010_AlOl_bsis,
              author = {Alber, D.M. and Olson, L.N.},
               title = {Coarsening Invariance and Bucket-Sorted Independent Sets for
                        Algebraic Multigrid},
             journal = {Electronic Transactions on Numerical Analysis},
                year = {2010},
              volume = {37},
               pages = {367--385},
    }
                  
  • 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.
      PDF   DOI: 10.1002/jcc.21446
    
    @article{2010_BoChCyOl_lspbe,
              author = {Bond, Stephen D. and Chaudhry, Jehanzeb Hameed and Cyr, Eric
                        C. and Olson, Luke N.},
               title = {A First-Order Systems Least-Squares Finite Element Method
                        for the {P}oisson-{B}oltzmann Equation},
             journal = {Journal of Computational Chemistry},
                year = {2010},
              volume = {31},
              number = {8},
               pages = {1625--1635},
           publisher = {Wiley Subscription Services, Inc., A Wiley Company},
    }
                  
  • 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.
      PDF   DOI: 10.1002/nla.669
    
    @article{2010_OlScTu_evosoc,
              author = {Olson, Luke N. and Schroder, Jacob and Tuminaro, Raymond
                        S.},
               title = {A new perspective on strength measures in algebraic
                        multigrid},
             journal = {Numerical Linear Algebra with Applications},
                year = {2010},
              volume = {17},
              number = {4},
               pages = {713--733},
           publisher = {John Wiley \& Sons, Ltd.},
    }
                  
  • Schroder, J., Tuminaro, R., Olson, L., Generalized Strength of Connection in Algebraic Multigrid, CSRI Summer Proceedings 2007, Sandia National Laboratory, 2007.
      PDF
    
    @inproceedings{2007_ScTuOl_socproceedings,
              author = {Schroder, J. and Tuminaro, R. and Olson, L.},
               title = {Generalized Strength of Connection in Algebraic Multigrid},
                year = {2007},
           booktitle = {CSRI Summer Proceedings 2007, Sandia National Laboratory},
               month = {December},
    }
                  
  • Bell, Nathan, Olson, Luke N., Algebraic multigrid for k-form Laplacians, Numerical Linear Algebra with Applications, 15 (2008), 165-185.
      PDF   DOI: 10.1002/nla.577
    
    @article{2008_BeOl_xsa,
              author = {Bell, Nathan and Olson, Luke N.},
               title = {Algebraic multigrid for $k$-form {L}aplacians},
             journal = {Numerical Linear Algebra with Applications},
                year = {2008},
              volume = {15},
              number = {2--3},
               pages = {165--185},
    }
                  
  • 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.
      PDF   DOI: 10.1109/APS.2007.4396692
    
    @inproceedings{2007_LiOlJi_spectralcurl,
              author = {Lin, Xi and Olson, Luke and Jin, Jianming},
               title = {An interpolatory spectral element method using curl-
                        conforming vector basis functions on tetrahedra},
                year = {2007},
           booktitle = {Antennas and Propagation Society International Symposium,
                        2007 IEEE},
               month = {June},
               pages = {5095--5098},
    }
                  
  • Alber, David M., Olson, Luke N., Parallel coarse-grid selection, Numerical Linear Algebra with Applications, 14 (2007), 611-643.
      PDF   DOI: 10.1002/nla.541
    
    @article{2007_AlOl_pcgselect,
              author = {Alber, David M. and Olson, Luke N.},
               title = {Parallel coarse-grid selection},
             journal = {Numerical Linear Algebra with Applications},
                year = {2007},
              volume = {14},
              number = {8},
               pages = {611--643},
    }
                  
  • 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.
      PDF   DOI: 10.1137/060663465
    
    @article{2007_Olson_hoamgtri,
              author = {Olson, Luke},
               title = {Algebraic multigrid preconditioning of high-order spectral
                        elements for elliptic problems on a simplicial mesh},
             journal = {SIAM J. Sci. Comput.},
                year = {2007},
              volume = {29},
              number = {5},
               pages = {2189--2209},
    }
                  
  • 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).
      PDF   DOI: 10.1007/978-3-540-34469-8_39
    
    @inproceedings{2007_HeOlWi_asmhelm,
              author = {Hesthaven, J. S. and Olson, L. N. and Wilcox, L. C},
               title = {Developments in Overlapping {S}chwarz Preconditioning of
                        High-Order Nodal Discontinuous {G}alerkin Discretizations},
                year = {2007},
           booktitle = {Domain Decomposition Methods in Science and Engineering
                        XVI},
              volume = {55},
               pages = {325--332},
           publisher = {Springer Berlin Heidelberg},
              series = {Lecture Notes in Computational Science and Engineering},
    }
                  
  • 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.
      PDF   DOI: 10.1016/j.jcp.2004.10.021
    
    @article{2005_HeMaMcOl_hoamg,
              author = {Heys, J. J. and Manteuffel, T. A. and McCormick, S. F. and
                        Olson, L. N.},
               title = {Algebraic multigrid for higher-order finite elements},
             journal = {J. Comput. Phys.},
                year = {2005},
              volume = {204},
              number = {2},
               pages = {520--532},
    }
                  
  • 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.
      PDF   DOI: 10.1137/S1064827503430758
    
    @article{2005_dSMaMcOl_divls,
              author = {{d}e Sterck, H. and Manteuffel, Thomas A. and McCormick,
                        Stephen F. and Olson, Luke},
               title = {Numerical conservation properties of {$H({\rm
                        div})$}-conforming least-squares finite element methods for
                        the {B}urgers equation},
             journal = {SIAM J. Sci. Comput.},
                year = {2005},
              volume = {26},
              number = {5},
               pages = {1573--1597},
    }
                  
  • 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.
      PDF   DOI: 10.1137/S106482750240858X
    
    @article{2004_dSMaMcOl_hypls,
              author = {{d}e Sterck, H. and Manteuffel, Thomas A. and McCormick,
                        Stephen F. and Olson, Luke},
               title = {Least-squares finite element methods and algebraic multigrid
                        solvers for linear hyperbolic {PDE}s},
             journal = {SIAM J. Sci. Comput.},
                year = {2004},
              volume = {26},
              number = {1},
               pages = {31--54},
    }
                  
  • Olson, L. N., A Dual Least-Squares Finite Element Method for Hyperbolic PDEs, Eleventh Copper Mountain Conference On Multigrid Methods, 2003, (Best student paper).
      PDF
    
    @inproceedings{2003_Olson_dualls,
              author = {Olson, L. N.},
               title = {A Dual Least-Squares Finite Element Method for Hyperbolic
                        PDEs},
                year = {2003},
           booktitle = {Eleventh Copper Mountain Conference On Multigrid Methods},
                note = {(Best student paper)},
    }
                  
  • Olson, L. N., Multilevel Least-Squares Finite Element Methods for Hyperbolic PDEs, University of Colorado at Boulder, Department of Applied Mathematics, 2003.
      PDF
    
    @phdthesis{2003_Olson_thesis,
              author = {Olson, L. N.},
               title = {Multilevel Least-Squares Finite Element Methods for
                        Hyperbolic {PDEs}},
                year = {2003},
             address = {Department of Applied Mathematics},
              school = {University of Colorado at Boulder},
    }
                  

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.