Research Focus
  • Multigrid methods
  • Sparse matrix computations
  • Finite element methods
  • High performance computing
  • Scalable solvers on GPUs, large-scale systems
Students
Publications
  • Voronin, Alexey, MacLachlan, Scott, Olson, Luke N., Tuminaro, Raymond, Monolithic Algebraic Multigrid Preconditioners for the Stokes Equations, 2023, in review.
      URL 
    
@misc{2023_VoMaOlTu_monolithicamgstokes,
          author = {Voronin, Alexey and MacLachlan, Scott and Olson, Luke N. and
                    Tuminaro, Raymond},
           title = {Monolithic Algebraic Multigrid Preconditioners for the
                    Stokes Equations},
            year = {2023},
            note = {in review},
}
  • Sentz, Peter, Beckwith, Kristian, Cyr, Eric C., Olson, Luke N., Patel, Ravi, Reduced basis approximations of parameterized dynamical partial differential equations via neural networks, Foundations of Data Science, 2024.
      DOI: 10.3934/fods.2024044   URL 
    
@article{2022_SeBeCyOlPa_nnrb,
          author = {Sentz, Peter and Beckwith, Kristian and Cyr, Eric C. and
                    Olson, Luke N. and Patel, Ravi},
           title = {Reduced basis approximations of parameterized dynamical
                    partial differential equations via neural networks},
         journal = {Foundations of Data Science},
            year = {2024},
}
  • Zaman, Tareq, Nytko, Nicolas, Taghibakhshi, Ali, MacLachlan, Scott, Olson, Luke, West, Matthew, Generalizing Lloyd’s Algorithm for Graph Clustering, SIAM Journal on Scientific Computing, 46 (2024), A2819-A2847.
      DOI: 10.1137/23M1556800   URL 
    
@article{2024_ZaNyTaMaOlWe_lloyd,
          author = {Zaman, Tareq and Nytko, Nicolas and Taghibakhshi, Ali and
                    MacLachlan, Scott and Olson, Luke and West, Matthew},
           title = {Generalizing Lloyd’s Algorithm for Graph Clustering},
         journal = {SIAM Journal on Scientific Computing},
            year = {2024},
          eprint = {https://doi.org/10.1137/23M1556800},
          volume = {46},
          number = {5},
           pages = {A2819-A2847},
}
  • Zaman, Tareq, Nytko, Nicolas, Taghibakhshi, Ali, MacLachlan, Scott, Olson, Luke, West, Matthew, Generalizing reduction-based algebraic multigrid, Numerical Linear Algebra with Applications, 31 (2024), e2543.
      PDF   DOI: 10.1002/nla.2543   URL 
    
@article{2024_ZaNyTaMaOlWe_reductionamg,
          author = {Zaman, Tareq and Nytko, Nicolas and Taghibakhshi, Ali and
                    MacLachlan, Scott and Olson, Luke and West, Matthew},
           title = {Generalizing reduction-based algebraic multigrid},
         journal = {Numerical Linear Algebra with Applications},
            year = {2024},
          eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nla.2543},
          volume = {31},
          number = {3},
           pages = {e2543},
}
  • Bell, Nathan, Olson, Luke N., Schroder, Jacob, Southworth, Ben, PyAMG: Algebraic Multigrid Solvers in Python, Journal of Open Source Software, 8 (2023), 5495.
      PDF   DOI: 10.21105/joss.05495   URL 
    
@article{2023_PyAMG,
          author = {Bell, Nathan and Olson, Luke N. and Schroder, Jacob and
                    Southworth, Ben},
           title = {PyAMG: Algebraic Multigrid Solvers in Python},
         journal = {Journal of Open Source Software},
            year = {2023},
          volume = {8},
          number = {87},
           pages = {5495},
       publisher = {The Open Journal},
}
  • Janna, Carlo, Franceschini, Andrea, Schroder, Jacob B., Olson, Luke, Parallel Energy-Minimization Prolongation for Algebraic Multigrid, SIAM Journal on Scientific Computing, 45 (2023), A2561-A2584.
      PDF   DOI: 10.1137/22M1513794   URL 
    
@article{2023_JaFrScOl_paramg,
          author = {Janna, Carlo and Franceschini, Andrea and Schroder, Jacob B.
                    and Olson, Luke},
           title = {Parallel Energy-Minimization Prolongation for Algebraic
                    Multigrid},
         journal = {SIAM Journal on Scientific Computing},
            year = {2023},
          volume = {45},
          number = {5},
           pages = {A2561-A2584},
}
  • Zaman, Tareq Uz, MacLachlan, Scott P., Olson, Luke N., West, Matthew, Coarse-grid selection using simulated annealing, Journal of Computational and Applied Mathematics, 431 (2023), 115263.
      PDF   DOI: 10.1016/j.cam.2023.115263   URL 
    
@article{2023_ZaMaOlWe_cgselection,
          author = {Zaman, Tareq Uz and MacLachlan, Scott P. and Olson, Luke N.
                    and West, Matthew},
           title = {Coarse-grid selection using simulated annealing},
         journal = {Journal of Computational and Applied Mathematics},
            year = {2023},
          volume = {431},
           pages = {115263},
}
  • Lockhart, Shelby, Bienz, Amanda, Gropp, William D., Olson, Luke N., Characterizing the performance of node-aware strategies for irregular point-to-point communication on heterogeneous architectures, Parallel Computing, 2023, 103021.
      PDF   DOI: 10.1016/j.parco.2023.103021   URL 
    
@article{2023_LoBiGrOl_charperf,
          author = {Lockhart, Shelby and Bienz, Amanda and Gropp, William D. and
                    Olson, Luke N.},
           title = {Characterizing the performance of node-aware strategies for
                    irregular point-to-point communication on heterogeneous
                    architectures},
         journal = {Parallel Computing},
            year = {2023},
           pages = {103021},
}
  • Taghibakhshi, Ali, Nytko, Nicolas, Zaman, Tareq Uz, MacLachlan, Scott, Olson, Luke, West, Matthew, Learning Interface Conditions in Domain Decomposition Solvers, Advances in Neural Information Processing Systems, 35 (2022).
      PDF   URL 
    
@inproceedings{2022_TaNyZaMaOlWe_learndd,
          author = {Taghibakhshi, Ali and Nytko, Nicolas and Zaman, Tareq Uz and
                    MacLachlan, Scott and Olson, Luke and West, Matthew},
           title = {Learning Interface Conditions in Domain Decomposition
                    Solvers},
            year = {2022},
       booktitle = {Advances in Neural Information Processing Systems},
          volume = {35},
           pages = {7222--7235},
}
  • Lockhart, Shelby, Bienz, Amanda, Gropp, William, Olson, Luke, Performance Analysis and Optimal Node-Aware Communication for Enlarged Conjugate Gradient Methods, ACM Trans. Parallel Comput., 2023.
      PDF   DOI: 10.1145/3580003   URL 
    
@article{2023_LoBiGrOl_ecg,
          author = {Lockhart, Shelby and Bienz, Amanda and Gropp, William and
                    Olson, Luke},
           title = {Performance Analysis and Optimal Node-Aware Communication
                    for Enlarged Conjugate Gradient Methods},
         journal = {ACM Trans. Parallel Comput.},
            year = {2023},
         address = {New York, NY, USA},
           month = {1},
       publisher = {Association for Computing Machinery},
}
  • Spies, Lukas, Bienz, Amanda, Moulton, David, Olson, Luke, Reisner, Andrew, Tausch: A halo exchange library for large heterogeneous computing systems using MPI, OpenCL, and CUDA, Parallel Computing, 114 (2022), 102973.
      PDF   DOI: 10.1016/j.parco.2022.102973   URL 
    
@article{2022_SpBiMoOlRe_tausch,
          author = {Spies, Lukas and Bienz, Amanda and Moulton, David and Olson,
                    Luke and Reisner, Andrew},
           title = {{Tausch}: A halo exchange library for large heterogeneous
                    computing systems using {MPI}, {OpenCL}, and {CUDA}},
         journal = {Parallel Computing},
            year = {2022},
          volume = {114},
           pages = {102973},
}
  • Bell, Nathan, Olson, Luke N., Schroder, Jacob, PyAMG: Algebraic Multigrid Solvers in Python, Journal of Open Source Software, 7 (2022), 4142.
      PDF   DOI: 10.21105/joss.04142   URL 
    
@article{2022_BeOlSc_pyamg,
          author = {Bell, Nathan and Olson, Luke N. and Schroder, Jacob},
           title = {{PyAMG}: Algebraic Multigrid Solvers in Python},
         journal = {Journal of Open Source Software},
            year = {2022},
          volume = {7},
          number = {72},
           pages = {4142},
       publisher = {The Open Journal},
}
  • Lockhart, Shelby, Gardner, David J., Woodward, Carol S., Thomas, Stephen, Olson, Luke N., Performance of Low Synchronization Orthogonalization Methods in Anderson Accelerated Fixed Point Solvers, Proceedings of the 2022 SIAM Conference on Parallel Processing for Scientific Computing, 2022.
      PDF   DOI: 10.1137/1.9781611977141.5   URL 
    
@inproceedings{2022_LoGaWoThOl_anderson,
          author = {Lockhart, Shelby and Gardner, David J. and Woodward, Carol
                    S. and Thomas, Stephen and Olson, Luke N.},
           title = {Performance of Low Synchronization Orthogonalization Methods
                    in {A}nderson Accelerated Fixed Point Solvers},
            year = {2022},
       booktitle = {Proceedings of the 2022 SIAM Conference on Parallel
                    Processing for Scientific Computing},
         chapter = {},
           pages = {49--59},
}
  • Voronin, Alexey, He, Yunhui, MacLachlan, Scott, Olson, Luke N., Tuminaro, Raymond, Low-order preconditioning of the Stokes equations, Numerical Linear Algebra with Applications, 29 (2022), e2426.
      PDF   DOI: 10.1002/nla.2426   URL 
    
@article{2022_VoHeMaOlTu_iso,
          author = {Voronin, Alexey and He, Yunhui and MacLachlan, Scott and
                    Olson, Luke N. and Tuminaro, Raymond},
           title = {Low-order preconditioning of the {S}tokes equations},
         journal = {Numerical Linear Algebra with Applications},
            year = {2022},
          volume = {29},
          number = {3},
           pages = {e2426},
}
  • Taghibakhshi, Ali, MacLachlan, Scott, Olson, Luke, West, Matthew, Optimization-Based Algebraic Multigrid Coarsening Using Reinforcement Learning, Advances in Neural Information Processing Systems, 34 (2021).
      PDF   URL 
    
@inproceedings{2021_TaMaOlWe_optmg,
          author = {Taghibakhshi, Ali and MacLachlan, Scott and Olson, Luke and
                    West, Matthew},
           title = {Optimization-Based Algebraic Multigrid Coarsening Using
                    Reinforcement Learning},
            year = {2021},
       booktitle = {Advances in Neural Information Processing Systems},
          volume = {34},
           pages = {12129--12140},
}
  • Bienz, Amanda, Olson, Luke N., Gropp, William D., Lockhart, Shelby, Modeling Data Movement Performance on Heterogeneous Architectures, 2021 IEEE High Performance Extreme Computing Conference (HPEC), , (2021).
      PDF   DOI: 10.1109/HPEC49654.2021.9622742 
    
@inproceedings{2021_BeOlGrLo_gpu,
          author = {Bienz, Amanda and Olson, Luke N. and Gropp, William D. and
                    Lockhart, Shelby},
           title = {Modeling Data Movement Performance on Heterogeneous
                    Architectures},
            year = {2021},
       booktitle = {2021 {IEEE} High Performance Extreme Computing Conference
                    ({HPEC})},
          volume = {},
          number = {},
           pages = {1--7},
}
  • Chaudhry, Jehanzeb H., Olson, Luke N., Sentz, Peter, A Least-Squares Finite Element Reduced Basis Method, SIAM Journal on Scientific Computing, 43 (2021), A1081-A1107.
      PDF   DOI: 10.1137/20M1323552   URL 
    
@article{2021_ChOlSe_lsrb,
          author = {Chaudhry, Jehanzeb H. and Olson, Luke N. and Sentz, Peter},
           title = {A Least-Squares Finite Element Reduced Basis Method},
         journal = {SIAM Journal on Scientific Computing},
            year = {2021},
          volume = {43},
          number = {2},
           pages = {A1081-A1107},
}
  • Reisner, Andrew, Bernddt, Markus, Moulton, J. David, Olson, Luke N., Scalable line and plane relaxation in a parallel structured multigrid solver, Parallel Computing, 100 (2020), 102705.
      PDF   DOI: 10.1016/j.parco.2020.102705   URL 
    
@article{2020_ReBeMoOl_plane,
          author = {Reisner, Andrew and Bernddt, Markus and Moulton, J. David
                    and Olson, Luke N.},
           title = {Scalable line and plane relaxation in a parallel structured
                    multigrid solver},
         journal = {Parallel Computing},
            year = {2020},
          volume = {100},
           pages = {102705},
}
  • Bienz, Amanda, Gropp, William D., Olson, Luke N., Reducing communication in algebraic multigrid with multi-step node aware communication, The International Journal of High Performance Computing Applications, 34 (2020), 547-561.
      PDF   DOI: 10.1177/1094342020925535   URL 
    
@article{2020_BiGrOl_reducing,
          author = {Bienz, Amanda and Gropp, William D. and Olson, Luke N.},
           title = {Reducing communication in algebraic multigrid with multi-
                    step node aware communication},
         journal = {The International Journal of High Performance Computing
                    Applications},
            year = {2020},
          volume = {34},
          number = {5},
           pages = {547--561},
}
  • Ibeid, Huda, Olson, Luke, Gropp, William, FFT, FMM, and multigrid on the road to exascale: Performance challenges and opportunities, Journal of Parallel and Distributed Computing, 136 (2020), 63-74.
      PDF   DOI: 10.1016/j.jpdc.2019.09.014   URL 
    
@article{2020_IbOlGr_road,
          author = {Ibeid, Huda and Olson, Luke and Gropp, William},
           title = {{FFT}, {FMM}, and multigrid on the road to exascale:
                    Performance challenges and opportunities},
         journal = {Journal of Parallel and Distributed Computing},
            year = {2020},
          volume = {136},
           pages = {63--74},
}
  • Horn, E., Fulp, D., Calhoun, J., Olson, L., FaultSight: A Fault Analysis Tool for HPC Researchers, 2019 IEEE/ACM 9th Workshop on Fault Tolerance for HPC at eXtreme Scale (FTXS), , (2019).
      PDF   DOI: 10.1109/FTXS49593.2019.00008 
    
@inproceedings{2019_HoFuCaOl_faultsight,
          author = {{Horn}, E. and {Fulp}, D. and {Calhoun}, J. and {Olson},
                    L.},
           title = {{FaultSight}: A Fault Analysis Tool for HPC Researchers},
            year = {2019},
       booktitle = {2019 IEEE/ACM 9th Workshop on Fault Tolerance for HPC at
                    eXtreme Scale (FTXS)},
          volume = {},
          number = {},
           pages = {21--30},
}
  • Ibeid, H., Meng, S., Dobon, O., Olson, L., Gropp, W., Learning with Analytical Models, 2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), , (2019).
      PDF   DOI: 10.1109/IPDPSW.2019.00128 
    
@inproceedings{2019_IbMeDoOlGr_learning,
          author = {{Ibeid}, H. and {Meng}, S. and {Dobon}, O. and {Olson}, L.
                    and {Gropp}, W.},
           title = {Learning with Analytical Models},
            year = {2019},
       booktitle = {2019 IEEE International Parallel and Distributed Processing
                    Symposium Workshops (IPDPSW)},
          volume = {},
          number = {},
           pages = {778--786},
}
  • Bienz, A., Olson, L., Gropp, W., Node-Aware Improvements to Allreduce, 2019 IEEE/ACM Workshop on Exascale MPI (ExaMPI), , (2019).
      PDF   DOI: 10.1109/ExaMPI49596.2019.00008 
    
@inproceedings{2019_BiOlGr,
          author = {{Bienz}, A. and {Olson}, L. and {Gropp}, W.},
           title = {Node-Aware Improvements to Allreduce},
            year = {2019},
       booktitle = {2019 IEEE/ACM Workshop on Exascale MPI (ExaMPI)},
          volume = {},
          number = {},
           pages = {19--28},
}
  • Glimberg, Stefan Lemvig, Engsig-Karup, Allan Peter, Olson, Luke N., A massively scalable distributed multigrid framework for nonlinear marine hydrodynamics, The International Journal of High Performance Computing Applications, 33 (2019), 855-868.
      PDF   DOI: 10.1177/1094342019826662 
    
@article{2019_GlEKOl_hydro,
          author = {Glimberg, Stefan Lemvig and Engsig-Karup, Allan Peter and
                    Olson, Luke N.},
           title = {A massively scalable distributed multigrid framework for
                    nonlinear marine hydrodynamics},
         journal = {The International Journal of High Performance Computing
                    Applications},
            year = {2019},
          volume = {33},
          number = {5},
           pages = {855--868},
}
  • Bienz, Amanda, Gropp, William D., Olson, Luke N., Node aware sparse matrix–vector multiplication, Journal of Parallel and Distributed Computing, 130 (2019), 166-178.
      PDF   DOI: 10.1016/j.jpdc.2019.03.016   URL 
    
@article{2018_BiGrOl_nodeawarespmv,
          author = {Bienz, Amanda and Gropp, William D. and Olson, Luke N.},
           title = {Node aware sparse matrix–vector multiplication},
         journal = {Journal of Parallel and Distributed Computing},
            year = {2019},
          volume = {130},
           pages = {166--178},
}
  • Bienz, Amanda, Gropp, William D., Olson, Luke N., Improving Performance Models for Irregular Point-to-Point Communication, Proceedings of the 25th European MPI Users' Group Meeting, New York, NY, USA, ACM, 2018.
      PDF   DOI: 10.1145/3236367.3236368   URL 
    
@inproceedings{2018_BiGrOl_improvedmodels,
          author = {Bienz, Amanda and Gropp, William D. and Olson, Luke N.},
           title = {Improving Performance Models for Irregular Point-to-Point
                    Communication},
            year = {2018},
         address = {New York, NY, USA},
       booktitle = {Proceedings of the 25th European MPI Users' Group Meeting},
           pages = {7:1--7:8},
       publisher = {ACM},
          series = {EuroMPI'18},
}
  • Calhoun, Jon, Cappello, Franck, Olson, Luke N., Snir, Marc, Gropp, William D., Exploring the feasibility of lossy compression for PDE simulations, The International Journal of High Performance Computing Applications, 33 (2019), 397-410.
      PDF   DOI: 10.1177/1094342018762036   URL 
    
@article{2019_CaCaOlSnGr_lossy,
          author = {Calhoun, Jon and Cappello, Franck and Olson, Luke N. and
                    Snir, Marc and Gropp, William D.},
           title = {Exploring the feasibility of lossy compression for {PDE}
                    simulations},
         journal = {The International Journal of High Performance Computing
                    Applications},
            year = {2019},
          volume = {33},
          number = {2},
           pages = {397--410},
}
  • Reisner, A., Olson, L., Moulton, J., Scaling Structured Multigrid to 500K+ Cores Through Coarse-Grid Redistribution, SIAM Journal on Scientific Computing, 40 (2018), C581-C604.
      PDF   DOI: 10.1137/17M1146440   URL 
    
@article{2018_ReOlMo_scalingstructured,
          author = {Reisner, A. and Olson, L. and Moulton, J.},
           title = {Scaling Structured Multigrid to {500K+} Cores Through
                    Coarse-Grid Redistribution},
         journal = {SIAM Journal on Scientific Computing},
            year = {2018},
          volume = {40},
          number = {4},
           pages = {C581-C604},
}
  • Beams, Natalie N., Kl\"ockner, Andreas, Olson, Luke N., High-order finite element–integral equation coupling on embedded meshes, Journal of Computational Physics, 375 (2018), 1295-1313.
      PDF   DOI: 10.1016/j.jcp.2018.08.032   URL 
    
@article{2018_BeKlOl_feie,
          author = {Beams, Natalie N. and Kl\"ockner, Andreas and Olson, Luke
                    N.},
           title = {High-order finite element–integral equation coupling on
                    embedded meshes},
         journal = {Journal of Computational Physics},
            year = {2018},
          volume = {375},
           pages = {1295--1313},
}
  • Manteuffel, Thomas A., Olson, Luke N., Schroder, Jacob B., Southworth, Ben S., A Root-Node-Based Algebraic Multigrid Method, SIAM Journal on Scientific Computing, 39 (2017), S723-S756.
      PDF   DOI: 10.1137/16M1082706   URL 
    
@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 = {2017},
          volume = {39},
          number = {5},
           pages = {S723-S756},
}
  • 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.
      PDF   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.
      PDF   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., Algebraic Multigrid Methods, Encyclopedia of Applied and Computational Mathematics, Springer Berlin Heidelberg, 2015.
      PDF   DOI: 10.1007/978-3-540-70529-1 
    
@incollection{2015_Ol_encamg,
          author = {Olson, Luke N.},
           title = {Algebraic Multigrid Methods},
            year = {2015},
       booktitle = {Encyclopedia of Applied and Computational Mathematics},
          editor = {Bj\"orn Engquist},
           pages = {977--981},
       publisher = {Springer Berlin Heidelberg},
}
  • Olson, Luke N., Geometric Multigrid Methods, Encyclopedia of Applied and Computational Mathematics, Springer Berlin Heidelberg, 2015.
      PDF   DOI: 10.1007/978-3-540-70529-1 
    
@incollection{2015_Ol_encmg,
          author = {Olson, Luke N.},
           title = {Geometric Multigrid Methods},
            year = {2015},
       booktitle = {Encyclopedia of Applied and Computational Mathematics},
          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 = {9},
            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   URL 
    
@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 {GPU}s Using Merge
                    Path},
            year = {2015},
       booktitle = {Parallel and Distributed Processing Symposium (IPDPS), 2015
                    IEEE International},
           month = {5},
           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 = {1},
}
  • Dalton, Steven, Olson, Luke, Bell, Nathan, Optimizing Sparse Matrix-Matrix Multiplication for the GPU, ACM Transactions on Mathematical Software, 41 (2015), 25:1-25:20.
      PDF   DOI: 10.1145/2699470   URL 
    
@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},
         address = {New York, NY, USA},
           month = {10},
          volume = {41},
          number = {4},
           pages = {25:1--25:20},
       publisher = {ACM},
}
  • 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 = {5},
           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   URL 
    
@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},
          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).
      PDF   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 = {1},
          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, 6, 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 = {6},
          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 {P}oisson-{B}oltzmann 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 = {7},
}
  • 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 {G}alerkin 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).
      PDF   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 {R}eno},
         journal = {SIAM News},
            year = {2011},
           month = {6},
          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 {S}tokes 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 {S}tokes Equations With Improved Mass Conservation},
            year = {2010},
       booktitle = {CSRI Summer Proceedings 2010, Sandia National Laboratory},
           month = {12},
}
  • 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 = {12},
}
  • 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 = {6},
           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 Journal on Scientific Computing, 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 Journal on Scientific Computing},
            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, Journal of Computational Physics, 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 = {Journal of Computational Physics},
            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 Journal on Scientific Computing, 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 Journal on Scientific Computing},
            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 Journal on Scientific Computing, 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 Journal on Scientific Computing},
            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.