Luke Olson


Research history     ::     Ongoing projects     ::     Related interests
Quick links on this page:


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

Research directions



Steven Dalton (PhD expected 2013/14)

  • Cusp
  • algebraic multigrd on the GPU, sparse computations


Yuki Kimura  (Chemical and Biomolecular Engineering)

  • cellular chemotaxis, finite elements, large scale simulation


Natalie Beams  (Mechanical Science and Engineering)

  • fast summation methods, boundary element methods, blood flow simulations

Group Alumni...

James Lai  PhD, 2012(now at Microsoft)

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

Jacob Schroder PhD, 2010  (now at University of Colorado at Boulder  Lawrence Livermore National Laboratories)

Nathan Bell, PhD, 2008  (now at Nvidia  Google)

David Alber, PhD, 2007  (now at NREL  Microsoft  WalkScore)



Funded Projects...


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

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


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

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


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

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


Multilevel Schwarz Preconditioners for Adaptive High-Order Discontinuous Galerkin Methods   (NSF DMS 0612448, PI: L Olson, $178,418, 2006-2009)

  • domain decomposition and coarse solvers for electromagnetics
  • algebraic multigrid methods for electromagnetic wave problems
  • multigrid strategies for high-order elements
  • multigrid strategies for discontinuous elements


Fast Solutions Methods for Multiscale Cellular Mechanics in Microcirculation   (A. Isfahani CSE Fellowship at Illinois with J. Freund, Mechanical Science)

  • red blood cell flow
  • spectral boundary integral methods
  • deflated iterative Krylov methods
  • particle-mesh Ewald


First-Order System Least Squares for Biomolecular Electrodiffusion   (Jehanzeb Hameed Chaudhry CSE Fellowship at Illinois with Stephen bond, CS; and Alek Aksimentiev, Physics)

  • steric effects of biomolecular simulations
  • advanced finite element methods for PBE and PNPE


test » Learn More PlanewavePlanewave used in a multigrid hierarchy for the Helmholtz scattering problem
test » Learn More High-order aggregationAggregation of high-order nodes in a discontinuous Galerkin mesh.
test » Learn More HoleA hole found in a sensor network problem (with multigrid)
test » Learn More AggregatesAggregates using Lloyd aggregations.
test » Learn More HoleA hole found in a sensor network problem (with multigrid)
test » Learn More Aggregates Just some aggregates generated by PyAMG
test » Learn More Circular aggregatesAggregates in a recirculating flow problem using the Evolution measure
test » Learn More Long rangeLong range connections in multigrid for high-order discontinuous galerkin discretizations
test » Learn More Homology basisOne component of a homology basis for a rocker arm (solve with multigrid
test » Learn More k-form aggregationEdge aggregation for a Titan rocket mesh
test » Learn More low-order DGElements in a low-order discontinuous Galerkin preconditioner
test » Learn More Spurious modesSpurious modes in an H(div) least-squares formulation of a hyperbolic problem
test » Learn More least-squares flowA circular hyperbolic flow using least-squares finite element methods
test » Learn More High-order coarseningFine, coarse, and coarser levels of an algebraic heirarchy for high-order quadrilateral elemeents
test » Learn More low order FEGraphical view of a low order FE preconditioner for a high-order SE
test » Learn More Aggregation Close-upA close up of aggregation of nodes using the Evolution Measure
test » Learn More AggregationAggregation of nodes using the classic measure
test » Learn More AggregationAggregation of nodes using the Evolution Measure
test » Learn More High-orderHigh-order nodal locations on the corner, edges, faces, and interior of an element are highlighted.
test » Learn More Parallel CoarseningDistributions of fine nodes in an algebraic multigrid method.
test » Learn More Parallel CoarseningCoarse nodes and fine nodes in an algebraic multigrid heirarchy are shown. Processor boundaries stand out.
test » Learn More Parallel CoarseningCommunicaiton on processor boundaries for coarse nodes in an algebraic multigrid heirarchy are highlighted.

Past Work...

lth lth bwn ucb uia lth lll cry