# Luke Olson

## Research

##### Research history :: Ongoing projects :: Related interests

## Summary...

Areas of interest: |
numerical analysis, scientific computing, high performance computing |

Keywords: |
numerical PDEs, finite elements, spectral elements, multigrid, iterative methods, GPUs, parallel |

Research directions

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

## Group...

#### 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)

- Thesis:
*Conservation and efficiency in least squares finite element methods* - algebraic multigrid, least-squares and discontinuous least-squares finite element methods, high-order, vector elements, Stokes flow

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

- Thesis:
*Finite element methods for implicit solvent models* - implicit solvation models, least-squares finite element methods, Poisson-Boltzmann equation, Poisson-Nerst-Planck, error adaptivity, adjoint estimators

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

- Thesis:
*Generalizing smoothed aggregation-based algebraic multigrid* - PyAMG
- algebraic multigrid, complex non-symmetric matrices, high-order discontinuous Galerkin

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

- Thesis:
*Algebraic Multigrid For Discrete Differential Forms* - scipy.sparse, PyAMG
- discrete exterior calculus, algebraic multigrid, hodge decomposisions

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

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

## Publications...

Jehanzeb Hameed Chaudhry, Eric C. Cyr, Kuo Liu, Thomas A. Manteuffel, Luke N. Olson, and Lei Tang. A goal-oriented approach to least-squares finite element methods.

*SIAM Journal on Numerical Analysis*, 2011. in review. [ bib ]Nathan Bell, Steven Dalton, and Luke N. Olson. Exposing fine-grained parallelism in algebraic multigrid methods.

*SIAM Journal on Scientific Computing*, 2011. in review. [ bib ]Jehanzeb Hameed Chaudhry, Jeffrey Comer, Aleksei Aksimentiev, and Luke N. Olson. A finite element method for modified Poisson-Nernst-Planck equations to determine ion flow though a nanopore.

*Journal of Computational Physics*, 2011. in review. [ bib ]James Lai and Multigrid for high-order interpolatory

*h*(*curl*) conforming finite elements.*Numerical Linear Algebra with Applications*, 2011. in review. [ bib ]Jehanzeb Hameed Chaudhry, Stephen D. Bond, and Luke N. Olson. A weighted adaptive least-squares finite element method for the Poisson-Boltzmann equation.

*Applied Mathematics and Computation*, 2010. in review. [ bib ]James Lai and Algebraic multigrid for high-order hierarchical

*h*(*curl*) finite elements.*SIAM Journal on Scientific Computing*, 2011. to appear. [ bib ]Luke N. Olson and Jacob B. Schroder. Components of a more robust multilevel solver for emerging architectures and complex applications. In

*SciDAC 2011*, 2011. to appear. [ bib ]J. S. Hesthaven, L. N. Olson, and L. C Wilcox. Developments in overlapping Schwarz preconditioning of high-order nodal discontinuous Galerkin discretizations. In

*Domain Decomposition Methods in Science and Engineering XVI*, volume 55 of*Lecture Notes in Computational Science and Engineering*, pages 325-332. Springer Berlin Heidelberg, 2007. [ bib | doi | http | pdf ]

## Presentations...

Extending algebraic multigrid solvers: Next generation algorithms, applications, and architectures, July 2011. SciDAC 2011. [ pdf ]

Luke Olson and Jacob Schroder. Workshop: Pyamg tutorial, April 2011. Fifteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO. [ pdf ]

Algebraic multigrid on the gpu: Exposing fine-grained paallelism, April 2011. Fifteenth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO. [ pdf ]

## 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

## Images...

**High-order aggregation**Aggregation of high-order nodes in a discontinuous Galerkin mesh.

**least-squares flow**A circular hyperbolic flow using least-squares finite element methods