I am a computational mathematician in the Center for Applied Scientific Computing at LLNL. My research interests are in multigrid preconditioning, high-order finite element methods, PDE-constrained optimization, and high performance scientific computing, more generally.
I received my Ph.D. in Applied Mathematics from the University of Colorado, Boulder, under Xiao-Chuan Cai. Before coming to LLNL, I did a postdoc in the math department at Louisiana State University and another postdoc at the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg.
A. T. Barker, V. Dobrev, J. Gopalakrishnan and T. Kolev, A scalable preconditioner for a DPG method,
SIAM Journal on Scientific Computing, submitted (arxiv.org/abs/1612.00838).
A. T. Barker, C. S. Lee and P. S. Vassilevski, Spectral upscaling for graph Laplacian problems with
application to reservoir simulation, SIAM Journal on Scientific Computing, in press.
A. T. Barker, T. Rees and M. Stoll, A fast solver for an H1 regularized PDE-constrained optimization problem, Communications in Computational Physics 19 (2016) pp. 143-167.
A. T. Barker and M. Stoll, Domain decomposition in time for PDE–constrained optimization, Computer
Physics Communications 197 (2015) pp. 136–143.
B. Ayuso, A. T. Barker and P. S. Vassilevski, A combined preconditioning strategy for nonsymmetric systems, SIAM Journal on Scientific Computing 36 (2014) pp. A2533-A2556.
A. T. Barker, A minimal communication approach to parallel time integration, International Journal of Computer Mathematics 91 (2014) pp. 601-615.
A. T. Barker, S. C. Brenner, E.-H. Park and L.-Y. Sung, One-level additive Schwarz algorithms for the discontinuous Petrov-Galerkin method, technical report 2012, (arxiv.org/abs/1212.2645).
A. T. Barker and S. C. Brenner, A mixed finite element method for the Stokes equations based on a weakly over-penalized symmetric interior penalty approach, Journal of Scientific Computing 58 (2014) pp. 290–307.
A. T. Barker, S. C. Brenner, E.-H. Park, and L.-Y. Sung, A non-overlapping DD preconditioner for a weakly over-penalized symmetric interior penalty method, in R. Bank et. al., eds, Domain Decomposition Methods in Science and Engineering XX, Lecture Notes in Computational Science and Engineering 91, Springer (2013), pp. 247–254.
A. T. Barker, S. C. Brenner and L.-Y. Sung, Overlapping Schwarz domain decomposition preconditioners for the local discontinuous Galerkin method for elliptic problems, Journal of Numerical Mathematics 19 (2011), pp. 165–187.
A. T. Barker, S. C. Brenner, E.-H. Park and L.-Y. Sung, Two-level additive Schwarz preconditioners for a weakly overpenalized symmetric interior penalty method, Journal of Scientific Computing 47 (2011), pp. 27–49.
A. T. Barker and X.-C. Cai, Two-level methods for blood flow simulation, in Y. Huang et. al., eds, Domain Decomposition Methods in Science and Engineering XIX, Lecture Notes in Computational Science and Engineering 78, Springer (2011), pp. 141–148.
A. T. Barker and X.-C. Cai, Two-level Newton and hybrid Schwarz preconditioners for fluid-structure interaction, SIAM Journal on Scientific Computing 32 (2010), pp. 2390–2417.
A. T. Barker and X.-C. Cai, Scalable parallel methods for monolithic coupling in fluidstructure interaction with application to blood flow modeling, Journal of Computational Physics 229 (2010), pp. 64–259.
A. T. Barker, Evolutionary stability in the traveler's dilemma, College Mathematics Journal 40 (2009), pp. 33–38. Winner of the MAA George Polya Award for mathematical exposition, 2010.
A. T. Barker and X.-C. Cai, Newton-Krylov-Schwarz for fully coupled fluid-structure interaction with application, in M. Bercovier et. al., eds, Domain Decomposition Methods in Science and Engineering XVIII, Lecture Notes in Computational Science and Engineering 70, Springer (2010), pp. 275–282.