Journal Publications

S. Pawar, O. San, B. Aksoylu, A. Rasheed, and T. Kvamsdal, Physics guided machine learning using simplified theories, Physics of Fluids, 33 (2021), 011701, doi.

B. Aksoylu and G.A. Gazonas, On the choice of kernel function in nonlocal wave propagation, Journal of Peridynamics and Nonlocal Modeling, 2 (2020), pp.379-400, doi.

B. Aksoylu and G.A. Gazonas, On nonlocal problems with inhomogeneous local boundary conditions, Journal of Peridynamics and Nonlocal Modeling, 2 (2020), pp.1-25, doi.

B. Aksoylu, F. Celiker, and G.A. Gazonas, Higher order collocation methods for nonlocal problems and their asymptotic compatibility, Communications on Applied Mathematics and Computation, 2(2) (2020), pp. 261-303, doi.

B. Aksoylu and A. Kaya, On smoothers for multigrid of the second kind, Numerical Linear Algebra with Applications, 26(6) (2019), e2267, doi.

B. Aksoylu, F. Celiker, and O. Kilicer, Nonlocal problems with local boundary conditions in higher dimensions, Advances in Computational Mathematics, 45 (2019), pp. 453-492, doi.

B. Aksoylu and A. Kaya, Conditioning and error analysis of nonlocal operators with local boundary conditions, Journal of Computational and Applied Mathematics, 335 (2018), pp. 1-19, doi.

B. Aksoylu and F. Celiker, Nonlocal problems with local Dirichlet and Neumann boundary conditions, Journal of Mechanics of Materials and Structures, 12(4) (2017), pp. 425-437, doi.

B. Aksoylu, H.R. Beyer, and F. Celiker, Application and implementation of incorporating local boundary conditions into nonlocal problems, Numerical Functional Analysis and Optimization, 38(9) (2017), pp. 1077-1114, doi.

B. Aksoylu, H.R. Beyer, and F. Celiker, Theoretical foundations of incorporating local boundary conditions into nonlocal problems, Reports on Mathematical Physics, 80(1) (2017), pp. 39-71, doi.

H.R. Beyer, B. Aksoylu and F. Celiker, On a class of nonlocal wave equations from applications, Journal of Mathematical Physics, 57(6) (2016), 062902, doi.

B. Aksoylu and Z. Unlu, Conditioning analysis of nonlocal integral operators in fractional Sobolev spaces, SIAM Journal on Numerical Analysis, 52 (2014), pp. 653-677, doi.

B. Aksoylu and Z. Unlu, Robust preconditioners for the high-contrast Stokes equation, Journal of Computational and Applied Mathematics, 259 (2014), pp. 944-954, doi.

B. Aksoylu, S. Bond, E. Cyr, and M. Holst, Goal-oriented adaptivity and multilevel preconditioning for the Poisson-Boltzmann equation, Journal of Scientific Computing, 52 (2012), pp. 202-225, doi.

B. Aksoylu and M.L. Parks, Variational theory and domain decomposition for nonlocal problems, Applied Mathematics and Computation, 217 (2011), pp. 6498-6515, doi.

B. Aksoylu and Z. Yeter, Robust multigrid preconditioners for the high-contrast biharmonic plate equation, Numerical Linear Algebra with Applications, 18 (2011), pp. 733--750, doi.

B. Aksoylu and T. Mengesha, Results on nonlocal boundary value problems, Numerical Functional Analysis and Optimization, 31 (2010), pp. 1301-1317, doi.

B. Aksoylu and Z. Yeter, Robust multigrid preconditioners for cell-centered finite volume discretization of the high-contrast diffusion equation, Computing and Visualization in Science, 13 (2010), pp. 229-245, doi.

B. Aksoylu and H.R. Beyer, Results on diffusion equation with rough coefficients, SIAM Journal on Mathematical Analysis, 42 (2010), pp. 406-426, doi, arXiv.

B. Aksoylu and H.R. Beyer, On the characterization of asymptotic cases of the diffusion equation with rough coefficients and applications to preconditioning, Numerical Functional Analysis and Optimization, 30 (2009), pp. 405-420, doi, arXiv.

O. Korobkin, B. Aksoylu, M. Holst, E. Pazos, and M. Tiglio, Solving the Einstein constraint equations on multi-block triangulations using finite element methods, Classical Quantum Gravity, 26 (2009) 145007 (28 pp), doi, arXiv.

B. Aksoylu and H. Klie, A family of physics-based preconditioners for solving elliptic equations on highly heterogeneous media, Applied Numerical Mathematics, 59 (2009), pp. 1159-1186, doi.

B. Aksoylu, I.G. Graham, H. Klie, and R. Scheichl, Towards a rigorously justified algebraic preconditioner for high-contrast diffusion problems, Computing and Visualization in Science, 11 (2008) pp. 319-331, doi.

B. Aksoylu and M. Holst, Optimality of multilevel preconditioners for local mesh refinement in three dimensions , SIAM Journal on Numerical Analysis, 44 (2006), pp. 1005-1025. doi.

B. Aksoylu, A. Khodakovsky and P. Schröder, Multilevel solvers for unstructured surface meshes, SIAM Journal on Scientific Computing, 26 (2005), pp. 1146-1165. doi.

B. Aksoylu, S. Bond, and M. Holst, An odyssey into local refinement and multilevel preconditioning III: Implementation and numerical experiments, SIAM Journal on Scientific Computing, 25 (2003), pp. 478-498, doi.

Book Chapters and Conference Proceedings

B. Aksoylu and G.A. Gazonas, Inhomogeneous local boundary conditions in nonlocal problems, 6th European Conference on Computational Mechanics (ECCM 6) and 7th European Conference on Computational Fluid Dynamics (ECFD 7), (ECCOMAS2018), 11-15 June 2018, Glasgow, UK.

B. Aksoylu, F. Celiker, and O. Kilicer, Nonlocal operators with local boundary conditions: An overview, Handbook of Nonlocal Continuum Mechanics for Materials and Structures, Voyiadjis G. (eds), (2019), pp. 1293-1330, Springer, Cham, doi.

B. Aksoylu and F. Celiker, Comparison of nonlocal operators utilizing perturbation analysis, Springer Lecture Notes in Computational Science and Engineering, Proceedings of the European Numerical Mathematics and Advanced Applications ENUMATH2015, 112 (2016), pp. 589-606, doi.

B. Aksoylu and Z. Unlu, Numerical study of the high-contrast Stokes equation and its robust preconditioning, Advances in Applied Mathematics and Approximation Theory, Contributions from AMAT 2012, Springer Proceedings in Mathematics & Statistics, Anastassiou, George A.; Duman, Oktay (Eds.), 41 (2013), pp. 237-262, doi.

B. Aksoylu, T. Mengesha, and M.L. Parks, Variational theory and domain decomposition for nonlocal problems, Extended Abstract for the 11th US Congress on Computational Mechanics (USNCCM11) Minneapolis, July 25-28, 2011.

B. Aksoylu, I.G. Graham, H. Klie, and R. Scheichl, A rigorously justified robust algebraic preconditioner for high-contrast diffusion problems, Extended abstract for the 8th World Congress on Computational Mechanics (WCCM2008) and the 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS2008), June 30-July 4, 2008.

B. Aksoylu and H. Klie, Physics-based preconditioners for solving PDEs on highly heterogeneous media, In proceedings of ICIAM 2007, Proceedings in Applied Mathematics and Mechanics, 7 (2007), pp. 1020703-1020704, doi.

Selected Technical Reports and Miscellanea

B. Aksoylu, D. Bernstein, S.D. Bond, and M. Holst, Generating initial data in general relativity using adaptive finite element methods, LSU Center for Computation and Technology (CCT) Technical Report 2008-9, arXiv.

B. Aksoylu, H. Klie, and M.F. Wheeler, Physics-based preconditioners for porous media flow applications, University of Texas at Austin ICES Technical Report 07-08 (August, 2007). (Technical Report at ICES).

B. Aksoylu and M. Holst, An odyssey into local refinement and multilevel preconditioning II: Stabilizing hierarchical basis methods , University of Texas at Austin ICES Technical Report 05-04 (January, 2005). (Technical Report at ICES).

B. Aksoylu and M. Holst, An odyssey into local refinement and multilevel preconditioning I: Optimality of the BPX preconditioner , University of Texas at Austin ICES Technical Report 05-03 (January, 2005). (Technical Report at ICES).

B. Aksoylu, M. Holst, and S. Bond, Implementation and theoretical aspects of the BPX preconditioner in the three dimensional local mesh refinement setting, University of Texas at Austin ICES Technical Report 04-50 (October, 2004). (Technical Report at ICES).

B. Aksoylu, Adaptive multilevel numerical methods with applications in diffusive biomolecular reactions, Ph.D. Dissertation, Department of Mathematics, Computational and Applied Mathematics Group, University of California, San Diego, June 2001.

N.A. Baker, M.J. Holst, B. Aksoylu, R.E. Bank, J.A. McCammon, D. Sept, and F. Wang, Toward computational cell biology, San Diego Supercomputer Center quarterly publication, EnVision, Vol. 16, No. 3, (2000).