Publications authored by Burak Aksoylu

Locally refined 3D mesh Locally refined 3D mesh 3D local refinement 2D local refinement Models for parameterization

Journal Publications


A12. B. Aksoylu, S. Bond, E. Cyr, and M. Holst, Adaptive solution of the Poisson-Boltzmann equation using goal-oriented error indicators, in preparation.

A11. B. Aksoylu and Z. Yeter, Robust multigrid preconditioners for the high-contrast biharmonic plate equation, (2009), submitted, also available at arXiv 0910.0487.

A10. B. Aksoylu and M. L. Parks, Towards domain decomposition for nonlocal problems, (2009), submitted, also available at arXiv 0909.4504.

A9. B. Aksoylu and Z. Yeter, Robust multigrid preconditioners for cell-centered finite volume discretization of the high-contrast diffusion equation, (2009), submitted, also available at arXiv 0904.1885.

A8. B. Aksoylu and H. R. Beyer, Results on diffusion equation with rough coefficients, SIAM Journal on Mathematical Analysis, (2009), accepted, also available at arXiv 0810.3427.

A7. 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: 10.1080/01630560902987162, also available at arXiv 0902.0788. (Paper at Taylor and Francis).

A6. 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: 10.1088/0264-9381/26/14/145007, also available at arXiv 0801.1823.

A5. 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: 10.1007/s00791-008-0105-1.

A4. 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: 10.1016/j.apnum.2008.06.002 .

A3. 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. (Paper at SIAM).

A2. B. Aksoylu, A. Khodakovsky and P. Schröder, Multilevel solvers for unstructured surface meshes, SIAM Journal on Scientific Computing, 26 (2005), pp. 1146-1165. (Paper at SIAM).

A1. 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. (Paper at SIAM).

Technical Reports, Conference Proceedings, Etc.

B13. B. Aksoylu and Z. Yeter, Robust multigrid preconditioners for the high-contrast biharmonic plate equation, LSU Center for Computation and Technology (CCT) Technical Report 2009-15, also available at arXiv 0910.0487.

B12. B. Aksoylu and M. L. Parks, Towards domain decomposition for nonlocal problems, LSU Center for Computation and Technology (CCT) Technical Report 2009-12, also available at arXiv 0909.4504.

B11. B. Aksoylu and Z. Yeter, Robust multigrid preconditioners for cell-centered finite volume discretization of the high-contrast diffusion equation, LSU Center for Computation and Technology (CCT) Technical Report 2009-7, also available at arXiv 0904.1885.

B10. 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, also available at arXiv 0801.3142.

B9. 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 (WCCM8) and the 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), Venice, 30 June - 4 July 2008.

B8. B. Aksoylu, I. G. Graham, H. Klie, and R. Scheichl, Towards a rigorously justified algebraic preconditioner for high-contrast diffusion problems, University of Texas at Austin ICES Technical Report 07-35 (November, 2007). (Technical Report at ICES).

B7. B. Aksoylu and H. Klie, Physics-based preconditioners for solving PDEs on highly heterogeneous media, In proceedings of ICIAM 2007, Proc. Appl. Math. Mech. 7 (2007), pp. 1020703-1020704, doi: 10.1002/pamm.200700324. (Proceeding at PAMM)

B6. B. Aksoylu and H. Klie, Physics-based preconditioners for solving PDEs on highly heterogeneous media, LSU Center for Computation and Technology (CCT) Technical Report 2007-1. (Technical Report at CCT).

B5. 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).

B4. 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).

B3. 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).

B2. 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).

B1. 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.