Will Pazner

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Preprints:

Publications:

• Will Pazner. Subspace and auxiliary space preconditioners for high-order interior penalty discretizations in H(div). ESAIM: Mathematical Modelling and Numerical Analysis, 59(4):1909–1936, July 2025. arXiv eprint 2411.14561. (doi:10.1051/m2an/2025045)
• Guosheng Fu, Hangjie Ji, Will Pazner, and Wuchen Li. Mean field control of droplet dynamics with high-order finite-element computations. Journal of Fluid Mechanics, 999, November 2024. arXiv eprint 2402.05923. (doi:10.1017/jfm.2024.983)
• Julian Andrej, et al. High-performance finite elements with MFEM. The International Journal of High Performance Computing Applications, June 2024. arXiv eprint 2402.15940. Winner of 2025 LLNL's director excellence in publication award. (doi:10.1177/10943420241261981)
• Will Pazner, Tzanio Kolev, and Panayot S. Vassilevski. Matrix-free high-performance saddle-point solvers for high-order problems in H(div). SIAM Journal on Scientific Computing, 46(3):B179–B204, May 2024. arXiv eprint 2304.12387. (doi:10.1137/23m1568806)
• Guosheng Fu, Stanley Osher, Will Pazner, and Wuchen Li. Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation. Journal of Computational Physics, page 112994, April 2024. arXiv eprint 2306.06287. (doi:10.1016/j.jcp.2024.112994)
• Will Pazner, Tzanio Kolev, and Jean-Sylvain Camier. End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations. The International Journal of High Performance Computing Applications, June 2023. arXiv eprint 2210.12253. (doi:10.1177/10943420231175462)
• Will Pazner, Tzanio Kolev, and Clark R. Dohrmann. Low-order preconditioning for the high-order finite element de Rham complex. SIAM Journal on Scientific Computing, 45(2):A675–A702, April 2023. arXiv eprint 2203.02465. (doi:10.1137/22M1486534)
• Michael Franco, Per-Olof Persson, and Will Pazner. Iterative subregion correction preconditioners with adaptive tolerance for problems with geometrically localized stiffness. Communications on Applied Mathematics and Computation, March 2023. (doi:10.1007/s42967-023-00254-0)
• Samuel Olivier, Will Pazner, Terry Haut, and Ben Yee. A family of independent variable Eddington factor methods with efficient linear solvers. Journal of Computational Physics, page 111747, November 2022. arXiv eprint 2111.12255. (doi:10.1016/j.jcp.2022.111747)
• Andrés M. Rueda-Ramírez, Will Pazner, and Gregor J. Gassner. Subcell limiting strategies for discontinuous Galerkin spectral element methods. Computers & Fluids, 247:105627, October 2022. arXiv eprint 2202.00576. (doi:10.1016/j.compfluid.2022.105627)
• Ben S. Southworth, Oliver A. Krzysik, and Will Pazner. Fast parallel solution of fully implicit Runge–Kutta and discontinuous Galerkin in time for numerical PDEs, part II: nonlinearities and DAEs. SIAM Journal on Scientific Computing, 44(2):A636–A663, March 2022. arXiv eprint 2101.01776. (doi:10.1137/21m1390438)
• Ben S. Southworth, Oliver A. Krzysik, Will Pazner, and Hans De Sterck. Fast parallel solution of fully implicit Runge–Kutta and discontinuous Galerkin in time for numerical PDEs, part I: the linear setting. SIAM Journal on Scientific Computing, 44(1):A416–A443, February 2022. arXiv eprint 2101.00512. (doi:10.1137/21m1389742)
• Tzanio Kolev and Will Pazner. Conservative and accurate solution transfer between high-order and low-order refined finite element spaces. SIAM Journal on Scientific Computing, 44(1):A1–A27, January 2022. arXiv eprint 2103.05283. Winner of 2023 LLNL's director excellence in publication award. (doi:10.1137/21m1403916)
• Will Pazner and Terry Haut. A short note on the accuracy of the discontinuous Galerkin method with reentrant faces. Journal of Computational Physics, page 110448, October 2021. arXiv eprint 2104.08339. (doi:10.1016/j.jcp.2021.110448)
• Will Pazner. Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting. Computer Methods in Applied Mechanics and Engineering, 382:113876, August 2021. arXiv eprint 2004.08503. (doi:10.1016/j.cma.2021.113876)
• Robert Anderson, et al. MFEM: A modular finite element methods library. Computers & Mathematics with Applications, July 2021. arXiv eprint 1911.09220. (doi:10.1016/j.camwa.2020.06.009)
• Jed Brown, et al. libCEED: Fast algebra for high-order element-based discretizations. Journal of Open Source Software, 6(63):2945, July 2021. (doi:10.21105/joss.02945)
• Will Pazner and Tzanio Kolev. Uniform subspace correction preconditioners for discontinuous Galerkin methods with hp-refinement. Communications on Applied Mathematics and Computation, July 2021. arXiv eprint 2009.01287. (doi:10.1007/s42967-021-00136-3)
• Tzanio Kolev, et al. Efficient exascale discretizations: High-order finite element methods. The International Journal of High Performance Computing Applications, June 2021. arXiv eprint 2109.04996. (doi:10.1177/10943420211020803)
• Will Pazner. Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods. SIAM Journal on Scientific Computing, 42(5):A3055–A3083, October 2020. arXiv eprint 1908.07071. (doi:10.1137/19m1282052)
• Michael Franco, Jean-Sylvain Camier, Julian Andrej, and Will Pazner. High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners. Computers & Fluids, page 104541, April 2020. arXiv eprint 1910.03032. (doi:10.1016/j.compfluid.2020.104541)
• Daniel Z. Huang, Will Pazner, Per-Olof Persson, and Matthew J. Zahr. High-order partitioned spectral deferred correction solvers for multiphysics problems. Journal of Computational Physics, page 109441, April 2020. (doi:10.1016/j.jcp.2020.109441)
• W. Pazner, N. Trask, and P.J. Atzberger. Stochastic discontinuous Galerkin methods (SDGM) based on fluctuation-dissipation balance. Results in Applied Mathematics, September 2019. arXiv eprint 1806.04317. (doi:10.1016/j.rinam.2019.100068)
• Will Pazner and Per-Olof Persson. Analysis and entropy stability of the line-based discontinuous Galerkin method. Journal of Scientific Computing, March 2019. arXiv eprint 1809.09815. (doi:10.1007/s10915-019-00942-1)
• Michael Franco, Per-Olof Persson, Will Pazner, and Matthew J. Zahr. An adjoint method using fully implicit Runge-Kutta schemes for optimization of flow problems. In AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics, January 2019. (doi:10.2514/6.2019-0351)
• Will Pazner, Michael Franco, and Per-Olof Persson. High-order wall-resolved large eddy simulation of transonic buffet on the OAT15A airfoil. In AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics, January 2019. (doi:10.2514/6.2019-1152)
• Will Pazner and Per-Olof Persson. Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods. Journal of Computational Physics, 354:344–369, February 2018. arXiv eprint 1704.04549. (doi:10.1016/j.jcp.2017.10.030)
• Will Pazner and Per-Olof Persson. On the convergence of iterative solvers for polygonal discontinuous Galerkin discretizations. Communications in Applied Mathematics and Computational Science, 13(1):27–51, February 2018. arXiv eprint 1801.04313. (doi:10.2140/camcos.2018.13.27)
• Will Pazner and Per-Olof Persson. Interior penalty tensor-product preconditioners for high-order discontinuous Galerkin discretizations. In Proceedings of the 2018 AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics, January 2018. (doi:10.2514/6.2018-1093)
• Will Pazner and Per-Olof Persson. High-order DNS and LES simulations using an implicit tensor-product discontinuous Galerkin method. In Proceedings of the 23rd AIAA Computational Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics, June 2017. First Place, AIAA Student Paper Competition. (doi:10.2514/6.2017-3948)
• Will Pazner and Per-Olof Persson. Stage-parallel fully implicit Runge-Kutta solvers for discontinuous Galerkin fluid simulations. Journal of Computational Physics, 335:700 – 717, April 2017. arXiv eprint 1701.07181. (doi:10.1016/j.jcp.2017.01.050)
• Will Pazner, Andrew Nonaka, John Bell, Marcus Day, and Michael Minion. A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry. Combustion Theory and Modeling, 20(3):521–547, March 2016. arXiv eprint 1512.06459. (doi:10.1080/13647830.2016.1150519)

Thesis:

• Will Pazner. Efficient solvers and preconditioners for the implicit time integration of discontinuous Galerkin methods. Ph.D. thesis, Brown University, 2018. (doi:10.26300/0syb-sb60)

Technical Reports:

• Tzanio Kolev, et al. Support ECP applications in their exascale challenge problem runs. Technical Report WBS 2.2.6.06, Milestone CEED-MS39, Exascale Computing Project, 2023. (doi:10.5281/zenodo.7820316)
• Tzanio Kolev, et al. Document and popularize CEED-developed software and standards. Technical Report WBS 2.2.6.06, Milestone CEED-MS41, Exascale Computing Project, 2023. (doi:10.5281/zenodo.10023494)
• Tzanio Kolev, et al. High-order algorithmic developments and optimizations for more robust exascale applications. Technical Report WBS 2.2.6.06, Milestone CEED-MS38, Exascale Computing Project, 2022. (doi:10.5281/zenodo.6514857)
• Stefanie Günther, Will Pazner, and Dongping Qi. Spline parameterization of neural network controls for deep learning. Technical report, Lawrence Livermore National Laboratory, 2021. arXiv eprint 2103.00301.
• Tzanio Kolev, et al. High-order algorithmic developments and optimizations for large-scale GPU-accelerated simulations. Technical Report WBS 2.2.6.06, Milestone CEED-MS36, Exascale Computing Project, 2021. (doi:10.5281/zenodo.4672664)
• Tzanio Kolev, et al. Port and optimize the CEED software stack to Aurora/Frontier EA systems. Technical Report WBS 2.2.6.06, Milestone CEED-MS37, Exascale Computing Project, 2021. (doi:10.5281/zenodo.5542244)