PDE & AMR

Many real-world applications require large-scale numerical solutions of PDEs. I work on scalable simulation algorithms and adaptive mesh refinement (AMR), which dynamically refines space/time resolution in regions where solution features require it.

Related project

Selected journal publications

• Shinhoo Kang and Emil M Constantinescu. Differentiable DG with neural operator source term correction. Submitted, 2025. [arXiv]
• Johann Rud*, Max Heldman, Emil M. Constantinescu, Qi Tang, and Xian-Zhu Tang. Scalable implicit solvers with dynamic mesh adaptation for a relativistic drift-kinetic Fokker-Planck-Boltzmann model. Journal of Computational Physics, Vol. 507; Pages 112954, 2024. [DOI] [arXiv] [PDF]
• Shinhoo Kang and Emil M Constantinescu. Learning subgrid-scale models with neural ordinary differential equations. Computers and Fluids, In Press, Vol. 261; Pages 105919, 2023. [DOI] [arXiv]
• Youngdae Kim, Debojyoti Ghosh, Emil M Constantinescu, and Ramesh Balakrishnan. GPU-accelerated WENO schemes for the DNS of compressible turbulent flows. Computers & Fluids, Vol. 251; Pages 105744, 2022. [DOI] [arXiv]
• Shinhoo Kang and Emil M Constantinescu. Entropy-preserving and entropy-stable relaxation IMEX and multirate time-stepping methods. Journal of Scientific Computing, Vol. 93(23), 2022. [DOI] [arXiv]
• Hong Zhang, Zhengyu Liu, Emil M Constantinescu, and Robert Jacob. Stability analysis of coupled advection-diffusion models with bulk interface condition. Journal of Scientific Computing, Vol. 93(33), 2022. [DOI]
• Shinhoo Kang, Emil M Constantinescu, Hong Zhang, and Robert Jacob. Mass-conserving implicit-explicit methods for coupled compressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering (CMAME), Vol. 384; Pages 113988, 2021. [DOI] [arXiv]
• Emil M Constantinescu. Implicit extensions of an explicit multirate Runge–Kutta scheme. Applied Mathematics Letters, Vol. 128; Pages 107871, 2021. [DOI] [arXiv]
• Oana Marin, Emil M Constantinescu, and Barry Smith. A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO. Vol. 47; Pages 101207, 2020. [DOI] [arXiv]
• Daniel S. Abdi, Francis X. Giraldo, Emil M. Constantinescu, Lester E. Carr III, Lucas C. Wilcox, and Timothy Warburton. Acceleration of an implicit-explicit non-hydrostatic unified model of the atmospheric (NUMA) on manycore processors. International Journal of High Performance Computing Applications, Vol. 33(2); Pages 242-267, 2019. [DOI] [arXiv] [PDF]
• Valeria Mele, Emil M Constantinescu, Luisa Carracciuolo, and Luisa D'Amore. A PETSc parallel-in-time solver based on MGRIT algorithm. {"Concurrency and Computation"=>"Practice and Experience"}, Vol. 30(24); Pages e4928, 2018. [DOI]
• Simone Marras, Michal A. Kopera, Emil M Constantinescu, Jenny Suckale, and Francis X. Giraldo. A residual-based shock capturing scheme for the continuous/discontinuous spectral element solution of the 2D shallow water equations. Advances in Water Resources, Vol. 114; Pages 45-63, 2018. [DOI] [arXiv]
• Debojyoti Ghosh and Emil M Constantinescu. A well-balanced conservative finite-difference algorithm for atmospheric flows. AAIA Journal, Vol. 54(4); Pages 1370-1385, 2016. [DOI] [PDF]
• Debojyoti Ghosh and Emil M Constantinescu. Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning. SIAM Journal on Scientific Computing (SISC), Vol. 38(3); Pages A1848-A1875, 2016. [DOI] [arXiv] [PDF]
• Debojyoti Ghosh, Emil M Constantinescu, and Jed Brown. Efficient implementation of non-linear compact schemes on massively-parallel platforms. SIAM Journal on Scientific Computing (SISC), Vol. 37(3); Pages C354-C383, 2015. [DOI]
• Francis X Giraldo, James F. Kelly, and Emil M Constantinescu. Implicit-explicit formulations of a three-dimensional nonhydrostatic unified model of the atmosphere (NUMA). SIAM Journal on Scientific Computing (SISC), Vol. 35(5); Pages B1162-B1194, 2013. [DOI]
• David E. Keyes, Lois Curfman McInnes, Carol Woodward, William Gropp, Eric Myra, Michael Pernice, John Bell, Jed Brown, Alain Clo, Jeffrey Connors, Emil M Constantinescu, Don Estep, Kate Evans, Charbel Farhat, Ammar Hakim, Glenn Hammond, Glen Hansen, Judith Hill, Tobin Isaac, Xiaomin Jiao, Kirk Jordan, Dinesh Kaushik, Efthimios Kaxiras, Alice Koniges, Kihwan Lee, Aaron Lott, Qiming Lu, John Magerlein, Reed Maxwell, Michael McCourt, Miriam Mehl, Roger Pawlowski, Amanda Peters Randles, Daniel Reynolds, Beatrice Rivière, Ulrich Rüde, Tim Scheibe, John Shadid, Brendan Sheehan, Mark Shephard, Andrew Siegel, Barry Smith, Xianzhu Tang, Cian Wilson, and Barbara Wohlmuth. Multiphysics simulations: Challenges and opportunities. International Journal of High Performance Computing Applications, Vol. 27(1); Pages 4-83, 2013. [DOI]
• Adrian Sandu and Emil M Constantinescu. Multirate explicit Adams methods for time integration of conservation laws. Journal of Scientific Computing, Vol. 38(2); Pages 229-249, 2009. [DOI] [PDF]
• Emil M Constantinescu, Adrian Sandu, and Gregory R. Carmichael. Modeling atmospheric chemistry and transport with dynamic adaptive resolution. Computational Geosciences, Vol. 12(2); Pages 133-151, 2008. [DOI]
• Emil M Constantinescu and Adrian Sandu. Multirate timestepping methods for hyperbolic conservation laws. Journal of Scientific Computing, Vol. 33(3); Pages 239-278, 2007. [DOI] [PDF]

Proceedings / presentations

• Junoh Jung and Emil M Constantinescu. Learning differentiable weak-form corrections to accelerate finite element simulations. To appear, 2026. [arXiv] [PDF]
• Simone Marras, Jenny Suckale, Francis X. Giraldo, and Emil M Constantinescu. An SGS-based stabilization for the high-order approximation of the shallow water equations. Springer's Lecture Notes in Computational Science and Engineering (LNCSE) Series, ICOSAHOM 2016, 2016.
• Debojyoti Ghosh and Emil M Constantinescu. Nonlinear compact finite-difference schemes with semi-implicit time stepping. Springer's Lecture Notes in Computational Science and Engineering (LNCSE) Series, ICOSAHOM 2014, Vol. 106; Pages 237-245, 2015. [DOI]
• Debojyoti Ghosh and Emil M Constantinescu. Well-balanced formulation of gravitational source terms for conservative finite-difference atmospheric flow solvers. 7th AIAA Atmospheric and Space Environments Conference (Aviation Forum), June 22-26, 2015, Dallas, TX, 2015.
• Emil M Constantinescu and Adrian Sandu. On multirate numerical integration methods. (invited) The European Consortium for Mathematics in Industry (ECMI-2008) in Progress in Industrial Mathematics at ECMI 2008, University College London, England, June 30 - July 4, 2008, Vol. 15(2); Pages 341-347, 2010. [DOI]
• Adrian Sandu and Emil M Constantinescu. Multirate time discretizations for hyperbolic partial differential equations. International Conference of Numerical Analysis and Applied Mathematics 2009 (ICNAAM 2009), Crete, Greece, September 18-22, 2009, Vol. 1168(1); Pages 1411-1414, 2009. [DOI]
• Dan Negrut, Mihai Anitescu, Anter El-Azab, Steve Benson, Emil M Constantinescu, Peter Zapol, and Toby Heyn. A real-space parallel optimization model reduction approach for electronic structure computation in large nanostructures using orbital-free density functional theory. IMECE 2006-15740, ASME International Mechanical Engineering Congress and Exposition, Chicago, IL, 2006.
• Emil M Constantinescu, Wenyuan Liao, and Adrian Sandu. Mesh refinement strategies in air quality modeling. High Performance Computing Symposium, San Diego, CA, April 2005, Pages 158-163, 2005.
• Emil M Constantinescu and Adrian Sandu. On adaptive mesh refinement for atmospheric pollution models. International Conference on Computational Science (ICCS), Atlanta, GA, May 22-25, 2005, Springer-Verlag in Lecture Notes in Computer Science, Pages 798-805, 2005.
• Chaitaniya Belwal, Adrian Sandu, and Emil M Constantinescu. Adaptive resolution modeling of regional air quality. ACM Symposium on Applied Computing (SAC 2004), Nicosia, Cyprus, March 14-17, 2004, Pages 235-239, 2004.

Technical reports

• Satish Balay, S. Abhyankar, Mark F. Adams, Jed Brown, P. Brune, K. Buschelman, Emil M Constantinescu, Lisandro Dalcin, S. Benson, A. Dener, and others. PETSc/TAO users manual revision 3.24. Argonne National Laboratory (ANL), Argonne, IL (United States), 2025.
• Debojyoti Ghosh, Emil M Constantinescu, and Jed Brown. Scalable nonlinear compact schemes. 2014. [PDF]
• D.E. Keyes, L.C. McInnes, C. Woodward, W.D. Gropp, E. Myra, M. Pernice, J. Bell, J. Brown, A. Clo, J. Connors, E. Constantinescu, D. Estep, K. Evans, C. Farhat, A. Hakim, G. Hammond, G. Hansen, J. Hill, T. Isaac, X. Jiao, K. Jordan, D. Kaushik, E. Kaxiras, A. Koniges, K. Lee, A. Lott, Q. Lu, J. Magerlein, R. Maxwell, M. McCourt, M. Mehl, R. Pawlowski, A. Peters, D. Reynolds, B. Rivière, U. Rüde, T. Scheibe, J. Shadid, B. Sheehan, M. Shephard, A. Siegel, B. Smith, X. Tang, C. Wilson, B. Wohlmuth. Multiphysics simulations: challenges and opportunities. 2012.
• Emil M Constantinescu and Adrian Sandu. On extrapolated multirate methods. 2008.
• Emil M Constantinescu and Adrian Sandu. Update on multirate timestepping methods for hyperbolic conservation laws. 2007. [PDF]
• Adrian Sandu and Emil M Constantinescu. Multirate explicit Adams methods for time integration of conservation laws. 2007. [PDF]
• Emil M Constantinescu and Adrian Sandu. Multirate timestepping methods for hyperbolic conservation laws. 2006. [PDF]