Emil M.
Constantinescu
Computational Mathematician
emconsta[at]mcs.anl.gov
Office #: 2151
• LANS
• Mathematics and Computer Science
• Argonne National Laboratory

• Scientist at large at CASE
• University of Chicago

Modeling and Simulation

Adaptive mesh refinement (AMR): Inadequate grid resolution can be an important source of errors in modeling various physical processes. For example in convection-diffusion problems, where large spatial gradients cause large errors, mesh refinement plays a key role. Adaptive refinement is important in large scale applications. AMR alleviates discretization model errors by refining the time/space mesh according to a criterion that maximizes the efficiency and the effectiveness of the method.

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Example

An Example is given below that illustrates the main idea of AMR and multirate. The 2D simulation models the transport of a (power plant) plume in the atmosphere (1 km mixing layer) with an Eastern wind (5 m/s) and a turbulent diffusivity of 100 m²/s. The simulation is run for 6 hours. The power plant is turned off and the plume dynamics is simulated for another six hours. Note how the fine grid resolution follows the features of the solution. Such an algorithm that dynamically adapts the grid for large scale models is presented in [Constantinescu et al. 2007; Comp. Geosci.]. The fine resolution accurately resolves the fine features of the solution. In order to efficiently implement this AMR approach, different timesteps should be used for different resolutions: large timesteps for coarse resolutions and small timesteps for fine resolutions resulting in multirate algorithms. Examples of such algorithms are found in [Constantinescu et al. 2007; Sci. Comp.] or [Sandu et al. 2007; Sci. Comp.]

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Selected journal publications, proceedings, presentations

    Journal publications:

• Adrian Sandu and Emil M. Constantinescu, "Multirate explicit Adams methods for time integration of conservation laws." Vol. 38(2), Pages 229-249, Journal of Scientific Computing, 2009. -> Technical report version.

   

• Emil M. Constantinescu, Adrian Sandu, and Gregory R. Carmichael, "Modeling atmospheric chemistry and transport with dynamic adaptive resolution." Vol. 12(2), Pages 133-151, Computational Geosciences, 2008.

   

• Emil M. Constantinescu and Adrian Sandu, "Multirate timestepping methods for hyperbolic conservation laws." Vol. 33(3), Pages 239-278, Journal of Scientific Computing, 2007. -> Technical report version.

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    Proceedings/Presentations/Posters:

• Adrian Sandu and Emil M. Constantinescu, "Multirate time discretizations for hyperbolic partial differential equations." Submitted to the International Conference of Numerical Analysis and Applied Mathematics 2009 (ICNAAM 2009), Crete, Greece, 18-22 September 2009.

   

• Emil M. Constantinescu and Adrian Sandu, "Extrapolated multirate numerical integration methods." ECMI 2008 (Springer Mathematics in Industry), 2008 -> Technical report version.

   

• Dan Negrut, Mihai Anitescu, Anter El-Azab, Steve Benson, Emil 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 and Adrian Sandu, "On adaptive mesh refinement for atmospheric pollution models." International Conference on Computational Science (ICCS) 2005, pages 798-806 Atlanta, GA, May 22-25, 2005.

   

• Emil M. Constantinescu, Wenyuan Liao, and Adrian Sandu, "Mesh refinement strategies in air quality modeling." High Performance Computing Symposium (HPC) 2005, pages 158-163 - San Diego, CA, April 2-8, 2005.

   

• Chaitaniya Belwal, Adrian Sandu, and Emil Constantinescu, "Adaptive resolution modeling of regional air quality." ACM Symposium on Applied Computing SAC 2004, pages 235-239, Nicosia, Cyprus, March 14-17, 2004.

   

• Adrian Sandu, Chaitaniya Belwal, and Emil Constantinescu, "Parallel adaptive simulations of regional air quality." Presented at SIAM Conference on Parallel Processing for Scientific Computing; February 25-27, 2004.

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    Technical Reports:

• Emil M. Constantinescu and Adrian Sandu, "On Extrapolated Multirate Methods." Technical Report TR-08-12, Computer Science, Virginia Tech, 2008.

   

• Adrian Sandu and Emil M. Constantinescu, "Multirate explicit Adams methods for time integration of conservation laws." Technical Report TR-07-30(989), Computer Science, Virginia Tech, 2007.

   

• Emil M. Constantinescu and Adrian Sandu, "Update on multirate timestepping methods for hyperbolic conservation laws." Technical Report TR-07-12(955), Computer Science, Virginia Tech, 2007.

   

• Emil M. Constantinescu and Adrian Sandu, "Multirate timestepping methods for hyperbolic conservation laws." Technical Report TR-06-15, Computer Science, Virginia Tech, 2006.

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Related Links:

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