Sparse dynamics for partial differential equations

Proceedings of the National Academy of Sciences of the United States of America

Volumn 110, Issue 17, 2013, Pages 6634-6639

  Schaeffer, Hayden ^a   Caflisch, Russel ^a   Hauck, Cory D ^b   Osher, Stanley ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

Multiphysics; Multiscale; Optimization

Indexed keywords

ARTICLE; DIFFUSION COEFFICIENT; DYNAMICS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; MATHEMATICS; PRIORITY JOURNAL;

CONVECTION; DIFFUSION; MATHEMATICS; MODELS, THEORETICAL;

EID: 84876837204     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1302752110     Document Type: Article

References (18)

1. Arnold VI (1989) Mathematical Methods of Classical Mechanics (Springer, New York), 2nd Ed.
2. Bensoussan A, Lions JL, Papanicolaou G (1978) Asymptotic Analysis for Periodic Structures (North-Holland, Amsterdam).
3. E W, Engquist B, Huang Z (2003) Heterogeneous multiscale method: A general methodology for multiscale modeling. Physical Review B 67(9):092101-1-092101-4.
4. Kevrekidis IG, et al. (2003) Equation-free, coarse-grained multiscale computation: Enabling microscopic simulators to perform system-level analysis. Commun Math Sci 1(4):715-762.
5. Nolen J, Papanicolaou G, Pironneau O (2008) A framework for adaptive multiscale methods for elliptic problems. Multiscale Model Simul 7(1):171-196.
6. Efendiev Y, Hou TY (2009) Multiscale Finite Element Methods: Theory and Applications (Springer, New York).
7. Hou TY, Wu XH (1997) A multiscale finite element method for elliptic problems in composite materials and porous media. J Comput Phys 134(1):169-189.
8. Daubechies I, Runborg O, Zou J (2007) A sparse spectral method for homogenization multiscale problems. Multiscale Model Simul 6(3):711-740.
9. E W, Engquist B (2003) Multiscale modeling and computation. Not Am Math Soc 50(50):1062-1070.
10. Candès EJ, Romberg J, Tao T (2006) Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory 52(2):489-509.
11. Donoho DL (2006) Compressed sensing. IEEE Transactions on Information Theory 52(4):1289-1306.
12. Schaeffer H, Osher S (2013) A low patch-rank interpretation of texture. SIAM J Imaging Sci 6(1):226-262.
13. Zhou M, et al. (2009) Non-parametric Bayesian dictionary learning for sparse image representations. Advances in Neural Information Processing Systems 22, eds Bengio Y, Schuurmans D, Lafferty J, Williams CKI, Culotta A. Available at (http://books.nips.cc/nips22.html).
14. Goldstein T, Osher S (2009) The split Bregman method for L1-regularized problems. SIAM J Imaging Sci 2(2):323-343.
15. Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D 60(1):259-268.
16. Cai JF, Osher S, Shen Z (2009) Split Bregman methods and frame based image restoration. Multiscale Modeling and Simulation 8(2):337-369.
17. Majda AJ, Bertozzi AL (2001) Vorticity and Incompressible Flow (Cambridge Univ Press, Cambridge, UK), Vol 27.
18. Farge M, Schneider K (2001) Coherent vortex simulation (CVS), a semi-deterministic turbulence model using wavelets. Flow, Turbulence and Combustion 66(4):393-426.