期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 110, 期 17, 页码 6634-6639出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1302752110
关键词
multiphysics; multiscale; optimization
资金
- Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program
- Office of Naval Research [N00014-11-1-719]
- Department of Energy (DOE) [DE-FG02-05ER25710]
- Office of Advanced Scientific Computing Research, DOE
- University of Tennessee-Battelle [DE-AC05-00OR22725]
We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.
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