Sparse Dynamics for PDE's

Stanley Osher
University of California, Los Angeles (UCLA)

Stan Osher (joint with H. Schaeffer, R. Caflisch and C. Hauck) 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 by simply applying soft thresholding to the coefficients of the basis approximation. As examples we used a Fourier approximation and soft thresholding to successfully reduce the dynamics of convection equations, diffusion equations, viscous shock approximations and vorticity equations with high frequency source terms.

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