We present the CORSING (COmpRessed SolvING) method for the numerical approximation of PDEs. Establishing an analogy between the bilinear form associated with the weak formulation of a PDE and the signal acquisition process, CORSING combines the classical Petrov-Galerkin method with compressed sensing. This allows for a dramatic dimensionality reduction of the PDE discretization and for an efficient recovery of sparse solutions.
Considering the advection-diffusion-reaction equation of fluid dynamics as a case study, we discuss some numerical examples in MATLAB and analyze the method from a theoretical perspective. In particular, we provide recovery error estimates in expectation and in probability, employing wavelets and Fourier basis functions.
Additional Information
Location: ESB 4133 (PIMS Lounge) Simone Brugiapaglia, Simon Fraser University