Using Compressive Sensing to solve Ax=b in OpenFOAM
 

Hi everyone,

Recently, Compressive Sensing method is popular in solving undetermined linear equations Ax=b, where the size of A is [m,n], and m < n. However, is it possible to use this method to solve the linear equations, but m=n? This method may be faster than direct and iterative methods in my point of view (i am not sure).

Solvers in OpenFOAM include BICCG, diagonalSolver, GAMG, ICCG, PBICG, PCG, smoothSolver. They are perfect, but it may be interesting to implement that in a new method.

Two papers that I have seen may be useful, and the basic mind is changing A_nn* x=b_n to A_nn*R_nm*u_m=b_n to solve undetermined linear equations, then using reconstruction method to obtain x. But I am looking for more detailed papers about this algorithm. Any one interested in or know much about this will be very appreciated.

1. Pragya Sharma,2015, Solving Helmholtz Equation with Compressed Sensing Enhanced Finite Element Methods. (Chapter 4)
2. Hou Dayou, 2015, Compressed Sensing Based on FE-BI for Solving Electromagnetic Scattering Problems.

Best,
Xiaoxue