The Fast Solution of the FE-BI Integral Equation Based on Compressed Sensing

When using the Finite Element-Boundary Integral(FE-BI) for solving the electromagnetic scattering problem of the electrically large object or the object which is meshed into lots of little elements, the filling amount of coefficient matrix is very large, and the computational complexity is also very high. A new method based on compressed sensing(CS) is proposed to improve the solving efficiency of the FE-BI integral equation. There is a new observation matrix which is the small-scale coefficient matrices formed by random source from the equation. Combined with a suitable sparse transform and recovery algorithm, it can accurately reconstruct the filed values of whole nodes. Thus the new method can achieve the fast solution of undetermined equation. Through the analysis of the medium body and the perfect conduct, it proved that the new method has a small amount of matrix filling and can greatly improve the computational efficiency.