In this paper, we apply the BBGF-KKR-MST (Broadband Green's function-KKR-Multiple Scattering Theory) to calculate Band Structures and Band Field Solutions in topological acoustics. A feature of BBGF is that the lattice Green's functions are broadband, and the transformations to cylindrical waves are calculated rapidly for many frequencies for speedy calculation of the determinant of the KKR equation. For the two bands of interest, only 5 cylindrical waves are sufficient so that the dimension of the eigenvalue matrix equation is only 5. The CPU time requirement, including setup and using MATLAB on a standard laptop, is 5 milliseconds for a band eigenvalue. Using the eigenvalue and the scattered field eigenvector, the field in the cell is calculated by higher order cylindrical waves. The exciting field of higher order cylindrical waves requires only 11 coefficients to represent the band field solutions in the cell. Comparisons are made with the results of the volume integral equation method and the commercial software COMSOL. The BBGF-KKR-MST method is significantly faster.