DBIM has a humongous computational cost, especially when the imaging domain and/or the amount of measured-field data is large. The main computational burden comes from the forward-scattering solutions that are required multiple times in each iteration, and for each illumination of the unknown object. As a remedy, the multilevel fast multipole algorithm (MLFMA) is used for solving the forward problems with O(N) computational complexity, where N is the number of unknown pixels in the image. The low complexity enables large forward solutions, however, thousands of them are required to solve a large inverse problem. Therefore, we use parallel computing to distribute the forward-scattering solutions among computing nodes of large supercomputers. Specifically, we use NCSAs Blue Waters supercomputer located in our institution. To get further speedup (more than 50 times), we parallelize MLFMA on CPU+GPU architectures. The results show that supercomputing accelerates a sequential solution thousands of times, and provides solutions of large inverse problems in near-real time.