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A new acceleration technique is presented for shooting and bouncing ray tracing in indoor environments. Tracing just a few rays, the algorithm finds the solid angles around the transmitter that transport electromagnetic power to the receiver. The accuracy is then improved by iteratively increasing the tessellation frequency of the source in the power-transporting solid angles. No rays will be sent through non-power-transporting solid angles, which results in significant reduction of the simulation time. An example of applying the method for studying indoor radio wave propagation is presented and the results are compared with a very high-resolution fully three-dimensional (3D) ray tracing simulation as the reference solution. It is observed that power-transporting solid angles constitute only a small fraction of the total space around the source through which the rays are launched. Therefore a high gain in terms of computational efficiency (about 680% saving in the simulation time) is achieved. Furthermore, concurrent application of the proposed method and binary space partitioning method is shown to be possible, which results in a very efficient ray tracing with about 1080% saving in simulation time.