This paper illustrates the ability of Gaussian beam shooting techniques to accommodate large propagation problems in multipath contexts. Frame based decomposition of fields provides a rigorous and flexible tool to perform beam launching. Paraxial beam tracking leads then to efficient algorithms, relying on the simultaneous spatial- spectral localization of paraxial Gaussian beams. The spatial divergence of beams however degrades the accuracy of beam field tracking formulas, especially when beams interact with localized obstacles after long range propagation. A beam re-expansion algorithm is proposed to address the problems of beam widening. It makes use of both spatially narrow/wide window frames. This algorithm allows for fast re-expansion of any paraxial beam onto a frame of wide windows radiating in the form of paraxial beams. The formulation is presented here for the 2D case, but will be presented in the context of 3D problems at the conference