The search-based intra-cavity beam cleanup systems are typical feedback loop systems which have been used in both gas
and solid-state laser cavity to enhance laser performance. The studies on search-based intra-cavity beam cleanup systems
mostly rely on experiments. However there are few reports about numerical simulation. In this paper, we attempt to use
numerical method to analysis the search-based intra-cavity beam cleanup system. These systems contain three main
elements: an adaptive laser cavity, a fitness sensor of laser performance and a computer-based search algorithm.
According to the compositions of beam cleanup systems, three modules have been set up in our numerical simulation
framework. We detail the theory, structure and numerical method of these modules in this paper. To demonstrate the
feasibility of the numerical method, we calculated the results based on stochastic parallel gradient descent algorithm.