Bowden, E. M., & Jung-Beeman, M. (2007). Methods for investigating the neural components of insight. Methods (San Diego, Calif.), 42(1), 87–99. https://doi.org/10.1016/j.ymeth.2006.11.007
2/
Kounios, J., & Beeman, M. (2009). The Aha! Moment: The cognitive neuroscience of insight. Current Directions in Psychological Science, 18(4), 210–216. https://doi.org/10.1111/j.1467-8721.2009.01638.x
3/
Kounios, J., & Beeman, M. (2014). The cognitive neuroscience of insight. Annual Review of Psychology, 65, 71–93. https://doi.org/10.1146/annurev-psych-010213-115154
For analytical problem solving (if you understood it as a thinking process engaging working memory & executive system), I would suspect executive brain network :) however, depends on your conceptualization of analytical problem solving and the concrete operational statement.