There has been a buzz around increased grid modernization for more than a decade. Grid modernization includes, but is not limited to, upgrades to the grid to enhance reliability, resilience, security, and access to clean energy sources. One significant change that has been happening in this context is the increased penetration of computing power and controlled devices like power electronics in the power grid. As this change happens, the operation and characteristics of the power grid are set to undergo a significant change. The power grid moves from an older electric machine dominated grid that used analog electronics for controls to a power electronics dominated grid that uses digital computing for controls. As this transition happens, there are significant problems of applied mathematics that will need to be resolved in power electronics and power grid. The problems include the ability to simulate in different timescales, while also leveraging the significantly improved computing capabilities available today. In this paper, the challenges related to simulation of power electronics are discussed and the challenge problems laid down that applied mathematics may help resolve in future.