2D numerical simulation of lunar response to gravitational waves using finite element method

The response of the Moon to gravitational waves has previously been modeled using analytical or semianalytical models that assume ideal lunar structures. Such models are advantageous for their high-speed calculation but fail to account for the extremely heterogeneous subsurface and/or interior structures of the Moon. Numerical calculations are needed, but it is challenging to model the topography and lateral heterogeneity of the Moon. In addition, the computational cost is great, because gravitational wave modeling usually requires long-physical-time simulations. As a first step toward overcoming the above difficulties, we employ a two-dimensional high-order finite element method (the spectral element method) to numerically simulate the lunar response to gravitational waves. We verify our method by comparing our numerical results with those semianalytical solutions. Based on such comparison, we also analyze the limitation of the two-dimensional simulation. Our work breaks a new way toward the precise simulation of a realistic lunar response to gravitational waves in the future and lays down a solid foundation for three-dimensional numerical simulations.