The Spectral Element Method (SEM) is a well-established high-order variant of the Finite Element Method (FEM) used for dynamic problems. It can be combined with the Finite Cell Method (FCM), an immersed boundary method, which eliminates the need for cumbersome mesh generation. The resulting method is called the Spectral Cell Method (SCM). It is applied to wave propagation problems. However, it has two main drawbacks. First, the mass matrix is no longer diagonal if cells are cut by the boundary. This limits the computational efficiency of time integration since a diagonal mass matrix enables time integration without solving any systems of equations. Second, cut cells typically have high eigenfrequencies and thus small critical time step sizes. Therefore, badly cut cells restrict the time step size for the explicit integration of the whole domain. This thesis addresses both drawbacks by developing and comparing time integration methods. Among those are a split solver, a leapfrog solver, an implicit method, and Implicit-Explicit (IMEX) methods. One of the IMEX solvers is based on Newmark methods, the other on Runge-Kutta-Nyström (RKN) methods. The different time integration algorithms are profiled on two benchmark examples. The IMEX methods perform best in terms of accuracy per runtime, particularly the Newmark IMEX variant. Following the comparative study, the Newmark IMEX algorithm is applied to the Full Waveform Inversion (FWI) to accelerate the wave simulations. Compared to the results in [1], a speed-up of factor 2.85 is achieved while simultaneously improving the quality of the inversion result.     «

The Spectral Element Method (SEM) is a well-established high-order variant of the Finite Element Method (FEM) used for dynamic problems. It can be combined with the Finite Cell Method (FCM), an immersed boundary method, which eliminates the need for cumbersome mesh generation. The resulting method is called the Spectral Cell Method (SCM). It is applied to wave propagation problems. However, it has two main drawbacks. First, the mass matrix is no longer diagonal if cells are cut by the boundary....     »