A model/solution-adaptive explicit-implicit time-marching technique for wave propagation analysis

In this work, an explicit-implicit time-marching procedure with model/ solution-adaptive time integration parameters is proposed for the analysis of hyperbolic models. The two time integrators of the methodology are locally evaluated, enabling their different spatial and temporal distributions. The first parameter defines the explicit/implicit subdomains of the model, and it is defined in a way that stability is always ensured, as well as period elongation errors are reduced; the second parameter controls the dissipative properties of the methodology, allowing spurious high-frequency modes to be properly eliminated, rendering reduced amplitude decay errors. In addition, the proposed explicit-implicit approach allows contracted systems of equations to be obtained, reducing the computational effort of the analysis. The main features of the novel methodology can be summarized as follows: (i) it is simple; (ii) it is locally defined; (iii) it has guaranteed stability; (iv) it is an efficient noniterative single-step procedure; (v) it provides enhanced accuracy; (vi) it enables advanced controllable algorithmic dissipation in the higher modes; (vii) it considers a link between the temporal and the spatial discretization; (viii) it stands as a single-solve framework based on reduced systems of equations; (ix) it is truly self-starting; and (x) it is entirely automatic.