A novel explicit three-sub-step time integration method for wave propagation problems

Abstract

A novel explicit three-sub-step time integration method is proposed. From linear analysis, it is designed to have at least second-order accuracy, tunable stability interval, tunable algorithmic dissipation and no overshooting behaviour. A distinctive feature is that the size of its stability interval can be adjusted to control the properties of the method. With the largest stability interval, the new method has better amplitude accuracy and smaller dispersion error for wave propagation problems, compared with some existing second-order explicit methods, and as the stability interval narrows, it shows improved period accuracy and stronger algorithmic dissipation. By selecting an appropriate stability interval, the proposed method can achieve properties better than or close to existing second-order methods, and by increasing or reducing the stability interval, it can be used with higher efficiency or stronger dissipation. The new method is applied to solve some illustrative wave propagation examples, and its numerical performance is compared with those of several widely used explicit methods.

Semi-analytical implicit direct time integration scheme on example of 1-D wave propagation problem

“…In this paper we elaborate this idea on the very popular example of 1-D wave propagation problem. A lot of authors demonstrate the advantages and peculiarities of application of their methods of time integration on example of the elastic long rod subjected to variable force, mention here only some recent works [4][5][6][7][8][9][10][11][12][13][14][15]. There are, at least, three reasons for that.…”

“…In our work we will use the simplest implicit central difference scheme [18], so we will not discuss here the abundance of modern developments in time integration schemes [4][5][6][7][8][9][10][11][12][13][14][15]. The main emphasis of paper is a new technique of accounting for the time integration interval t Δ in the space interpolation functions.…”