LAUSR

Abstract In this work, a novel family of explicit time marching techniques is proposed for wave propagation analyses. The main features of the new approach are: (i) the family is based only on single-step displacement–velocity relations, being very simple to implement; (ii) as usual in explicit analyses, it requires no system of equations to be dealt with, being very efficient; (iii) it is truly self-starting; (iv) it is second-order accurate; (v) it enables advanced controllable algorithmic dissipation in the higher modes; (vi) it is locally defined and based on adaptive time integrators, allowing enhanced accuracy to be obtained; (vii) it is function of the adopted temporal and spatial discretizations, as well as of the properties of the model and computed responses, establishing a link between these features; (viii) it is entirely automated, requiring no expertise from the user; (ix) it stands as an adaptive non-iterative approach, further improving its efficiency; (x) it is conditionally stable and its stability limit is twice that of the Central Difference Method; (xi) the stability limit of the method remains unaltered, despite the introduction of dissipation. The proposed technique is very versatile and effective, providing the main positive attributes that are requested from an efficacious explicit time marching procedure. Numerical results are presented at the end of the manuscript, illustrating the excellent performance of the novel methodology.