An enhanced explicit time-marching technique for wave propagation analysis considering adaptive time integrators

2020 ◽  
Vol 363 ◽  
pp. 112882
Author(s):  
Delfim Soares
Keyword(s):  
Wave Propagation ◽  
Time Integrators ◽  
Propagation Analysis ◽  
Time Marching ◽  
Adaptive Time

A Simple Explicit–Implicit Time-Marching Technique for Wave Propagation Analysis

2018 ◽  
Vol 16 (01) ◽  
pp. 1850082 ◽  
Author(s):  
Delfim Soares
Keyword(s):  
Wave Propagation ◽  
Time Integration ◽  
Critical Time ◽  
Implicit Time ◽  
Time Step ◽  
Stiffness Matrices ◽  
Time Integrators ◽  
Propagation Analysis ◽  
Time Marching ◽  
Critical Time Step

A new explicit–implicit time integration technique is proposed here for wave propagation analysis. In the present formulation, the time integrators of the model are selected at the element level, allowing each element to be considered as explicit or implicit. In the implicit elements, controllable algorithm dissipation is provided, enabling an [Formula: see text]-stable formulation. In the explicit elements, null amplitude decay is considered, enabling maximal critical time-step values. The new methodology renders a very simple and effective time-marching algorithm. Here, just displacement–velocity relations are considered, and no computation of accelerations is required. Moreover, explicit/implicit analyses can be carried out just by the tuning of local effective matrices, inputting or not stiffness matrices into their computations. At the end of the paper, numerical results are presented, illustrating the performance and potentialities of the new method.

Two Efficient Time-Marching Explicit Procedures Considering Spatially/Temporally-Defined Adaptive Time-Integrators

2021 ◽  
pp. 2150051
Author(s):  
Delfim Soares
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Results ◽  
Spatial Discretization ◽  
Adaptive Procedure ◽  
Excellent Performance ◽  
Time Integrators ◽  
Time Marching ◽  
Adaptive Time ◽  
Discretization Technique ◽  
Discretized Model

In this paper, two explicit time-marching techniques are discussed for the solution of hyperbolic models, which are based on adaptively computed parameters. In both these techniques, time integrators are locally and automatically evaluated, taking into account the properties of the spatially/temporally discretized model and the evolution of the computed responses. Thus, very versatile solution techniques are enabled, which allows computing highly accurate responses. Here, the so-called adaptive [Formula: see text] method is formulated based on the elements of the adopted spatial discretization (elemental formulation), whereas the so-called adaptive [Formula: see text] method is formulated based on the degrees of freedom of the discretized model (nodal formulation). In this context, each adaptive procedure can be better applied according to the specific features of the focused spatial discretization technique. At the end of the paper, numerical results are presented, illustrating the excellent performance of the discussed adaptive formulations.

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