Session: 01-08-02 Digitalization, AI/ML, Digital Twins - II

Submission Number: 156353

A Relaxation Scheme for Solving Convolutional Forces in Adaptive Time Step ODE Solvers 

Efficiently solving ordinary differential equations (ODEs) is of importance in simulation-based digital-twin solutions in the marine and offshore industry. Many existing engineering codes use a uniform-time-step approach in solving ODEs. For local instantaneous variations existing in the solutions from the equations of motions, a fine time-stepping setup is necessary, which leads to redundant computations  in global computations. An adaptive-time-step ODE solver offers potential improvement by adjusting time steps dynamically and minimizing the number of total steps required.   However, this solution can still encounter inefficiencies, especially when common operations like convolution integral are repeatedly computed within each major time step for evaluating the next state. 
To address this challenge, this study proposes a relaxation scheme within adaptive-time-step ODE solvers. The relaxation scheme dynamically smooth over repeated calculations with a below-threshold filtering mechanism on time consuming parts such as convolutions. This enables efficient solving within any finer major step when rapid changes occur.  
Applied to hydrodynamic problems, this method offers reduced computational complexity and improved solving speed. 
In addition, numerical results demonstrate that this approach maintains sound accuracy for numerical emulations to marine dynamic systems. This framework could serve as a foundation for further advancements in ODE solving optimization, particularly for applications where different categories of environmental loads are convolved. Furthermore, the efficient numerical scheme may enable efficient time-domain simulations involving multiple rigid floaters.
 

Presenting Author: Yu Ma University of Stavanger

Presenting Author Biography: Yu Ma is a PhD candidate, working in University of Stavanger, Norway.
His main research focus is on Agent-assisted design methods applied to next-generation aquaculture facilities.