An Adaptive time-stepping scheme with local convergence verification using support vector machines

Kawaguchi, Kenji; Ishikawa, Jun ; Maruyama, Yu 

An adaptive time-stepping scheme in accordance with the local convergence of computation often involves computationally expensive procedures. As a result, many computer simulators have avoided utilizing such an adaptive scheme, while its advantages are well recognized; the scheme not only efficiently allocates computational resources, but also makes the results of the computation more reliable. In this paper, we propose a fast adaptive time-stepping scheme, ATLAS (Adaptive Time-step Learning and Adjusting Scheme), which approximates such an expensive yet beneficial scheme by using support vector machines (SVMs). We demonstrate that ATLAS achieves higher accuracy with lower computational cost when compared with computations without it. ATLAS can incorporate existing solvers and other fast but unreliable adaptive schemes to meet the different criteria required in various applications.