Inexact Spectral Deferred Correction Methods for Long-Time Integration

Martin Weiser, Zuse Institute Berlin (ZIB) https://www.zib.de/weiser/

Abstract: Simulating wear testing of implants under cyclic loading requires a multiscale approach in time. Simple cycle jumping realizes an explicit Euler scheme for the averaged evolution of the shape. In this talk, we consider spectral deferred correction methods for higher order integration, and exploit the accuracy-effort trade-off available in finite element based simulations. This leads to inexact SDC methods, which can be much more efficient than standard SDC approaches. Based on work and accuracy models, a theoretically optimal choice of inexactness is derived. The efficiency of the resulting method is illustrated at some numerical examples.