Multi-level explicit local time-stepping methods for second-order wave equations

Abstract : Local mesh refinement severely impedes the efficiency of explicit time-stepping methods for numerical wave propagation. Local time-stepping (LTS) methods overcome the bottleneck due to a few small elements by allowing smaller time-steps precisely where those elements are located. Yet when the region of local mesh refinement itself contains a sub-region of even smaller elements, any local time-step again will be overly restricted. To remedy the repeated bottleneck caused by hierarchical mesh refinement, multi-level local time-stepping methods are proposed, which permit the use of the appropriate time-step at every level of mesh refinement. Based on the LTS methods from Diaz and Grote (2009), these multi-level LTS methods are explicit, yield arbitrarily high accuracy and conserve the energy. Numerical experiments illustrate the theoretical properties and the usefulness of these methods.
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Julien Diaz, Marcus Grote. Multi-level explicit local time-stepping methods for second-order wave equations. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2015, 291, pp.240-265. ⟨10.1016/j.cma.2015.03.027⟩. ⟨hal-01184090⟩

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