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Multi-level explicit local time-stepping methods for second-order wave equations
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DOI：10.1016/j.cma.2015.03.027.png)
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Abstract
En 中文
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, multilevel 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. (C) 2015 Elsevier B.V. All rights reserved.
Keywords:
Wave propagation
Finite element methods
Adaptivity
Explicit time integration
Leap-frog method
Local time-stepping
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