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ADAPTIVE MULTI-TIME-STEP METHODS FOR DYNAMIC CRACK PROPAGATIONMriganabh Boruah (11851130) 18 December 2021 (has links)
<p>Problems
in structural dynamics that involve rapid
evolution of the material at multiple scales
of length and time are challenging to solve numerically. One such problem
is that of a structure
un- dergoing fracture, where the material in the vicinity of a crack
front may experience high stresses and strains while the remainder of the
structure may be unaffected by it. Usually, such problems are solved using numerical
methods based on a finite element discretization in space and a finite
difference time-stepping scheme
to capture dynamic
response. Regions of interest within
the struc- ture, where high transients are expected, are usually modeled
with a fine discretization in space and time for better accuracy. In other regions
of the model where the response does not change
rapidly, a coarser
discretization suffices and helps keep the computational cost down. This
variation in spatial and temporal
discretization is achieved
through domain decomposition and multi-time-step
coupling methods which allow the use of different levels of mesh discretization
and time-steps in different regions of the mesh.</p>
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