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detected is not the critical pattern. In addition, these patterns represent a
very coarse sample comprising relatively few readings. Therefore, WSN node
readings (in each pre-selected sample) must be compared with the critical
patterns. Adaptive mesh refinement provides a well-adjusted finite element
mesh, which can be used for interpolating the values at a finer scale. The
interpolated values can be readily compared with the critical pattern values.
This would verify if the critical pattern was indeed encountered in one or more
of the WSNs.
To develop the finite element mesh, we propose a parallel processing ap-
proach to finite element mesh generation that harnesses the capability of
computational grid networks to process large-scale data. We propose a parallel
adaptive finite element mesh generated using a Domain Decomposition (DD)
concept. In Domain Decomposition, a domain of interest is decomposed into
multiple sub-domains. Each sub-domain is delegated to a single processing
node in the computational grid network.
9.2.2.2.1 Adaptive finite element analysis
The state of the mechan-
ical, structural, and electrical components may be effectively modeled using
the well-established numerical technique, adaptive FEA. A stress-strain based
finite element model was selected to distinguish between the various stress
states. To achieve a finite element solution that is close to the actual response
of the material, it can be assumed that the continuum is idealized using a
large number of elements. The size of each element is very small in compari-
son to the dimensions of the continuum. Therefore, the actual element stresses
will tend to be constant over each of the elements, and the solution can be
regarded as accurate for all practical purposes. However, doing so requires the
use of a very fine mesh. To avoid the computational cost associated with a
very fine mesh, an adaptive refinement of the mesh is carried out.
Figure 9.12 provides a detailed distribution of stresses over the L-plate from
the previous sub-section. However, the values obtained from the WSN will only
provide the readings at the center of each of the six WSN nodes embedded in
the plate. The values at other points in the WSN must be estimated using an
interpolation scheme that can refine the values measured by the sparse set of
WSN nodes to a continuum.
9.2.2.2.2 Parallel approach to finite element mesh generation
Fi-
nite element analysis is considered to be a purely sequential approach for
mesh generation. However, several studies have parallelized this approach.
These studies include the works by Jimack and Nadeem [100] on the parallel
domain decomposition algorithm for adaptive finite element solution of three-
dimensional convection-diffusion problems; and Fragakis and Onate [101] in
their work on parallel Delaunay triangulation for particle finite element meth-
ods. To generate the mesh for the L-plated surface in the previous sub-sections,
we implemented a geometric decomposition of the surface, as shown in Figure
