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Mobile ad-hoc networks are prone to a number of security threats. The fact that mobile ad-hoc networks lack fixed infrastructure and use wireless link for communication makes them very susceptible to an adversary's malicious attacks. Black hole attack is one of the severe security threats in ad-hoc networks which can be easily employed by exploiting(More)
— We present an a-posteriori method for computing rigorous upper and lower bounds of the J-integral in two dimensional linear elasticity. The J-integral, which is typically expressed as a contour integral, is recast as a surface integral which yields a quadratic continuous functional of the displacement. By expanding the quadratic output about an(More)
  • Z. C. Xuan
  • 2011
A parallel computing procedure for computing the bounds on the {\it J}-integral in functionally graded materials is presented based on a Neumann element a-posteriori error bound. The finite element solution of {\it J}-integral is first obtained on a coarser finite element mesh, then a-posteriori bounding procedure based on the finite element error estimate(More)
Verification of the computation of local quantities of interest, e.g. the displacements at a point, the stresses in a local area and the stress intensity factors at crack tips, plays an important role in improving the structural design for safety. In this paper, the smoothed finite element method (SFEM) is used for finding upper and lower bounds on the(More)
We present an a-posteriori method for computing rigorous upper and lower bounds of the J-integral in two dimensional linear elasticity. The J-integral, which is typically expressed as a contour integral, is recast as a surface integral which yields a quadratic continuous functional of the displacement. By expanding the quadratic output about an approximate(More)
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