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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)
Abstract— 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 Fourth International Symposium on Parallel…
  • 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)
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)
! Department of Computer Science, Tianjin University of Technology and Education, Tianjin 300222, China. § Institute of Mathematics, Helsinki University of Technology, P.O. Box 1100, FI-02015 TKK, Finland. " Modeling and Scientific Computing, IACS-CMCS, École Polytechnique Fédérale de Lausanne, EPFL, Station 8, CH-1015 Lausanne, Switzerland. † MOX–(More)
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