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The magic "Harry Potter's cloak" has been the dream of human beings for really long time. Recently, transformation optics inspired from the advent of metamaterials offers great versatility for manipulating wave propagation at will to create amazing illusion effects. In the present work, we proposed a novel transformation recipe, in which the cloaking shell somehow behaves like a "cloaking lens", to provide almost all desired features one can expect for a real magic cloak. The most exciting feature of the current recipe is that an object with arbitrary characteristics (e.g., size, shape or material properties) can be invisibilized perfectly with positive-index materials, which significantly benefits the practical realization of a broad-band cloaking device fabricated with existing materials. Moreover, the one concealed in the hidden region is able to undistortedly communicate with the surrounding world, while the lens-like cloaking shell will protect the cloaked source/sensor from being traced back by outside detectors by creating a virtual image., Comment: 13 pages, 3 figures

Based on some fundamental properties of finite element approximations, a mesh re-zoning scheme is proposed for finite element simulations of metal forming problems. It is demonstrated that this technique is indispensable in analyzing many difficult forming processes, especially when there exist corners or very irregular shapes on the boundaries. The algorithm is tested by a backward extrusion process and direct extrusion through a square die.