Using the framework introduced by Rowley and Colonius [14] we construct a discretely non-reflecting boundary condition for the one-way wave equation spatially discretized with an explicit fourth order centered difference scheme. The boundary condition, which can be extended to arbitrary order accuracy, is shown to be GKSstable. We continue by deriving discretely non-reflecting boundary conditio...

In 1934, Whitney posed the problem of how to recognize whether a function f defined on a closed subset X of R is the restriction of a function of class C. Whitney himself solved the one-dimensional case (i.e., for n = 1) in terms of finite differences [W1, W2, W3], giving the classical Whitney’s extension theorem. A geometrical solution for the case C(R) was given by G. Glaeser [G], who introdu...

The finite-difference time-domain (FDTD) technique has been used to model the one-dimensional (1-D) surface impedance of a lossy earth plane having discontinuities in two and three dimensions. Using a horizontal magnetic field aperture source located five cells from an absorbing boundary and 35 cells above the lossy earth plane, the surface impedance was accurately modeled at a distance of 0=50...

Due to the increasing complexity of electronic systems and subsystems, versatile simulation approaches, able to combine electromagnetic full-wave analysis with models of non linear electronic devices, are becoming very attractive. Among them, the so called Lumped Element (LE)-FDTD method, for its characteristic to easily account for non linearities is one of the most promising ones. Unfortunate...

Path generation is an important factor that affects the quality and efficiency of most layered manufacturing processes such as SLS, SLA and FDM. This paper introduces an efficient path generation algorithm. The principle of the algorithm and the implementation are presented. A comparative study is used to analyze the effectiveness of this method. The results of comparison on both path length an...

This paper deals with a non-standard implicit finite difference scheme that is defined on quasi-uniform mesh for approximate solutions of the Magneto-Hydro Dynamics (MHD) boundary layer flow an incompressible fluid past flat plate wide range magnetic parameter. The proposed approach allows imposing given conditions at infinity exactly. We show how to improve obtained numerical results via refin...

Shu and Osher introduced a conservative finite difference discretization for hyperbolic conservation laws using nodal values rather than the traditional cell averages. Their form was obtained by introducing mathematical relations that simplify the resulting numerical methods. Here we instead ‘‘derive’’ their form from the standard cell average approach. In the process, we clarify the origin of ...