13,917 research outputs found
An Improved Split-Step Wavelet Transform Method for Anomalous Radio Wave Propagation Modelling
Anomalous tropospheric propagation caused by ducting phenomenon is a major problem in wireless communication. Thus, it is important to study the behavior of radio wave propagation in tropospheric ducts. The Parabolic Wave Equation (PWE) method is considered most reliable to model anomalous radio wave propagation. In this work, an improved Split Step Wavelet transform Method (SSWM) is presented to solve PWE for the modeling of tropospheric propagation over finite and infinite conductive surfaces. A large number of numerical experiments are carried out to validate the performance of the proposed algorithm. Developed algorithm is compared with previously published techniques; Wavelet Galerkin Method (WGM) and Split-Step Fourier transform Method (SSFM). A very good agreement is found between SSWM and published techniques. It is also observed that the proposed algorithm is about 18 times faster than WGM and provide more details of propagation effects as compared to SSFM
A class of high-order Runge-Kutta-Chebyshev stability polynomials
The analytic form of a new class of factorized Runge-Kutta-Chebyshev (FRKC)
stability polynomials of arbitrary order is presented. Roots of FRKC
stability polynomials of degree are used to construct explicit schemes
comprising forward Euler stages with internal stability ensured through a
sequencing algorithm which limits the internal amplification factors to . The associated stability domain scales as along the real axis.
Marginally stable real-valued points on the interior of the stability domain
are removed via a prescribed damping procedure.
By construction, FRKC schemes meet all linear order conditions; for nonlinear
problems at orders above 2, complex splitting or Butcher series composition
methods are required. Linear order conditions of the FRKC stability polynomials
are verified at orders 2, 4, and 6 in numerical experiments. Comparative
studies with existing methods show the second-order unsplit FRKC2 scheme and
higher order (4 and 6) split FRKCs schemes are efficient for large moderately
stiff problems.Comment: 24 pages, 5 figures. Accepted for publication in Journal of
Computational Physics, 22 Jul 2015. Revise
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Global extrapolation procedures for linear partial differential equations
Global extrapolation procedures, in space and time are considered for the numerical Solution of linear partial differential equations. Global extrapolation procedures in time only are reviewed.
The procedures are tested on three problems from the literature, one of which has a nonlinear source term
Energy-corrected FEM and explicit time-stepping for parabolic problems
The presence of corners in the computational domain, in general, reduces the
regularity of solutions of parabolic problems and diminishes the convergence
properties of the finite element approximation introducing a so-called
"pollution effect". Standard remedies based on mesh refinement around the
singular corner result in very restrictive stability requirements on the
time-step size when explicit time integration is applied. In this article, we
introduce and analyse the energy-corrected finite element method for parabolic
problems, which works on quasi-uniform meshes, and, based on it, create fast
explicit time discretisation. We illustrate these results with extensive
numerical investigations not only confirming the theoretical results but also
showing the flexibility of the method, which can be applied in the presence of
multiple singular corners and a three-dimensional setting. We also propose a
fast explicit time-stepping scheme based on a piecewise cubic energy-corrected
discretisation in space completed with mass-lumping techniques and numerically
verify its efficiency
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