Numerical simulation and convergence analysis for a system of nonlinear singularly perturbed differential equations arising in population dynamics

In this article, we consider a system of nonlinear singularly perturbed differential equations with two different parameters. To solve this system, we develop a weighted monotone hybrid scheme on a nonuniform mesh. The proposed scheme is a combination of the midpoint scheme and the upwind scheme involving the weight parameters. The weight parameters enable the method to switch automatically from the midpoint scheme to the upwind scheme as the nodal points start moving from the inner region to the outer region. The nonuniform mesh in particular the adaptive grid is constructed using the idea of equidistributing a positive monitor function involving the solution gradient. The method is shown to be second order convergent with respect to the small parameters. Numerical experiments are presented to show the robustness of the proposed scheme and indicate that the estimate is optimal.     

A new coding scheme of QC-LDPC codes for optical transmission systems

Based on Galois Field (GF(q)) multiplicative group, a new coding scheme for Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes is proposed, and the new coding scheme has some advantages such as the simpler construction, the easier implementation encoding, the lower complexity of the encoding and decoding, the more flexible adjustment of the code length as well as the code rate and so forth. Under the condition of considering the characteristics of optical transmission systems, an irregular QC-LDPC (3843,3603) code to be suitable for optical transmission systems is constructed by applying the proposed new coding scheme. The simulation result shows that the net coding gain (NCG) of the irregular QC-LDPC (3843,3603) code is respectively improved 2.14 dB, 1.19 dB, 0.24 dB and 0.14 dB more than those of the classic RS (255,239) code in ITU-T G.975, the LDPC (32640,30592) code in ITU-T G.975.1, the regular SCG-LDPC (3969,3720) code constructed by the Systematically Constructed Gallager (SCG) coding scheme and the regular QC-LDPC (4221,3956) code at the bit error rate (BER) of 10-8. Furthermore, all the five codes have the same code rate of 93.7%. Therefore, the irregular QC-LDPC (3843,3603) code constructed by the proposed new coding scheme has the more excellent error-correction performance and can be better suitable for optical transmission systems.     

A new level‐dependent coarse grid correction scheme for indefinite Helmholtz problems

In this paper, we construct and analyze a level‐dependent coarse grid correction scheme for indefinite Helmholtz problems. This adapted multigrid (MG) method is capable of solving the Helmholtz equation on the finest grid using a series of MG cycles with a grid‐dependent complex shift, leading to a stable correction scheme on all levels. It is rigorously shown that the adaptation of the complex shift throughout the MG cycle maintains the functionality of the two‐grid correction scheme, as no smooth modes are amplified in or added to the error. In addition, a sufficiently smoothing relaxation scheme should be applied to ensure damping of the oscillatory error components. Numerical experiments on various benchmark problems show the method to be competitive with or even outperform the current state‐of‐the‐art MG‐preconditioned Krylov methods, for example, complex shifted Laplacian preconditioned flexible GMRES. Copyright © 2013 John Wiley & Sons, Ltd.     

An anti‐diffusive volume of fluid method for interfacial fluid flows

A volume of fluid (VOF) method is developed combining a first‐order limited downwind scheme with higher order accurate schemes. The method is characterized by retaining a sharp fluid interface and a reduction in numerical diffusion near the interface, but avoids complicated geometrical reconstruction as occurs in most volume tracing algorithms. To demonstrate the accuracy and robustness of the method, a selection of numerical experiments are presented involving a pure advection problem, a water wave impact caused by a dam breaking and liquid sloshing in a partially filled tank. Copyright © 2011 John Wiley & Sons, Ltd.     

A simplified adaptive Cartesian grid system for solving the 2D shallow water equations

This paper presents a new simplified grid system that provides local refinement and dynamic adaptation for solving the 2D shallow water equations (SWEs). Local refinement is realized by simply specifying different subdivision levels to the cells on a background uniform coarse grid that covers the computational domain. On such a non‐uniform grid, the structured property of a regular Cartesian mesh is maintained and neighbor information is determined by simple algebraic relationships, i.e. data structure becomes unnecessary. Dynamic grid adaptation is achieved by changing the subdivision level of a background cell. Therefore, grid generation and adaptation is greatly simplified and straightforward to implement. The new adaptive grid‐based SWE solver is tested by applying it to simulate three idealized test cases and promising results are obtained. The new grid system offers a simplified alternative to the existing approaches for providing adaptive mesh refinement in computational fluid dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.     

A novel adaptive logic for dynamic adaptive streaming over HTTP

In this paper, we propose an estimation method that estimates the throughput of upcoming video segments based on variations in the network throughput observed during the download of previous video segments. Then, we propose a rate-adaptive algorithm for Hypertext Transfer Protocol (HTTP) streaming. The proposed algorithm selects the quality of the video based on the estimated throughput and playback buffer occupancy. The proposed method selects high-quality video segments, while minimizing video quality changes and the risk of playback interruption, improving user’s experience. We evaluate the algorithm for single- and multi-user environments and demonstrate that it performs remarkably well under varying network conditions. Furthermore, we determine that it efficiently utilizes network resources to achieve a high video rate; competing HTTP clients achieve equitable video rates. We also confirm that variations in the playback buffer size and segment duration do not affect the performance of the proposed algorithm.     

Throughput-based fair bandwidth allocation in OBS networks

Fair bandwidth allocation (FBA) has been studied in optical burst switching (OBS) networks, with the main idea being to map the max-min fairness in traditional IP networks to the fair-loss probability in OBS networks. This approach has proven to be fair in terms of the bandwidth allocation for differential connections, but the use of the ErlangB formula to calculate the theoretical loss probability has made this approach applicable only to Poisson flows. Furthermore, it is necessary to have a reasonable fairness measure to evaluate FBA models. This article proposes an approach involving throughput-based-FBA, called TFBA, and recommends a new fairness measure that is based on the ratio of the actual throughput to the allocated bandwidth. An analytical model for the performance of the output link with TFBA is also proposed.     

A new numerical model for simulations of wave transformation,breaking and long‐shore currents in complex coastal regions

In this paper, we propose a model based on a new contravariant integral form of the fully nonlinear Boussinesq equations in order to simulate wave transformation phenomena, wave breaking, and nearshore currents in computational domains representing the complex morphology of real coastal regions. The aforementioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. A procedure developed in order to correct errors related to the difficulties of numerically satisfying the metric identities in the numerical integration of fully nonlinear Boussinesq equation on generalized boundary‐conforming grids is presented. The Boussinesq equation system is numerically solved by a hybrid finite volume–finite difference scheme. The proposed high‐order upwind weighted essentially non‐oscillatory finite volume scheme involves an exact Riemann solver and is based on a genuinely two‐dimensional reconstruction procedure, which uses a convex combination of biquadratic polynomials. The wave breaking is represented by discontinuities of the weak solution of the integral form of the nonlinear shallow water equations. The capacity of the proposed model to correctly represent wave propagation, wave breaking, and wave‐induced currents is verified against test cases present in the literature. The results obtained are compared with experimental measures, analytical solutions, or alternative numerical solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

A vertex‐centered linearity‐preserving discretization of diffusion problems on polygonal meshes

This paper introduces a vertex‐centered linearity‐preserving finite volume scheme for the heterogeneous anisotropic diffusion equations on general polygonal meshes. The unknowns of this scheme are purely the values at the mesh vertices, and no auxiliary unknowns are utilized. The scheme is locally conservative with respect to the dual mesh, captures exactly the linear solutions, leads to a symmetric positive definite matrix, and yields a nine‐point stencil on structured quadrilateral meshes. The coercivity of the scheme is rigorously analyzed on arbitrary mesh size under some weak geometry assumptions. Also, the relation with the finite volume element method is discussed. Finally, some numerical tests show the optimal convergence rates for the discrete solution and flux on various mesh types and for various diffusion tensors. Copyright © 2015 John Wiley & Sons, Ltd.