Real-Time Implementation of Spectrum Sensing Techniques in Cognitive Radios

Wireless communication requirements of higher sampling frequencies and bandwidth are ever increasing. For this purpose, exploitation of underutilized spectrum bands was one the challenging research targets. Cognitive Radio (CR) is a promising solution to overcome the “limited bandwidth” issue. Software defined radio (SDR) is the enabler of CR. The aim of the thesis is to adopt the vacant TV channels for secondary users. Spectrum sensing prototype has been proposed to detect TV white space (TVWS). The prototype has been developed using Universal Software Radio Peripheral (USRP) and examined to sense TVWS in the real time world. The conducting analysis of obtained measurements showed the state of unoccupied spectrum bands in the UHF band ranges from 500 MHz to 698 MHz in the urban area ofWindsor, Ontario, Canada. Two different spectrum sensing techniques namely, the energy detector, and pilot-tone detector were employed to get the result with minimum computational complexity. Experiments show that the presence of incumbent users can be easily detected using the spectrum sensing techniques mentioned in the thesis. The experimental results have demonstrated the validity of the proposed prototyp

An adaptive discrete Newton method for a regularization-free Bingham model

Developing a numerical and algorithmic tool which correctly identifies unyielded regions in the yield stress fluid flow is a challenging task. Two approaches are commonly used to handle the singular behaviour at the yield surface, i.e. the Augmented Lagrangian approach and the regularization approach, respectively. Generally in the regularization approach for the resulting nonlinear and linear problems, solvers do not perform efficiently when the regularization parameter gets very small. In this work, we use a formulation introducing a new auxiliary stress [1]. The three field formulation of yield stress fluids corresponds to a regularization-free Bingham formulation. The resulting set of equations arising from the three field formulation is treated efficiently and accurately by a monolithic finite element method. The velocity and pressure are discretized by the higher order stable FEM pair Q_2⁄(P_1^disc ) and the auxiliary stress is discretized by the Q_2 element. Furthermore, this problem is highly nonlinear and presents a big challenge to any nonlinear solver. We developed a new adaptive discrete Newton's method, which evaluates the Jacobian with the directional divided difference approach [2]. The step size in this process is an important key: We relate this size to the rate of the actual nonlinear reduction for achieving a robust adaptive Newton's method. The resulting linear subproblems are solved using a geometrical multigrid solver. We analyse the solvability of the problem along with the adaptive Newton method for Bingham fluids by doing numerical studies for different prototypical configurations, i.e. "Viscoplastic fluid flow in a channel" [2], "Lid Driven Cavity", "Flow around cylinder", and "Bingham flow in a square reservoir", respectively. References [1] A. Aposporidis, E. Haber, M. A. Olshanskii, A. Veneziani. A Mixed Formulation of the Bingham Fluid Flow Problem: Analysis and Numerical Solution, Comput. Methods Appl. Mech. Engrg. 1 (2011), 2434–2446. [2] A. Fatima, S. Turek, A. Ouazzi, M. A. Afaq. An Adaptive Discrete Newton Method for Regularization-Free Bingham Model, 6th ECCOMAS Young Investigators Conference 7th-9th July 2021, Valencia, Spain. doi: 10.4995/YIC2021.2021.12389

Impact of Charge on Traversable Wormhole Solutions in f(R,T)f(R,T) Theory

This paper examines the effects of charge on traversable wormhole structure in $f(R,T)$ theory. For this purpose, we use the embedding class-I approach to build a wormhole shape function from the static spherically symmetric spacetime. The developed shape function satisfies all the required conditions and connects two asymptotically flat regions of spacetime. We consider different models of this modified theory to examine the traversable wormhole solutions through null energy condition and also check their stable state. We conclude that viable and stable wormhole solutions are obtained under the influence of charge in this gravitational theory.Comment: 21 pages, 5 figure

An adaptive discrete Newton method for regularization-free Bingham model

[EN] Developing a numerical and algorithmic tool which correctly identifies unyielded regions in yield stress fluid flow is a challenging task. Two approaches are commonly used to handle the singular behaviour at the yield surface, i.e. the Augmented Lagrangian approach and the regularization approach, respectively. Generally in the regularization approach, solvers do not perform efficiently when the regularization parameter gets very small. In this work, we use a formulation introducing a new auxiliary stress. The three field formulation of the yield stress fluid corresponds to a regularization-free Bingham formulation. The resulting set of equations arising from the three field formulation is solved efficiently and accurately by a monolithic finite element method. The velocity and pressure are discretized by the higher order stable FEM pair Q2/Pdisc 1 and the auxiliary stress is discretized by the Q2 element. Furthermore, this problem is highly nonlinear and presents a big challenge to any nonlinear solver. Therefore, we developed a new adaptive discrete Newton method, which evaluates the Jacobian with the divided difference approach. We relate the step length to the rate of the actual nonlinear reduction for achieving a robust adaptive Newton method. We analyse the solvability of the problem along with the adaptive Newton method for Bingham fluids by doing numerical studies for a prototypical configuration ”viscoplastic fluid flow in a channel”.We would like to thank the Deutsche Forschungsgemeinschaft (DFG) for their financial support under the DFG Priority Program SPP 1962. The authors also acknowledge the support by LS3 and LiDO3 team at ITMC, TU Dortmund UniversityFatima, A.; Turek, S.; Ouazzi, A.; Afaq, MA. (2022). An adaptive discrete Newton method for regularization-free Bingham model. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 180-189. https://doi.org/10.4995/YIC2021.2021.12389OCS18018

Monolithic Newton-Multigrid Solver for Multiphase Flow Problems with Surface Tension

We have developed a monolithic Newton-multigrid solver for multiphase flow problems which solves velocity, pressure and interface position simultaneously. The main idea of our work is based on the formulations discussed in [1], where it points out the feasibility of a fully implicit monolithic solver for multiphase flow problems via two formulations, a curvature free level set approach and a curvature free cut-off material function approach. Both formulations are fully implicit and have the advantages of requiring less regularity, since neither normals nor curvature are explicitly calculated, and no capillary time restriction has to be respected. Furthermore, standard Navier-Stokes solvers might be used, which do not have to take into account inhomogeneous force terms. The reinitialization issue is integrated within the formulations. The nonlinearity is treated with a Newton-type solver with divided difference evaluation of the Jacobian matrices. The resulting linearized system inside of the outer Newton solver is a typical saddle point problem which is solved using a geometrical multigrid method with Vanka-like smoother using higher order stable Q_2/P_1^disc FEM for velocity and pressure and Q_2 for all other variables. The method is implemented into an existing software package for the numerical simulation of multiphase flows (FeatFlow). The robustness and accuracy of this solver is tested for two different test cases, static bubble and oscillating bubble, respectively

An Adaptive Discrete Newton Method for Regularization-Free Bingham Model

Developing a numerical and algorithmic tool which correctly identifies unyielded regions in yield stress fluid flow is a challenging task. Two approaches are commonly used to handle the singular behaviour at the yield surface, i.e. the Augmented Lagrangian approach and the regularization approach, respectively. Generally in the regularization approach, solvers do not perform efficiently when the regularization parameter gets very small. In this work, we use a formulation introducing a new auxiliary stress. The three field formulation of the yield stress fluid corresponds to a regularization-free Bingham formulation. The resulting set of equations arising from the three field formulation is solved efficiently and accurately by a monolithic finite element method. The velocity and pressure are discretized by the higher order stable FEM pair Q_2/P_1^disc and the auxiliary stress is discretized by the Q_2 element. Furthermore, this problem is highly nonlinear and presents a big challenge to any nonlinear solver. Therefore, we developed a new adaptive discrete Newton method, which evaluates the Jacobian with the divided difference approach. We relate the step length to the rate of the actual nonlinear reduction for achieving a robust adaptive Newton method. We analyse the solvability of the problem along with the adaptive Newton method for Bingham fluids by doing numerical studies for a prototypical configuration ”viscoplastic fluid flow in a channel”

Robust Monolithic Multigrid FEM Solver for Three Field Formulation of Incompressible Flow Problems

Numerical simulation of three field formulations of incompressible flow problems is of interest for many industrial applications, for instance macroscopic modeling of Bing-ham, viscoelastic and multiphase flows, which usually consists in supplementing the mass and momentum equations with a differential constitutive equation for the stress field. The variational formulation rising from such continuum mechanics problems leads to a three field formulation with saddle point structure. The solvability of the problem requires different compatibility conditions (LBB conditions) [1] to be satisfied. Moreover, these constraints over the choice of the spaces may conflict/challenge the robustness and the efficiency of the solver. For illustrating the main points, we will consider the three field formulation of the Navier-Stokes problem in terms of velocity, stress, and pressure. Clearly, the weak form imposes the compatibility constraints over the choice of velocity, stress, and pressure spaces. So far, the velocity-pressure combi-nation took much more attention from the numerical analysis and computational fluid dynamic community, which leads to some best interpolation choices for both accuracy and efficiency, as for instance the combination Q2/P1disc. To maintain the computational advantages of the Navier-Stokes solver in two field formulations, it may be more suitable to have a Q2 interpolation for the stress as well, which is not stable in the absence of pure viscous term [2]. We proceed by adding an edge oriented stabilization to overcome such situation. Furthermore, we show the robustness and the efficiency of the resulting discretization in comparison with the Navier-Stokes solver both in two field as well as in three field formulation in the presence of pure viscous term. Moreover, the benefit of adding the edge oriented finite element stabilization (EOFEM) [3, 4] in the absence of the pure viscous term is tested. The nonlinearity is treated with a Newton-type solver [5] with divided difference evaluation of the Jacobian matrices [6, 7]. The resulting linearized system inside of the outer Newton solver is a typical saddle point problem which is solved using a geometrical multigrid method with Vanka-like smoother [8, 9]. The method is implemented into the FeatFlow [10] software package for the numerical simulation. The stability and robustness of the method is numerically investigated for ”flow around cylinder” benchmark [7, 11]

Monolithic Newton-Multigrid Solver for Multiphase Flow Problems with Surface Tension

[EN] We have developed a monolithic Newton-multigrid solver for multiphase flow problems which solves velocity, pressure and interface position simultaneously. The main idea of our work is based on the formulations discussed in [1], where it points out the feasibility of a fully implicit monolithic solver for multiphase flow problems via two formulations, a curvature-free level set approach and a curvature-free cutoff material function approach. Both formulations are fully implicit and have the advantages of requiring less regularity, since neither normals nor curvature are explicitly calculated, and no capillary time restriction. Furthermore, standard Navier-Stokes solvers might be used, which do not have to take into account inhomogeneous force terms. The reinitialization issue is integrated with a nonlinear terms within the formulations.The nonlinearity is treated with a Newton-type solver with divided difference evaluation of the Jacobian matrices. The resulting linearized system inside of the outer Newton solver is a typical saddle point problem which is solved using the geometrical multigrid with Vanka-like smoother using higher order stable FEM pair $Q_2/P^{\text{disc}}_1$ for velocity and pressure and $Q_2$ for all other variables. The method is implemented into an existing software packages for the numerical simulation of multiphase flows (FeatFlow). The robustness and accuracy of this solver is tested for two different test cases, i.e. static bubble and oscillating bubble, respectively [2].Muhammad Aaqib Afaq would like to thank Erasmus Mundus INTACT project, funded by the European Union as part of the Erasmus Mundus programme and the National University of Sciences and Technology (NUST) for their financial support. The authors also acknowledge the support by LS3 and LiDO3 team at ITMC, TU Dortmund University.Afaq, MA.; Turek, S.; Ouazzi, A.; Fatima, A. (2022). Monolithic Newton-Multigrid Solver for Multiphase Flow Problems with Surface Tension. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 190-199. https://doi.org/10.4995/YIC2021.2021.12390OCS19019