This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of no...This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential,the absence of the compactness condition of Palais-Smale,and the L^(∞)-bound for any possible weak solution.To establish multiplicity results,we utilize the fountain theorem and the dual fountain theorem as main tools.Also,we give the L^(∞)-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique.As an application,we give the existence of a sequence of infinitely many weak solutions converging to zero in L^(∞)-norm.To derive this result,we employ the modified functional method and the dual fountain theorem.展开更多
The occurrence of‘sensing holes’not only hinders seamless data col-lection but also leads to misinterpretation of information in certain areas under extensive data analysis.In order to overcome this,various sensor r...The occurrence of‘sensing holes’not only hinders seamless data col-lection but also leads to misinterpretation of information in certain areas under extensive data analysis.In order to overcome this,various sensor relocation stra-tegies have been proposed,but the existing relocation strategies revealed pro-blems such as the ping-pong,shaded area,network disconnection,etc.This paper conducted research on relocation protocols in a distributed environment that is very suitable for real-world situations and efficiently recovering the problem of sensing holes.First,a simulation was performed on the distribution of the shaded area for data collection,which is a problem with the existing representative relo-cation protocol.After that,a data collection capability was newly added to the relay node,which had been in charge of only communication between cluster zones so far,and with this additional functionality,the performance of the revised sensor relocation algorithm was dramatically improved to overcome the existing problems.In addition,the performance and validity of the proposed algorithm were verified through various simulations.展开更多
The finite element method is a key player in computational electromag-netics for designing RF(Radio Frequency)components such as waveguides.The frequency-domain analysis is fundamental to identify the characteristics ...The finite element method is a key player in computational electromag-netics for designing RF(Radio Frequency)components such as waveguides.The frequency-domain analysis is fundamental to identify the characteristics of the components.For the conventional frequency-domain electromagnetic analysis using FEM(Finite Element Method),the system matrix is complex-numbered as well as indefinite.The iterative solvers can be faster than the direct solver when the solver convergence is guaranteed and done in a few steps.However,such complex-numbered and indefinite systems are hard to exploit the merit of the iterative solver.It is also hard to benefit from matrix factorization techniques due to varying system matrix parts according to frequency.Overall,it is hard to adopt conventional iterative solvers even though the system matrix is sparse.A new parallel iterative FEM solver for frequency domain analysis is implemented for inhomogeneous waveguide structures in this paper.In this implementation,the previous solution of the iterative solver of Matlab(Matrix Laboratory)employ-ing the preconditioner is used for the initial guess for the next step’s solution process.The overlapped parallel stage using Matlab’s Parallel Computing Toolbox is also proposed to alleviate the cold starting,which ruins the convergence of early steps in each parallel stage.Numerical experiments based on waveguide structures have demonstrated the accuracy and efficiency of the proposed scheme.展开更多
Mobile sensor nodes such as hopping sensors are of critical importance in data collection.However,the occurrence of sensing holes is unavoidable due to the energy limitation of the nodes.Thus,it is evident that the re...Mobile sensor nodes such as hopping sensors are of critical importance in data collection.However,the occurrence of sensing holes is unavoidable due to the energy limitation of the nodes.Thus,it is evident that the relocation of mobile sensors is the most desirable method to recover the sensing holes.The previous research conducted by the authors so far demonstrated the most realistic hopping sensor relocation scheme,which is suitable for the distributed environment.In previous studies,the cluster header plays an essential role in detecting the sensing hole and requesting the neighboring cluster to recover the sensing hole that occurred in the sensor node.However,the limitations of the cluster header in the previously proposed relocation protocol are not fully considered.Because the cluster header jumps more frequently than non-header nodes,its energy con-sumption is relatively high compared to other nodes.Therefore,it is most likely to lead to header node failure and can lead to data loss on the network.In this paper,the jumping ability and energy consumption of the cluster header are seriously considered.Additional ability to replace cluster headers in case of failure is also implemented.Simulation results show that the data collection time can be further increased,which demonstrates the validity of the proposed algorithms.展开更多
文摘This paper is devoted to demonstrating several multiplicity results of nontrivial weak solutions to double phase problems of Kirchhoff type with Hardy potentials.The main features of the paper are the appearance of non-local Kirchhoff coefficients and the Hardy potential,the absence of the compactness condition of Palais-Smale,and the L^(∞)-bound for any possible weak solution.To establish multiplicity results,we utilize the fountain theorem and the dual fountain theorem as main tools.Also,we give the L^(∞)-bound for any possible weak solution by exploiting the De Giorgi iteration method and a truncated energy technique.As an application,we give the existence of a sequence of infinitely many weak solutions converging to zero in L^(∞)-norm.To derive this result,we employ the modified functional method and the dual fountain theorem.
基金supported by Incheon National University Research Grant in 2021(2021-0295).
文摘The occurrence of‘sensing holes’not only hinders seamless data col-lection but also leads to misinterpretation of information in certain areas under extensive data analysis.In order to overcome this,various sensor relocation stra-tegies have been proposed,but the existing relocation strategies revealed pro-blems such as the ping-pong,shaded area,network disconnection,etc.This paper conducted research on relocation protocols in a distributed environment that is very suitable for real-world situations and efficiently recovering the problem of sensing holes.First,a simulation was performed on the distribution of the shaded area for data collection,which is a problem with the existing representative relo-cation protocol.After that,a data collection capability was newly added to the relay node,which had been in charge of only communication between cluster zones so far,and with this additional functionality,the performance of the revised sensor relocation algorithm was dramatically improved to overcome the existing problems.In addition,the performance and validity of the proposed algorithm were verified through various simulations.
基金supported by Institute of Information&communications Technology Planning&Evaluation(ITP)grant funded by the Korea govermment(MSIT)(No.2019-0-00098,Advanced and Integrated Software Development for Electromagnetic Analysis)supported by Research Assistance Program(2021)in the Incheon National University.
文摘The finite element method is a key player in computational electromag-netics for designing RF(Radio Frequency)components such as waveguides.The frequency-domain analysis is fundamental to identify the characteristics of the components.For the conventional frequency-domain electromagnetic analysis using FEM(Finite Element Method),the system matrix is complex-numbered as well as indefinite.The iterative solvers can be faster than the direct solver when the solver convergence is guaranteed and done in a few steps.However,such complex-numbered and indefinite systems are hard to exploit the merit of the iterative solver.It is also hard to benefit from matrix factorization techniques due to varying system matrix parts according to frequency.Overall,it is hard to adopt conventional iterative solvers even though the system matrix is sparse.A new parallel iterative FEM solver for frequency domain analysis is implemented for inhomogeneous waveguide structures in this paper.In this implementation,the previous solution of the iterative solver of Matlab(Matrix Laboratory)employ-ing the preconditioner is used for the initial guess for the next step’s solution process.The overlapped parallel stage using Matlab’s Parallel Computing Toolbox is also proposed to alleviate the cold starting,which ruins the convergence of early steps in each parallel stage.Numerical experiments based on waveguide structures have demonstrated the accuracy and efficiency of the proposed scheme.
基金supported by Incheon National University Research Grant in 2020(2020–0437)。
文摘Mobile sensor nodes such as hopping sensors are of critical importance in data collection.However,the occurrence of sensing holes is unavoidable due to the energy limitation of the nodes.Thus,it is evident that the relocation of mobile sensors is the most desirable method to recover the sensing holes.The previous research conducted by the authors so far demonstrated the most realistic hopping sensor relocation scheme,which is suitable for the distributed environment.In previous studies,the cluster header plays an essential role in detecting the sensing hole and requesting the neighboring cluster to recover the sensing hole that occurred in the sensor node.However,the limitations of the cluster header in the previously proposed relocation protocol are not fully considered.Because the cluster header jumps more frequently than non-header nodes,its energy con-sumption is relatively high compared to other nodes.Therefore,it is most likely to lead to header node failure and can lead to data loss on the network.In this paper,the jumping ability and energy consumption of the cluster header are seriously considered.Additional ability to replace cluster headers in case of failure is also implemented.Simulation results show that the data collection time can be further increased,which demonstrates the validity of the proposed algorithms.
