Non-Split PML Boundary Condition for Finite Element Time-Domain Modeling of Ground Penetrating Radar

As a highly efficient absorbing boundary condition, Perfectly Matched Layer (PML) has been widely used in Finite Difference Time Domain (FDTD) simulation of Ground Penetrating Radar (GPR) based on the first order electromagnetic wave equation. However, the PML boundary condition is difficult to apply in GPR Finite Element Time Domain (FETD) simulation based on the second order electromagnetic wave equation. This paper developed a non-split perfectly matched layer (NPML) boundary condition for GPR FETD simulation based on the second order electromagnetic wave equation. Taking two-dimensional TM wave equation as an example, the second order frequency domain equation of GPR was derived according to the definition of complex extending coordinate transformation. Then it transformed into time domain by means of auxiliary differential equation method, and its FETD equation is derived based on Galerkin method. On this basis, a GPR FETD forward program based on NPML boundary condition is developed. The merits of NPML boundary condition are certified by compared with wave field snapshots, signal and reflection errors of homogeneous medium model with split and non-split PML boundary conditions. The comparison demonstrated that the NPML algorithm can reduce memory occupation and improve calculation efficiency. Furthermore, numerical simulation of a complex model verifies the good absorption effects of the NPML boundary condition in complex structures.

Construction of an Energy-Efficient Detour Non-Split Dominating Set in WSN

Wireless sensor networks(WSNs)are one of the most important improvements due to their remarkable capacities and their continuous growth in various applications.However,the lifetime of WSNs is very confined because of the delimited energy limit of their sensor nodes.This is the reason why energy conservation is considered the main exploration worry for WSNs.For this energy-efficient routing is required to save energy and to subsequently drag out the lifetime of WSNs.In this report we use the Ant Colony Optimization(ACO)method and are evaluated using the Genetic Algorithm(GA),based on the Detour non-split dominant set(GA)In this research,we use the energy efficiency returnee non-split dominating set(DNSDS).A set S⊆V is supposed to be a DNSDS of G when the graph G=(V,E)is expressed as both detours as well as a non-split dominating set of G.Let the detour non-split domination number be addressed asγ_dns(G)and is the minimum order of its detour non-split dominating set.Any DNSDS of orderγdns(G)is aγdns-set of G.Here,theγ_dns(G)of various standard graphs is resolved and some of its general properties are contemplated.A connected graph usually has an order n with detour non-split domination number as n or n–1 are characterized.Also connected graphs of order n≥4 and detour diameter D≤4 with detour non-split dominating number n or n−1 or n−2 are additionally portrayed.While considering any pair of positive integers to be specific a and b,there exists a connected graph G which is normally indicated as dn(G)=a,γ(G)=b andγdns(G)=a+b−2,hereγdns(G)indicates the detour domination number and dn(G)indicates the detour number of a graph.The time is taken for the construction and the size of DNSDS are considered for examining the performance of the proposed method.The simulation result confirms that the DNSDS nodes are energy efficient.

The implementation of an improved NPML absorbing boundary condition in elastic wave modeling

In elastic wave forward modeling, absorbing boundary conditions （ABC） are used to mitigate undesired reflections from the model truncation boundaries. The perfectly matched layer （PML） has proved to be the best available ABC. However, the traditional splitting PML （SPML） ABC has some serious disadvantages： for example, global SPML ABCs require much more computing memory, although the implementation is easy. The implementation of local SPML ABCs also has some difficulties, since edges and corners must be considered. The traditional non-splitting perfectly matched layer （NPML） ABC has complex computation because of the convolution. In this paper, based on non-splitting perfectly matched layer （NPML） ABCs combined with the complex frequency-shifted stretching function （CFS）, we introduce a novel numerical implementation method for PML absorbing boundary conditions with simple calculation equations, small memory requirement, and easy programming.

Comparison of Semi-Lagrangian Discontinuous Galerkin Schemes for Linear and Nonlinear Transport Simulations

Transport problems arise across diverse fields of science and engineering.Semi-Lagran-gian(SL)discontinuous Galerkin(DG)methods are a class of high-order deterministic transport solvers that enjoy advantages of both the SL approach and the DG spatial discre-tization.In this paper,we review existing SLDG methods to date and compare numerically their performance.In particular,we make a comparison between the splitting and non-splitting SLDG methods for multi-dimensional transport simulations.Through extensive numerical results,we offer a practical guide for choosing optimal SLDG solvers for linear and nonlinear transport simulations.

On a certain non-split cubic surface

This paper establishes an asymptotic formula with a power-saving error term for the number of rational points of bounded height on the singular cubic surface of P3 Qgiven by the following equation x0（x12+ x22）-x33= 0 in agreement with the Manin-Peyre conjectures.