In a graph G, the first and second degrees of a vertex v is equal to thenumber of their first and second neighbors and are denoted by d(v/G) andd 2 (v/G), respectively. The first, second and third leap Zagreb indices are thesum of squares of second degrees of vertices of G, the sum of products of second degrees of pairs of adjacent vertices in G and the sum of products of firs...

In this work, a method for the simulation of guided wave propagation in solids defined by implicit surfaces is presented. The employs structured grids spectral elements combination with fictitious domain approach to represent complex geometrical features through signed distance functions. A novel approach, based on moment fitting, introduced restore diagonal mass matrix property intersected int...

This work gives a Lie operator derivation of various Boris solvers via detailed study trajectory errors in constant magnetic field. These the gyrocenter location and gyroradius are foundational basis for why existed, independent any finite-difference schemes. shows that there two distinct ways eliminating these so charged particle field is exactly on cyclotron orbit. One way reproduces known se...

ABSTRACT The detection of gravitational waves has opened a new era for astronomy, allowing the combined use wave and electromagnetic emissions to directly probe physics compact objects, still poorly understood. So far, theoretical modelling these sources mainly relied on standard numerical techniques as grid-based methods or smoothed particle hydrodynamics, with only few recent attempts at usin...

The fault diagnosis of rolling element bearing is great significance to avoid serious accidents and huge economic losses. However, the characteristics nonlinear, non-stationary vibration signals make feature extraction signal become a challenging work. This paper proposes an improved variational mode decomposition (IVMD) algorithm for bearing, which has advantages extracting optimal from decomp...

Explicit local time-stepping methods are derived for the time dependent Maxwell equations in conducting and non-conducting media. By using smaller time steps precisely where smaller elements in the mesh are located, these methods overcome the bottleneck caused by local mesh refinement in explicit time integrators. When combined with a finite element discretization in space with an essentially d...

A discontinuous Galerkin method is proposed for the numerical solution of the three-dimensional time-domain Maxwell's equations. A leap frog scheme is used for advancing in time. The scheme resulting can handle highly heterogeneous material, non diffusive and highly adaptable (it has been implemented on tetrahedral or hexahedral grids, including non-conforming). In some cases, some divergence c...