The spectral element method (SEM) is a high order numerical method for solving partial differential equations that inherits the accuracy of spectral methods and the geometrical flexibility of the finite element method. These lectures provide an introduction to the SEM for graduate students in Earth science. The construction of the method is described for a model problem in 1D and 2D. The elemen...

The computational efficiency of Finite Element Methods (FEMs) on parallel architectures is severely limited by conventional sparse iterative solvers. Conventional solvers are based on a sequence of global algebraic operations that limits their parallel efficiency. Traditionally, sophisticated programming techniques tailored to specific CPU architectures are used to improve the poor performance ...

We consider the solution of a second order elliptic PDE with inhomogeneous Dirichlet data by means of adaptive lowest-order FEM. As is usually done in practice, the given Dirichlet data are discretized by nodal interpolation. As model example serves the Poisson equation with mixed Dirichlet-Neumann boundary conditions. For error estimation, we use an edge-based residual error estimator which re...

Numerical simulation of the behaviour of human lumbar spine segments, moreover, parameter-identification of the component organs of human lumbar FSUs are presented in traction therapies, by using FEM analysis. First, a simple 2D model, than a refined 2D model, and finally a refined 3D model were applied for modeling lumbar FSUs. For global numerical simulation of traction therapies the material...

Numerical simulation of the deformation process during flat rolling of multifilament HTS tapes has been investigated using a commercial FEM program, ELFEN. The numerical models were built up in 2D and 3D using a DruckerPragerKap model for the powder. Three different roll diameters (024 mm, 0 8 5 mm and 0126 mm) have been investigated. It is found that it is possible to perform numerical simulat...

In some geophysical problems, it is sometimes possible to divide the subsurface resistivity distribution as a one dimensional (1D) contribution plus some two dimensional (2D) inhomogeneities. Assuming this scenario, we split the electromagnetic fields into their primary and secondary components, the former corresponding to the 1D contribution, and the latter to the 2D inhomogeneities. While the...

Purpose Thermal analysis of electrical machines is usually performed by using numerical methods or lumped parameter thermal networks depending on the desired accuracy. The analytical prediction temperature distribution based formal resolution partial differential equations (PDEs) harmonic modeling technique (or Fourier method) uncommon in machines. Therefore, this paper aims to present a two-di...

This paper presents a novel double-stator permanent-magnet machine integrated with a triple rotor magnetic gear structure, which is proposed to address problems of mechanical geared generators for low-speed applications. Torque transmission is based on three rotors consisting of prime permanent-magnet (PM) poles in the middle rotor and field PM poles in the inner and outer rotors. The proposed ...

Highly enhanced Raman scattering of graphene on a plasmonic nano-structure platform is demonstrated. The plasmonic platform consists of silver nano-structures in a periodic array on top of a gold mirror. The gold mirror is used to move the hot spot to the top surface of the silver nano-structures, where the graphene is located. Two different nano-structures, ring and crescent, are studied. The ...