High order differential form-based elements for the computation of electromagnetic field

2000 ◽  
Vol 36 (4) ◽  
pp. 1472-1478 ◽  
Author(s):  
N. Ida ◽  
Z. Ren
Keyword(s):  
Electromagnetic Field ◽  
Differential Form ◽  
High Order

Investigation of 3D Internal Flow Using New Flux-Reconstruction High Order Method

2012 ◽  
Author(s):  
Yi Lu ◽  
Xin Yuan ◽  
W. N. Dawes
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Differential Form ◽  
Internal Flow ◽  
High Order ◽  
New Method ◽  
Flux Reconstruction ◽  
Order Method ◽  
High Order Method

The new godunov-type high order method via flux-reconstruction, are capable of unifiying several popular methods including the discontinuous Galerkin, staggered-grid multi-domain method, or the spectral difference/spectral volume methods into a single family. Compared to discontinuous galerkin method, this new method retain the arbitrary order and compact properties but written in differential form and without mass matrix. The flux-reconstrcution method using general unstructured 2D/3D mesh including triangles, quadrilaterals, tetrahedrons, pyramids, prisms and hexahedrons are implemented. Compared to discontinuous galerkin method, FR is differential form without any quandature, so it runs faster and is easier to implement on GPU to achieve higher speed up ratio. The present paper investigates three different solving methods for this new method in order to cut down the hugh computational cost and memory requirement for fully implicit methods. Explicit multi-stage Runge-Kutta, nonlinear Lower-Upper Symmetry Gauss-Seidel (LU-SGS) and generalized minimal residual (GMRES) with matrix-free preconditioning methods are implemented and all these three methods use p-multigrid to smooth low-frequency errors on lower order. The results of 2D steady-state external/internal viscous flows are presented and the convergence properties for different solving method are compared. Efficiency and robustness are improved through symmetric Gauss-Seidel (SGS) iterations as preconditioning, a remarkable feature of the present GMRES+SGS method is that the storage of the full Jacobian matrix can be eliminated and only its diagonal stored. A laplacian artificial viscosity is tested to capture shock in one element and performs well for this new high order method, an L2 projection method is used to improve the perfomance of aliasing error in conservative form. The one equation Spalart-Allmaras turbulence model is unsed to solve the Raynolds average navier-stokes equations. MPI is used for parallel simulations for ralatively complex 3D internal flow when using high order method. Compared to other high order methods, results in this paper show that Flux-Reconstruction methods with efficient solving method performs well for 2D/3D general unstructured mesh in wide range of reynorlds number, and is also potential for “real geometry” simulations.

Determination of the Burgers vector of a dislocation in a Fe-Mn alloy by weak-beam image in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 330-331
Author(s):  
Y. Ishida ◽  
H. Ishida ◽  
K. Kohra ◽  
H. Ichinose
Keyword(s):  
High Order ◽  
Simulation Technique ◽  
The Other ◽  
Image Simulation ◽  
Diffraction Vector ◽  
Burgers Vector ◽  
Weak Beam ◽  
Beam Image ◽  
Edge Component

IntroductionA simple and accurate technique to determine the Burgers vector of a dislocation has become feasible with the advent of HVEM. The conventional image vanishing technique(1) using Bragg conditions with the diffraction vector perpendicular to the Burgers vector suffers from various drawbacks; The dislocation image appears even when the g.b = 0 criterion is satisfied, if the edge component of the dislocation is large. On the other hand, the image disappears for certain high order diffractions even when g.b ≠ 0. Furthermore, the determination of the magnitude of the Burgers vector is not easy with the criterion. Recent image simulation technique is free from the ambiguities but require too many parameters for the computation. The weak-beam “fringe counting” technique investigated in the present study is immune from the problems. Even the magnitude of the Burgers vector is determined from the number of the terminating thickness fringes at the exit of the dislocation in wedge shaped foil surfaces.

The usefulness of high index low symmetry zone axes for holz line analysis

1987 ◽  
Vol 45 ◽  
pp. 384-385
Author(s):  
C. M. Sung ◽  
D. B. Williams
Keyword(s):  
Lattice Parameter ◽  
High Order ◽  
Zone Axis ◽  
High Index ◽  
High Symmetry ◽  
Second Phases ◽  
Line Patterns ◽  
Low Symmetry ◽  
Line Analysis

Researchers have tended to use high symmetry zone axes (e.g. <111> <114>) for High Order Laue Zone (HOLZ) line analysis since Jones et al reported the origin of HOLZ lines and described some of their applications. But it is not always easy to find HOLZ lines from a specific high symmetry zone axis during microscope operation, especially from second phases on a scale of tens of nanometers. Therefore it would be very convenient if we can use HOLZ lines from low symmetry zone axes and simulate these patterns in order to measure lattice parameter changes through HOLZ line shifts. HOLZ patterns of high index low symmetry zone axes are shown in Fig. 1, which were obtained from pure Al at -186°C using a double tilt cooling holder. Their corresponding simulated HOLZ line patterns are shown along with ten other low symmetry orientations in Fig. 2. The simulations were based upon kinematical diffraction conditions.

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