Academic literature on the topic 'Hp-refinement'

The effect of alloying the Eu element on primary Si refinement in varied purity Al–16Si alloys was studied by scanning electron microscopy (SEM), thermal analysis, micro x–ray diffraction (μ–XRD), electron probe microanalysis (EPMA), and transmission electron microscopy (TEM). The results indicate that the P impurity element in hypereutectic Al–Si alloys has a great influence on the rare earths’ refinement efficiency of primary Si. Coinstantaneous primary Si refinement and eutectic Si modification by Eu was obtained in high purity (HP) Al–16Si and commercial purity (CP) Al–16Si–0.06P alloys, but the primary Si was gradually coarsened in CP Al–16Si alloys. An excellent integration of ultimate tensile strength (144.8 MPa) and elongation (9.8%) of CP hypereutectic Al–16Si–0.06P alloy was obtained by adding 0.15% Eu. The refinement of primary Si in Eu–modified HP Al–16Si alloys was related to the constitutional undercooling of Eu. There was no sufficient Eu element partition into the primary Si particles, and fewer parallel twins, rather than multiple twins, were observed within them. The refinement of primary Si in CP Al–16Si–0.06P alloys was caused by the overlay of two kinds of mechanisms including the heterogeneous nucleation mechanism of AlP and the constitutional supercooling mechanism of Eu. However, in order to refine the primary Si in CP hypereutectic Al–16Si alloys, the Eu:P weight ratio should not exceed 3.33, otherwise the refinement efficiency of primary Si will be reduced due to mutual poisoning between Eu and P. This work can be used to interpret the controversy concerning the influence of rare earths on the primary Si in hypereutectic Al–Si alloys, thereby elucidating the importance of alloy purity to primary Si refinement by rare earths.

Growth restriction plays an important role in grain refinement and is often linked with as-cast grain size of Al-Alloys. It has been suggested that Ti is the most powerful solute element for growth restriction among all the commonly used alloying elements. In this work, the growth restriction effect of Ti on the grain refinement of high purity Al (HP-Al, 99.99%) and commercial purity Al (CP-Al, 99.7%) has been investigated using the Alcan TP-1 tests. Grain refining tests were conducted with the same inoculation of potent TiB2 at a fixed level and free Titanium addition. The results showed that, when the TiB2 inoculation was fixed to be equivalent to the particle number density of 0.2% Al-5Ti-1B addition, CP-Al has a fully equiaxed grain structure with only 46 ppm solute Ti, while HP-Al has a fully equiaxed grain structure with much higher Ti addition (960 ppm).

A novel, highly efficient and accurate adaptive higher-order finite element method (hp-FEM) is proposed for electromagnetic field problems. Presented in this paper are the vector expression of Maxwell's equations, three kinds of boundary conditions, stability weak formulation of Maxwell's equations, and automatic hp-adaptivity strategy. This method can select optimal refinement and calculation strategies based on the practical formation model and error estimation. Numerical experiments show that the new hp-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom, which provides more accurate results than those obtained using the adaptive h-FEM. The methodology is freely available online in the form of a general public licensed C++ library Hermes (http://hpfem.org/hermes).

We develop the energy norm a posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the error measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.