On control of adaptation in parallel mesh generation

A black-box methodology of a parallel generation of adaptive anisotropic meshes is described. A control of mesh adaptation, important for robustness and flexibility, may effect parallel properties of the methodology. This is demonstrated with a 3D example.     

Device processing and characterisation of high temperature silicon carbide Schottky diodes

High temperature silicon carbide diodes with nickel silicide Schottky contacts were fabricated by deposition of titanium-nickel metal film on 4H-SiC epitaxial wafer followed by annealing at 550 °C in vacuum. Room temperature boron implantation have been used to form single zone junction termination extension. 4H-SiC epitaxial structures designed to have theoretical parallel-plain breakdown voltages of 1900 and 3600 V have been used for this research. The diodes revealed soft recoverable avalanche breakdown at voltages of 1450 and 3400 V, respectively, which are about 80% and 95% of theoretical values. I-V characteristics of fabricated 4H-SiC Schottky diodes have been measured at temperatures from room temperature up to 400 °C. The diodes revealed unchangeable barrier heights and ideality factors as well as positive coefficients of breakdown voltage.     

GaN grown by hydride vapor phase epitaxy on p-type 6H-SiC layers

6H-SiC/GaN pn-heterostructures were grown by subsequent epitaxial growth of p-SiC by low temperature liquid phase epitaxy (LTLPE) and n-GaN by hydride vapor phase epitaxy (HVPE). For the first time, p-type epitaxial layers grown on 6H-SiC wafers were used as substrates for GaN HVPE growth. The GaN layers exhibit high crystal quality which was determined by x-ray diffraction. The full width at a half maximum (FWHM) for the ω-scan rocking curve for (0002) GaN reflection was ∼120 arcsec. The photoluminescence spectra for these films were dominated by band-edge emission. The FWHM of the edge PL peak at 361 nm was about 5 nm (80K).     

Circulant block-factorization preconditioners for elliptic problems

New circulant block-factorization preconditioners are introduced and studied. The general approach is first formulated for the case of block tridiagonal sparse matrices. Then estimates of the relative condition number for a model Dirichlet boundary value problem are derived. In the case ofy-periodic problems the circulant block-factorization preconditioner is shown to give an optimal convergence rate. Finally, using a proper imbedding of the original Dirichlet boundary value problem to ay-periodic one a preconditioner of optimal convergence rate for the general case is obtained. The total computational cost of the preconditioner isO (N logN) (based on FFT), whereN is the number of unknowns. That is, the algorithm is nearly optimal. Various numerical tests that demonstrate the features of the circulant block-factorization preconditioners are presented.     

Experimental determination of electron drift velocity in 4H-SiC p+-n-n+ avalanche diodes

4H-SiC p⁺-n-n⁺ diodes of low series resistivity (<1×10^-4 Ω·cm²) were fabricated and packaged. The diodes exhibited homogeneous avalanche breakdown at voltages U_b=250-270 V according to the doping level of the n layer. The temperature coefficient of the breakdown voltage was measured to be 2.6×10^-4 k^-1 in the temperature range 300 to 573 K. These diodes were capable of dissipating a pulsed power density of 3.7 MW/cm² under avalanche current conditions. The transient thermal resistance of the diode was measured to be 0.6 K/W for a 100-ns pulse width, An experimental determination of the electron saturated drift velocity along the c-axis in 4H-SIC was performed for the first time, It was estimated to be 0.8×10⁷ cm/s at room temperature and 0.75×10⁷ cm/s at approximately 360 K     

Performance of certain iterative methods in solving implicit difference schemes for 2-D Navier–Stokes equations

The performance of three iterative methods, local SOR, preconditioned generalized conjugate gradient methods such as ORTHOMIN(1) and the GCG–LS method with preconditioning matrices derived by incomplete (modified and unmodified) pointwise factorizations of the matrix corresponding to implicit finite difference schemes for the 2-D Navier–Stokes equations, is compared. The relative merits of these methods in terms of CPU time, average number of iterations with respect to the Reynolds number and discretization parameters are emphasized.     

Adaptive AMG with coarsening based on compatible weighted matching

We introduce a new composite adaptive Algebraic Multigrid (composite \(\alpha \) AMG) method to solve systems of linear equations without a-priori knowledge or assumption on characteristics of near-null components of the AMG preconditioned problem referred to as algebraic smoothness. Our version of \(\alpha \) AMG is a composite solver built through a bootstrap strategy aimed to obtain a desired convergence rate. The coarsening process employed to build each new solver component relies on a pairwise aggregation scheme based on weighted matching in a graph, successfully exploited for reordering algorithms in sparse direct methods to enhance diagonal dominance, and compatible relaxation. The proposed compatible matching process replaces the commonly used characterization of strength of connection in both the coarse space selection and in the interpolation scheme. The goal is to design a method leading to scalable AMG for a wide class of problems that go beyond the standard elliptic Partial Differential Equations (PDEs). In the present work, we introduce the method and demonstrate its potential when applied to symmetric positive definite linear systems arising from finite element discretization of highly anisotropic elliptic PDEs on structured and unstructured meshes. We also report on some preliminary tests for 2D and 3D elasticity problems as well as on problems from the University of Florida Sparse Matrix Collection.     

Parallel iterative multilevel solution of mixed finite element systems for scalar equations

A combination of several contemporary techniques is used for the efficient parallel solution of the mixed finite element systems on locally refined Grids. Implementation experience and numerical results are reported. Copyright © 2005 John Wiley & Sons, Ltd.     

Finite volume methods with local refinement for convection-diffusion problems

Computing - Based on approximation of the balance relation for convection-diffusion problems, finite difference schemes on rectangular locally refined grids are derived and studied. A priori...