A quantitative analysis of blurring and its dependence on the stencil-substrate gap and the deposition parameters in stencil lithography, a high resolution shadow mask technique, is presented. The blurring is manifested in two ways: first, the structure directly deposited on the substrate is larger than the stencil aperture due to geometrical factors, and second, a halo of material is formed su...

This paper explores autotuning strategies for serial divide-and-conquer stencil computations, comparing the efficacy of traditional “heuristic” autotuning with that of “pruned-exhaustive” autotuning. We present a pruned-exhaustive autotuner called Ztune that searches for optimal divide-and-conquer trees for stencil computations. Ztune uses three pruning properties — space-time equivalence, divi...

Many problems formulated in terms of partial differential equations lead to stencil-type structures after applying an appropriate structured discretization. On the one hand, exploiting these stencil structures in simulations can lead to massive performance improvements, compared to forming a sparse matrix. On the other hand, the generality of the simulation is restricted, depending on the exact...

Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new, higher order-accurate, low dissipation numerical method which requires no additional dissipation or local ”fixes” for stable execution. We describe PPML, a loc...

In this paper we study a parallel form of the SOR method for the numerical solution of the Convection Diffusion equation suitable for GPUs using CUDA. To exploit the parallelism offered by GPUs we consider the fine grain parallelism model. This is achieved by considering the local relaxation version of SOR. More specifically, we use SOR with red black ordering with two sets of parameters ωi j a...

An efficient approach for the simulation of finite-size particles with interface resolution was presented by Uhlmann (J. Comput. Phys, Vol. 209, pp. 448-476, 2005). The present paper proposes several enhancements of this method which considerably improve the results and extend the range of applicability. An important step is a simple low-cost iterative procedure for the Euler-Lagrange coupling ...

A class of generalized high order finite compact difference schemes is proposed for shock/vortex, shock/boundary layer interaction problems. The finite compact difference scheme takes the region between two shocks as a compact stencil. The high order WENO fluxes on shock stencils are used as the internal boundary fluxes for the compact scheme. A lemma of the property of smoothness estimators on...

The shallow-water equations model hydrostatic flow below a free surface for cases in which the ratio between the vertical and horizontal length scales is small and are used to describe waves in lakes, rivers, oceans, and the atmosphere. The equations admit discontinuous solutions, and numerical solutions are typically computed using high-resolution schemes. For many practical problems, there is...

To improve the resolution and accuracy of high-order weighted compact nonlinear scheme (WCNS), a new ?-adaptive algorithm based on local smoothness indicators is proposed. The introduces global indicator to adjust value ? according flow characteristics. Specifically, increases in smooth regions, which can help cover up disparity sub-stencils make approach background linear scheme. As result, op...

Nonnegative directional splittings of anisotropic diffusion operators in the divergence form are investigated. Conditions are established for nonnegative directional splittings to hold in a neighborhood of an arbitrary interior point. The result is used to construct monotone finite difference schemes for the boundary value problem of anisotropic diffusion operators. It is shown that such a mono...