Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. While AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. In particular, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid h...

We consider an extended mixed nite element formulation for groundwater ow and transport problems with either a tensor hydraulic conductivity or a tensor dispersion. While the aquifer domain can be geometrically general, in our formulation the computational domain is rectangular. The approximating spaces for the mixed method are deened on a smooth curvilinear grid, obtained by a global mapping o...

SUMMARY We introduce a multigrid method with a stencil collapsing technique for linear systems whose coefficient matrix An ∈ R the eigenvalues of A are given by its generating symbol f , a [0, 2π) d-periodic function, as λ j = f (2πj1/n1, 2πj2/n2,. .. , 2πj d /n d). In the case of banded (multilevel) circulant systems, multigrid is an optimal, i.e. O(n) solver, which is superior to FFT techniqu...

Wave propagation forward modeling is a widely used computational method in oil and gas exploration. The iterative stencil loops in such problems have broad applications in scientific computing. However, executing such loops can be highly time-consuming, which greatly limits their performance and power efficiency. In this paper, we accelerate the forward-modeling technique on the latest multi-co...

We report on a fully CMOS compatible fabrication method for ambipolar silicon nanowire FinFETs. The low thermal budget processing, compatible with monolithic 3D device integration, makes use of low pressure chemical vapor deposition (LPCVD) of amorphous Si (a-Si) and SiO2 layers as well as metal gate patterning using stencil lithography, demonstrated for the first time. FinFETs with stenciled A...

In this paper we investigate how stencil computations can be implemented on state-of-the-art general purpose graphics processing units (GPGPUs). Stencil codes can be found at the core of many numerical solvers and physical simulation codes and are therefore of particular interest to scientific computing research. GPGPUs have gained a lot of attention recently because of their superior floating ...

Application codes reliably achieve performance far less than the advertised capabilities of existing architectures, and this problem is worsening with increasingly-parallel machines. For large-scale numerical applications, stencil operations are often impose the greater part of the computational cost, and the primary sources of ineeciency are the costs of message passing and poor cache utilizat...

We define a -causal discretization of static convex Hamilton-Jacobi Partial Differential Equations (HJ PDEs) such that the solution value at a grid node is dependent only on solution values that are smaller by at least . We develop a Monotone Acceptance Ordered Upwind Method (MAOUM) that first determines a consistent, -causal stencil for each grid node and then solves the discrete equation in a...

This work introduces a generalized framework for automatically tuning stencil computations to achieve superior performance on a broad range of multicore architectures. Stencil (nearest-neighbor) based kernels constitute the core of many important scientific applications involving block-structured grids. Auto-tuning systems search over optimization strategies to find the combination of tunable p...

Stencil printing remains the technology route of choice for flip chip bumping because of its economical advantages over traditionally costly evaporation and electroplating processes. This paper provides the first research results on stencil printing of 80 μm and 60 μm pitch peripheral array configurations with Type 7 Sn63/Pb37 solder paste. In specific, the paste particle size ranges from 2 μm ...