A modi ed triangle based adaptive di erence stencil for the numerical approximation of scalar hyperbolic conservation laws in two space dimensions is constructed. The scheme satis es the maximum principle and approximates the ux with second order accuracy. 3

Stencil-based kernels constitute the core of many scientific applications on block-structured grids. These calculations form the basis for a wide range of scientific applications from simple Jacobi iterations to complex multigrid and block structured adaptive PDE solvers. Unfortunately, these codes achieve a low fraction of peak performance, due primarily to the disparity between processor and ...

In this paper, we review the current development of stencil lithography for scalable microand nanomanufacturing as a resistless and reusable patterning technique. We first introduce the motivation and advantages of stencil lithography for large-area microand nanopatterning. Then we review the progress of using rigid membranes such as SiNx and Si as stencil masks as well as stacking layers. We a...

Finite difference WENO schemes have established themselves as very worthy performers for entire classes of applications that involve hyperbolic conservation laws. In this paper we report on two major advances that make finite difference WENO schemes more efficient. The first advance consists of realizing that WENO schemes require us to carry out stencil operations very efficiently. In this pape...

Efficient frequency-domain full-waveform inversion (FWI) of long-offset node data can be performed with a few frequencies. The seismic response these frequencies computed compact finite-difference stencils on regular Cartesian grid direct or hybrid direct/iterative methods. Compactness, which is necessary to mitigate the fill-in induced by lower-upper factorization, implemented second-order ste...

A stencil computation determines the values of points in a grid of some dimensionality by repeatedly evaluating a given function of a grid point and its neighbors. The parallelization and optimization of stencil computations are subject of ongoing research. The most prevalent approach is the subdivision of the iteration domain into smaller pieces, called tiles. We give an overview of a method t...

For Laplace’s equation, we discuss whether it is possible to construct a linear positive finite volume (FV) scheme on arbitrary unstructured grids. Dealing with the arbitrary grids, we state a control volume which guarantees a positive FV scheme with linear reconstruction of the solution. The control volume is defined by a property of the analytical solution to the equation and does not depend ...

Here we present an inexpensive method to fabricate microscopic cellular cultures, which does not require any surface modification of the substrate prior to cell seeding. The method utilizes a reusable elastomeric stencil (i.e., a membrane containing thru holes) which seals spontaneously against the surface. The stencil is applied to the cell-culture substrate before seeding. During seeding, the...

We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order k 0 at mesh faces. The method hinges on local discrete reconstruction operators for the diffusive and advective derivatives and a weak enforcement of boundary conditions. Fairly general meshes with polytopal and nonmatching cells are suppor...