This paper describes a compiler transformation on stencil operators that automatically converts a standard stencil representation into an accumulation. We use this as an enabling transformation to optimize the stencil operators in the context of Geometric Multigrid (GMG), a widely used method to solve partial differential equations. GMG has four stencil operators, the smoother, residual, restri...

We present an efficient implementation of 7–point and 27–point stencils on high-end Nvidia GPUs. A new method of reading the data from the global memory to the shared memory of thread blocks is developed. The method avoids conditional statements and requires only two coalesced instructions to load the tile data with the halo. Additional optimizations include storing only one XY tile of data at ...

This paper analyzes a high-accuracy approximation to the mth-order linear ordinary differential equation Mu = f. At mesh points, U is the estimate of u; and U satisfies MnU = Inf, where MnU is a linear combination of values of U at m + 1 stencil points (adjacent mesh points) and Inf is a linear combination of values of f at J auxiliary points, which are between the first and last stencil points...

In various industries such as power plants, ultrasonic non-destructive testing (NDT) is widely used because of cost effectiveness and sub-surface defect/flaw detection capability. Piezoelectric films made of sol-gel composites could be useful as ultrasonic transducers due to high tempearature durability, reasonable signal strength, curved surface suitability, relatively low center frequency suc...

Weighted essentially non-oscillatory (WENO) schemes are effective numerical methods to compute flows having shocks and steep gradients. WENO schemes are based on the successful essentially non-oscillatory (ENO) schemes introduced in [9] and [10]. The initial WENO scheme is constructed in [6], and further research in WENO can be found in papers such as [2], [4] and [5]. Both ENO and WENO schemes...

Flow visualization tools based on particle methods continue to be an important utility of ow simulation. Additionally, sparse grids are of increasing interest in numerical simulations. In 13] we presented the advantages of particle tracing on uniform sparse grids. Here we present and compare two diierent approaches to accelerate particle tracing on sparse grids. Furthermore, a new approach is p...

Solving a scalar wave equation by the finite-difference (FD) method is key step for advanced seismic imaging, in which numerical accuracy significantly affected FD stencil. High-order spatial and temporal approximations of stencil can effectively improve mitigate dispersion error. However, huge costs high-order stenciling computation storage hinder application large-scale modeling. In this pape...

One of the major advantages of stencil lithography is the possibility to use stencils many times. However, when stencils contain nanoapertures, the clogging of the membranes limits the useful life time of the stencils. The clogging is due to the accumulation of material deposited inside the apertures of the stencil. Here, we report a study on the effect of the clogging on the life time of stenc...

The Residual Distribution (RD) schemes are an alternative to standard high order accurate finite volume schemes. They have several advantages: a better accuracy, a much more compact stencil, easy parallelization. However, they face several problems, at least for steady problems which are the only cases considered here. The solution is obtained via an iterative method. The iterative convergence ...