Our aim is to apply program transformations to stencil codes in order to yield the highest possible performance. We recognize memory bandwidth as a major limitation in stencil code performance. We conducted a study in which we applied optimizing transformations to two Jacobi smoother kernels: one 3D 1st-order 7-point stencil and one 3D 3rd-order 19-point stencil. To obtain high performance, the...

Solving partial differential equations results in a continuum of regular and irregular stencil computation implementations. In this paper, we use heat diffusion on a bar to show how regular and irregular stencil computations are related, and then illustrate five complicating issues that occur in implementing the continuum of regular and irregular stencil computations in full applications. These...

In this paper, we extend a previous work on a compact scheme for the steady Navier Stokes equations [Li, Tang, and Fornberg (1995), Int. J. Numer. Methods Fluids, 20, 1137 1151] to the unsteady case. By exploiting the coupling relation between the streamfunction and vorticity equations, the Navier Stokes equations are discretized in space within a 3_3 stencil such that a fourth order accuracy i...

The recently developed Flexible Local Approximation MEthod (FLAME) produces accurate difference schemes by replacing the usual Taylor expansion with Trefftz functions – local solutions of the underlying differential equation. The paper introduces a significant extension of FLAME: a least-squares fit instead of the exact match of the approximate solution at the stencil nodes. As a consequence of...

Partitioned Global Address Space (PGAS) programming languages have emerged as a means by which to program parallel computers, which are becoming larger and more complicated. For such languages, regular stencil codes are still one of the most important goals. We implemented three methods of stencil communication in a compiler for a PGAS language XcalableMP, which are 1) based on derived-datatype...

In this paper, we apply in-core optimization techniques to high-order stencil computations, including: (1) cache blocking for efficient L2 cache use; (2) register blocking and data-level parallelism via single-instruction multipledata (SIMD) techniques to increase L1 cache efficiency; and (3) software prefetching techniques. Our generic approach is tested with a kernel extracted from a 6 th -or...

This paper analyzes a number of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, and elastic waves. The spatial operators analyzed include compact schemes, noncompact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-mar...

We present an efficient solution to the eikonal equation on parametric manifolds, based on the fast marching approach. This method overcomes the problem of a non-orthogonal coordinate system on the manifold by creating an appropriate numerical stencil. The method is tested numerically and demonstrated by calculating distances on various parametric manifolds. It is further used for two applicati...