The Local Discontinuous Galerkin (LDG) method is one of several discontinuous Galerkin (DG) methods that has been extensively studied in recent years. In this presentation we discuss several computational issues. After a brief introduction of the method applied to a second order linear operator, we describe the general structure of the discrete linear system and discuss the influence of the met...

We present a finite difference scheme, applicable to general irregular planar domains, to approximate the biharmonic equation. The irregular domain is embedded in a Cartesian grid. In order to approximate ∆Φ at a grid point we interpolate the data on the (irregular) stencil by a polynomial of degree six. The finite difference scheme is ∆2QΦ(0, 0), where QΦ is the interpolation polynomial. The i...

We present a JIT compiler with auto-tuning capabilities fusing multiple stencil computations. Data arrays for scientific computing of image processing often exceed cache-memory size. To take advantage of spatial and temporal locality, a common method is to partition the images into tiling blocks for multicore architectures. In realistic scenarios, the multiple image algorithms, most of which ar...

We discuss our experience in using Bamboo to automatically optimize a stencil method on an Intel Xeon Phi-based cluster. We describe our solutions to three challenges: tolerating the high cost of inter-node communication, mapping program parallelism to multicore and many-core processors, and balancing workloads on-node across heterogeneous resources. We present results on TACC’s Stampede system...

A high-order discontinuous Galerkin finite element discretization and p-multigrid solution procedure for the compressible Navier-Stokes equations are presented. The discretization has an element-compact stencil such that only elements sharing a face are coupled, regardless of the solution space. This limited coupling maximizes the effectiveness of the p-multigrid solver, which relies on an elem...

There are two main requirements for practical simulation of unsteady ow at high Reynolds number: the algorithm must accurately propagate discontinuous ow elds without excessive artiicial viscosity, and it must have some adaptive capability to concentrate computational eeort where it is most needed. We satisfy the rst of these requirements with a second-order Godunov method similar to those used...

The author presents a polynomial-based algorithm for high-order multidimensional interpolation at the coarse-fine interface in the context of adaptive mesh refinement on structured Cartesian grids. The proposed algorithm reduces coarse-fine interpolation to matrix-vector products by exploiting the static mesh geometry and a family of nonsingularity-preserving stencil transformations. As such, n...

We propose a new single-phase local transmissibility upscaling method for adapted grids in 3-D domains that uses spatially varying and compact multi-point flux approximations (MPFA). The multi-point stencils used to calculate the fluxes across coarse grid cell faces are required to honor three generic flow problems as closely as possible while maximizing compactness. We also present a corrector...

We present a method to utilize the Shadow Volume Algorithm by Crow and Williams without using a stencil buffer. We show that the shadow mask can be generated in the alpha channel or even in the screen buffer, if a hardware-accelerated stencil buffer is not available. In comparison to the original stencil buffer method, a small speed up can be achieved, if the shadow mask is computed in the alph...

In this study, a new selective filtering technique is proposed for the Lattice Boltzmann Method. This technique is based on an adaptive implementation of the selective filter coefficient σ. The proposed model makes the latter coefficient dependent on the shear stress in order to restrict the use of the spatial filtering technique in sheared stress region where numerical instabilities may occur....