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We study the performance of the multigrid method applied to spectral element (SE) discretizations of the Poisson and Helmholtz equations. Smoothers based on finite element (FE) discretizations, overlapping Schwarz methods, and point-Jacobi are considered in conjunction with conjugate gradient and GMRES acceleration techniques. It is found that Schwarz(More)
We develop a fast direct solver for parallel solution of \coarse grid" problems, Ax = b, such as arise when domain decomposition or multigrid methods are applied to elliptic partial diierential equations in d space dimensions. The approach is based upon a (quasi-) sparse factorization of the inverse of A. If the dimension of the system is n and the number(More)
We describe the development and implementation of an efficient spectral element code for simulating transitional flows in complex three-dimensional domains. Critical to this effort is the use of geometrically nonconforming elements that allow localized refinement in regions of interest, coupled with a stabilized high-order time-split formulation of the(More)
Autotuning technology has emerged recently as a systematic process for evaluating alternative implementations of a computation, in order to select the best-performing solution for a particular architecture. Specialization optimizes code customized to a particular class of input data set. In this paper, we demonstrate how compiler-based autotuning that(More)
We present a high-order discontinuous Galerkin discretization of the unsteady in-compressible Navier-Stokes equations in convection-dominated flows using triangular and tetrahedral meshes. The scheme is based on a semi-explicit temporal discretization with explicit treatment of the nonlinear term and implicit treatment of the Stokes operator. The nonlinear(More)
In light of the pressing need for development and testing of reliable parameterizations of gravity current entrainment in ocean general circulation models, two existing entrainment parameterization schemes, K-profile parameterization (KPP) and one based on TurnerÕs work (TP), are compared using idealized experiments of dense water flow over a constant-slope(More)
[1] By recognizing that oceanic overflows follow the seafloor morphology, which shows a self-similar structure at spatial scales ranging from 100 km to 1 m, the impact of topographic bumps on entrainment in gravity currents is investigated using a 3D nonhydrostatic spectral element model. It is found that a bumpy surface can lead to a significant(More)
We describe Fourier pseudospectral time-domain simulations, carried out in order to study light interacting with a metallic nanoscale object. The difficulty of using Fourier methods to accurately predict the electromagnetic scattering in such problems arises from the discontinuity in the dielectric function along the surface of the metallic object. Standard(More)