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he popularity of cost-effective clusters built from commodity hardware has opened up a new platform for the execution of software originally designed for tightly coupled supercomputers. Because these clusters can be built to include any number of processors ranging from fewer than 10 to thousands, researchers in high-performance scientific computation at… (More)

We present a high-order formulation for solving hyperbolic conservation laws using the Discon-tinuous Galerkin Method (DGM). We introduce an orthogonal basis for the spatial discretization and use explicit Runge-Kutta time discretization. Some results of higher-order adaptive refinement calculations are presented for in-viscid Rayleigh Taylor flow… (More)

SUMMARY An anisotropic adaptive analysis procedure based on a discontinuous Galerkin finite element discretization and local mesh modification of simplex elements is presented. The procedure is applied to transient 2-and 3-dimensional problems governed by Euler's equation. A smoothness indicator is used to isolate jump features where an aligned mesh metric… (More)

We describe a procedure for the adaptive h-refinement solution of the incompressible MHD equations in stream function form using a stabilized finite element formulation. The mesh is adapted based on a posteriori spatial error estimates of the magnetic field using both recovery and order extrapolation techniques. The step size for time integration is chosen… (More)

Cluster and grid computing has made hierarchical and heterogeneous computing systems increasingly common as target environments for large-scale scientific computation. A cluster may consist of a network of multiprocessors. A grid computation may involve communication across slow interfaces. Modern supercomputers are often large clusters with hierarchical… (More)

We construct massively parallel adaptive finite element methods for the solution of hyperbolic conservation laws. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent… (More)