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We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. 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… (More)

- Joseph E. Flaherty, Raymond M. Loy, Mark S. Shephard, Boleslaw K. Szymanski, James D. Teresco, Louis H. Ziantz
- J. Parallel Distrib. Comput.
- 1997

Consideration is given to the techniques required to support adaptive analysis of automatically generated unstruc-tured meshes on distributed memory MIMD parallel computers. The key areas of new development are focused on the support of effective parallel computations when the structure of the numerical discretization, the mesh, is evolving, and in fact… (More)

- Lilia Krivodonova, Joseph E. Flaherty
- Adv. Comput. Math.
- 2003

- Slimane Adjerid, Belkacem Belguendouz, Joseph E. Flaherty
- SIAM J. Scientific Computing
- 1999

Adjerid et al. 2] and Yu 19, 20] show that a posteriori estimates of spatial discretiza-tion errors of piecewise bi-p polynomial nite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is… (More)

- Karen D. Devine, Erik G. Boman, +5 authors Luis G. Gervasio
- 2004

Data partitioning and load balancing are important components of parallel computations. Many different partitioning strategies have been developed, with great effectiveness in parallel applications. But the load-balancing problem is not yet solved completely; new applications and architectures require new partitioning features. Existing algorithms must be… (More)

- Jean-François Remacle, Joseph E. Flaherty, Mark S. Shephard
- SIAM Review
- 2003

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)

In parallel simulations, partitioning and load-balancing algorithms compute the distribution of application data and work to processors. The effectiveness of this distribution greatly influences the performance of a parallel simulation. Decompositions that balance processor loads while keeping the application's communication costs low are preferred.… (More)

- James D. Teresco, J. Fair, Joseph E. Flaherty
- Computing in Science & Engineering
- 2005

Although researchers can develop software on small, local clusters and move it later to larger clusters and supercomputers, the software must run efficiently in both environments. Two efforts aim to improve the efficiency of scientific computation on clusters through resource-aware dynamic load balancing. The popularity of cost-effective clusters built from… (More)

- David C. Arney, Joseph E. Flaherty
- ACM Trans. Math. Softw.
- 1990

We discuss mesh-moving, static mesh-regeneration, and local mesh-refinement algorithms that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse base mesh of quadrilateral cells is moved by an… (More)