Mark A. Christon

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The Accelerated Strategic Computing Initiative (ASCI) is focused upon advancing three-dimensional, full-physics calculations to the point where \full-system" simulation may be applied to virtual testing. The ASCI program involves Sandia, Los Alamos and Lawrence Livermore National Laboratories. At Sandia National Laboratories, ASCI applications include large(More)
High-resolution finite volume methods for solving systems of conservation laws have been widely embraced in research areas ranging from astrophysics to geophysics and aero-thermodynamics. These methods are typically at least second-order accurate in space and time, deliver non-oscillatory solutions in the presence of near discontinuities, e.g., shocks, and(More)
The Reproducing Kernel Particle Method (RKPM) has many attractive properties that make it ideal for treating a broad class of physical problems. RKPM may be implemented in a \mesh-full" or a \mesh-free" manner and provides the ability to tune the method, via the selection of a window function and its associated dilation parameter, in order to achieve the(More)
The research summarized in this paper is part of a multi-year effort focused on evaluating the viability of wavelet bases for the solution of partial di erential equations. The primary objective for this work has been to establish a foundation for hierarchical/wavelet simulation methods based upon numerical performance, computational e ciency, and the(More)
This paper discusses the design and implementation of solution algorithms suitable for performing transient, incompressible viscous ow simulations on massively parallel computers. The nite element formulation for incompressible ow along with the ad-hoc modi cations for explicit time integration are discussed with an emphasis on implementation aspects for(More)
The results presented here constitute a brief summary of an on-going multi-year e ort to investigate hierarchical/wavelet bases for solving PDE's and establish a rigorous foundation for these methods. A new, hierarchical, wavelet-Galerkin solution strategy based upon the Donovan-GeronimoHardin-Massopust (DGHM) compactly-supported multi-wavelet is presented(More)
This paper presents an overview of the issues associated with applying a domain-decomposition message-passing paradigm to the parallel implementation of both explicit and semi-implicit projection algorithms. The use of an element-based domain decomposition with an e cient solution strategy for the pressure eld is shown to yield a scalable, parallel solution(More)
The Reproducing Kernel Particle Method (RKPM) is a discretization technique for partial di erential equations that uses the method of weighted residuals to produce either \mesh-free" or \mesh-full" methods. The technique employs classical reproducing kernel theory and incorporates modi ed kernels to account for inconsistencies arising from the (unavoidable)(More)
Two alternative approaches to the solution of discrete ordinate transport are considered in the context of general unstructured grids. The more traditional approach considered is the solution of a lower triangular system of equations for the spatial intensity distribution. Alternatively, the iterative solution of the system of equations arising from a more(More)