Advanced Discretizations Research and Development

Bochev, Ridzal, Hetmaniuk

Research drivers

• Analysis of the translation process: analytic - - - discrete (discretization)
• Formulation of stable, accurate and physically correct discrete models,
• Development of software tools that enable such models (Intrepid)

Relevance to ASCR/DOE-SC and SNL

Compatible methods enable high-fidelity predictive simulations by managing the information loss that is inherently present in the discretization process.

Research approach

Abstract discretization framework based on algebraic topology that allows to preserve key properties of analytic structures (Hodge decomposition, cohomology, exact sequence) needed for stability and physical consistency of the discrete model.

Accomplishments

14 papers, 1 book, 2 book chapters, 2 short courses, 29 invited/plenary/colloquium talks 2 focused workshops (CSRI, IMA); 4 special sessions (SIAM CS/E, FEF07) Formulation of new AMG solvers for Maxwell’s (with R. Tuminaro) Formulation of a novel software design concept for compatible discretizations Development of interoperable tools for compatible discretizations (release in FY09)

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