Publications

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Surface effects are critical to the accurate simulation of electromagnetics (EM) as current tends to concentrate near material surfaces. Sandia EM applications, which include exploding bridge wires for detonator design, electromagnetic launch of flyer plates for material testing and gun design, lightning blast-through for weapon safety, electromagnetic armor, and magnetic flux compression generators, all require accurate resolution of surface effects. These applications operate in a large deformation regime, where body-fitted meshes are impractical and multimaterial elements are the only feasible option. State-of-the-art methods use various mixture models to approximate the multi-physics of these elements. The empirical nature of these models can significantly compromise the accuracy of the simulation in this very important surface region. We propose to substantially improve the predictive capability of electromagnetic simulations by removing the need for empirical mixture models at material surfaces. We do this by developing an eXtended Finite Element Method (XFEM) and an associated Conformal Decomposition Finite Element Method (CDFEM) which satisfy the physically required compatibility conditions at material interfaces. We demonstrate the effectiveness of these methods for diffusion and diffusion-like problems on node, edge and face elements in 2D and 3D. We also present preliminary work on h -hierarchical elements and remap algorithms.

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Transport algorithms are highly important for dynamical modeling of the atmosphere, where it is critical that scalar tracer species are conserved and satisfy physical bounds. We present an optimization-based algorithm for the conservative transport of scalar quantities (i.e. mass) on the cubed sphere grid, which preserves local solution bounds without the use of flux limiters. The optimization variables are the net mass updates to the cell, the objective is to minimize the discrepancy between these variables and suitable high-order cell mass update (the "target"), and the constraints are derived from the local solution bounds and the conservation of the total mass. The resulting robust and efficient algorithm for conservative and local bound-preserving transport on the sphere further demonstrates the flexibility and scope of the recently developed optimization-based modeling approach [1, 2]. © 2014 Springer-Verlag.

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We present a new extended finite element method with algebraic constraints (XFEM-AC) for recovering weakly discontinuous solutions across internal element interfaces. If necessary, cut elements are further partitioned by a local secondary cut into body-fitting subelements. Each resulting subelement contributes an enrichment of the parent element. The enriched solutions are then tied using algebraic constraints, which enforce C0 continuity across both cuts. These constraints impose equivalence of the enriched and body-fitted finite element solutions, and are the key differentiating feature of the XFEM-AC. In so doing, a stable mixed formulation is obtained without having to explicitly construct a compatible Lagrange multiplier space and prove a formal inf-sup condition. Likewise, convergence of the XFEM-AC solution follows from its equivalence to the interface-fitted finite element solution. This relationship is further exploited to improve the numerical solution of the resulting XFEM-AC linear system. Examples are shown demonstrating the new approach for both steady-state and transient diffusion problems. © 2013 Elsevier B.V.

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Arctic sea ice is an important component of the global climate system, reflecting a significant amount of solar radiation, insulating the ocean from the atmosphere and influencing ocean circulation by modifying the salinity of the upper ocean. The thickness and extent of Arctic sea ice have shown a significant decline in recent decades with implications for global climate as well as regional geopolitics. Increasing interest in exploration as well as climate feedback effects make predictive mathematical modeling of sea ice a task of tremendous practical import. Satellite data obtained over the last few decades have provided a wealth of information on sea ice motion and deformation. The data clearly show that ice deformation is focused along narrow linear features and this type of deformation is not well-represented in existing models. To improve sea ice dynamics we have incorporated an anisotropic rheology into the Los Alamos National Laboratory global sea ice model, CICE. Sensitivity analyses were performed using the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA) to determine the impact of material parameters on sea ice response functions. Two material strength parameters that exhibited the most significant impact on responses were further analyzed to evaluate their influence on quantitative comparisons between model output and data. The sensitivity analysis along with ten year model runs indicate that while the anisotropic rheology provides some benefit in velocity predictions, additional improvements are required to make this material model a viable alternative for global sea ice simulations.

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