A Conservative Optimization-based Semi-Lagrangian Spectral Element Method for Passive Tracer Transport
Abstract not provided.
Publications
A conservative, optimization-based semi-lagrangian spectral element method for passive tracer transport
COUPLED PROBLEMS 2015 - Proceedings of the 6th International Conference on Coupled Problems in Science and Engineering
We present a new optimization-based, conservative, and quasi-monotone method for passive tracer transport. The scheme combines high-order spectral element discretization in space with semi-Lagrangian time stepping. Solution of a singly linearly constrained quadratic program with simple bounds enforces conservation and physically motivated solution bounds. The scheme can handle efficiently a large number of passive tracers because the semi-Lagrangian time stepping only needs to evolve the grid points where the primitive variables are stored and allows for larger time steps than a conventional explicit spectral element method. Numerical examples show that the use of optimization to enforce physical properties does not affect significantly the spectral accuracy for smooth solutions. Performance studies reveal the benefits of high-order approximations, including for discontinuous solutions.
A New Control Volume Finite Element Method for the Drift-Diffusion Equations on Unstructured Grids
Abstract not provided.
A new control volume finite element method for the stable and accurate solution of the drift-diffusion equations on general unstructured grids
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Abstract not provided.
A parameter-free stabilized finite element method for scalar advection-diffusion problems
Central European Journal of Mathematics
Abstract not provided.
A Partitioned Method for Explicit Elastodynamics Based on a Generalized Dual Schur Complement
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A Performance Portable Discrete Element Sea Ice Model
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A Performance Portable Discrete Element Sea Ice Model for Earth System Modeling
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A virtual control coupling approach for problems with non-coincident discrete interfaces
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Independent meshing of subdomains separated by an interface can lead to spatially non-coincident discrete interfaces. We present an optimization-based coupling method for such problems, which does not require a common mesh refinement of the interface, has optimal H1 convergence rates, and passes a patch test. The method minimizes the mismatch of the state and normal stress extensions on discrete interfaces subject to the subdomain equations, while interface “fluxes” provide virtual Neumann controls.
A virtual control, mesh-free coupling method for non-coincident interfaces
Proceedings of the 6th European Conference on Computational Mechanics: Solids, Structures and Coupled Problems, ECCM 2018 and 7th European Conference on Computational Fluid Dynamics, ECFD 2018
We present an optimization approach with two controls for coupling elliptic partial differential equations posed on subdomains sharing an interface that is discretized independently on each subdomain, introducing gaps and overlaps. We use two virtual Neumann controls, one defined on each discrete interface, thereby eliminating the need for a virtual common refinement interface mesh. Global flux conservation is achieved by including the square of the difference of the total flux on each interface in the objective. We use Generalized Moving Least Squares (GMLS) reconstruction to evaluate and compare the subdomain solution and gradients at quadrature points used in the cost functional. The resulting method recovers globally linear solutions and shows optimal L2-norm and H1-norm convergence.
Advances in the Approximation Theory for Functional Reconstructions Using GMLS and Applications to Meshless Discretization of Differential Equations
Abstract not provided.
Advances in the Approximation Theory for Generalized Moving Least Squares
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Advances in the Approximation Theory of Generalized Moving Least Squares
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An Algebraic Multigrid Method for Compatible Least-Squares Formulations of Div-Curl Equations
Abstract not provided.
An explicit partitioned elastodynamics method based on Lagrange Multipliers
Abstract not provided.
An Optimization-Based Globally Flux-Conserving Coupling of Problems with Spatially Non-Coincident Interface Discretizations
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An overview of magneto-inertial fusion on the Z Machine at Sandia National Laboratories
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Arctic Climate Systems Analysis
This study began with a challenge from program area managers at Sandia National Laboratories to technical staff in the energy, climate, and infrastructure security areas: apply a systems-level perspective to existing science and technology program areas in order to determine technology gaps, identify new technical capabilities at Sandia that could be applied to these areas, and identify opportunities for innovation. The Arctic was selected as one of these areas for systems level analyses, and this report documents the results. In this study, an emphasis was placed on the arctic atmosphere since Sandia has been active in atmospheric research in the Arctic since 1997. This study begins with a discussion of the challenges and benefits of analyzing the Arctic as a system. It goes on to discuss current and future needs of the defense, scientific, energy, and intelligence communities for more comprehensive data products related to the Arctic; assess the current state of atmospheric measurement resources available for the Arctic; and explain how the capabilities at Sandia National Laboratories can be used to address the identified technological, data, and modeling needs of the defense, scientific, energy, and intelligence communities for Arctic support.
Arctic Sea Ice Internal Variability and Trends in E3SM
Abstract not provided.
Arctic sea ice mechanics with an elastic-decohesive constitutive model
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Arctic sea ice modeling with the material-point method
Arctic sea ice plays an important role in global climate by reflecting solar radiation and insulating the ocean from the atmosphere. Due to feedback effects, the Arctic sea ice cover is changing rapidly. To accurately model this change, high-resolution calculations must incorporate: (1) annual cycle of growth and melt due to radiative forcing; (2) mechanical deformation due to surface winds, ocean currents and Coriolis forces; and (3) localized effects of leads and ridges. We have demonstrated a new mathematical algorithm for solving the sea ice governing equations using the material-point method with an elastic-decohesive constitutive model. An initial comparison with the LANL CICE code indicates that the ice edge is sharper using Materials-Point Method (MPM), but that many of the overall features are similar.
Arctic Tipping Points Triggering Global Change
Abstract not provided.
Arctic Tipping Points Triggering Global Change
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ARCTIC TIPPING POINTS TRIGGERING GLOBAL CHANGE
Abstract not provided.
Bridging the gap: from algorithm development to mission impact a partitioned elastodynamics example
Abstract not provided.
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