Compatible meshfree discretization
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Publications
GMLS-Nets: A machine learning framework for unstructured data
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Field reconstruction from Raviart-Thomas Nedelec and finite volume degrees-of-freedom using Generalized Moving Least Squares
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Improved Neural Network Training: Layer-Parallelism Least-squares and Initialization
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Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint
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GMLS-Nets: Scientific Machine Learning Methods for Unstructured Data
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Compatible meshfree discretization
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Physics informed machine learning at SNL
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Spatially compatible meshfree discretization through GMLS and graph theory
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Bulk-Interface-Flux-Recovery (Bulk-IFR) Method for Coupling the Atmosphere-Ocean Interface
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A spatially adaptive high-order meshless method for fluid–structure interactions
Computer Methods in Applied Mechanics and Engineering
We present a scheme implementing an a posteriori refinement strategy in the context of a high-order meshless method for problems involving point singularities and fluid–solid interfaces. The generalized moving least squares (GMLS) discretization used in this work has been previously demonstrated to provide high-order compatible discretization of the Stokes and Darcy problems, offering a high-fidelity simulation tool for problems with moving boundaries. The meshless nature of the discretization is particularly attractive for adaptive h-refinement, especially when resolving the near-field aspects of variables and point singularities governing lubrication effects in fluid–structure interactions. We demonstrate that the resulting spatially adaptive GMLS method is able to achieve optimal convergence in the presence of singularities for both the div-grad and Stokes problems. Further, we present a series of simulations for flows of colloid suspensions, in which the refinement strategy efficiently achieved highly accurate solutions, particularly for colloids with complex geometries.
Compatible Particle Discretizations. Final LDRD Report
This report summarizes the work performed under a three year LDRD project aiming to develop mathematical and software foundations for compatible meshfree and particle discretizations. We review major technical accomplishments and project metrics such as publications, conference and colloquia presentations and organization of special sessions and minisimposia. The report concludes with a brief summary of ongoing projects and collaborations that utilize the products of this work.
Advances in meshfree methods: From SPH to compatible meshless discretization
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Mimetic meshfree methods or how to be compatible without a mesh
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The amazing powers of Generalized Moving Least-Squares
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Operator Regression for PDE Discovery
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Operator Regression for PDE Discovery
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Non-iterative partitioned methods based on monolithic formulations of the coupled problem
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Generalized Moving Least Squares: Approximation Theory and Applications
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The Compadre Toolkit for Native Degrees-of-Freedom
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Mimetic Conservation Principles for Meshfree Approximation
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Field reconstruction from native degrees-of-freedom using the Compadre Toolkit
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Advances in the Approximation Theory of Generalized Moving Least Squares
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Lagrange-Multiplier-Based Partitioned Method for Ocean-Atmosphere Coupling
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Mesh-hardened finite element analysis through a Generalized Moving Least-Squares approximation of variational problems
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Results 51–75 of 100