Generalized Moving Least Squares: Approximation Theory and Applications
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Publications
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Jump to search filtersThe Compadre Toolkit for Native Degrees-of-Freedom
Abstract not provided.
Non-iterative partitioned methods based on monolithic formulations of the coupled problem
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Mesh-hardened finite element analysis through a Generalized Moving Least-Squares approximation of variational problems
Abstract not provided.
Explicit Partitioned Methods based on Monolithic Formulations of the Coupled Problem
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Field reconstruction from native degrees-of-freedom using the Compadre Toolkit
Abstract not provided.
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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Mimetic Conservation Principles for Meshfree Approximation
Abstract not provided.
Advances in the Approximation Theory for Generalized Moving Least Squares
Abstract not provided.
Mesh-hardened finite element analysis through a Generalized Moving Least-Squares approximation of variational problems
Abstract not provided.
Optimization-based property-preserving methods
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Compatible meshless methods for DPEs
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The Compadre Toolkit
Abstract not provided.
Explicit Partitioned Methods for Interface Coupling
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Advances in the Approximation Theory for Functional Reconstructions Using GMLS and Applications to Meshless Discretization of Differential Equations
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Discretely conservative meshfree schemes for conservation laws
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Explicit Partitioned Methods for Interface Coupling
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A VIRTUAL CONTROL MESH-FREE COUPLING METHOD FOR NON-COINCIDENT INTERFACES
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Optimization-based property preserving finite element methods for transport equations
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Formulation and computation of dynamic, interface-compatible Whitney complexes in three dimensions
Journal of Computational Physics
A discrete De Rham complex enables compatible, structure-preserving discretizations for a broad range of partial differential equations problems. Such discretizations can correctly reproduce the physics of interface problems, provided the grid conforms to the interface. However, large deformations, complex geometries, and evolving interfaces makes generation of such grids difficult. We develop and demonstrate two formally equivalent approaches that, for a given background mesh, dynamically construct an interface-conforming discrete De Rham complex. Both approaches start by dividing cut elements into interface-conforming subelements but differ in how they build the finite element basis on these subelements. The first approach discards the existing non-conforming basis of the parent element and replaces it by a dynamic set of degrees of freedom of the same kind. The second approach defines the interface-conforming degrees of freedom on the subelements as superpositions of the basis functions of the parent element. These approaches generalize the Conformal Decomposition Finite Element Method (CDFEM) and the extended finite element method with algebraic constraints (XFEM-AC), respectively, across the De Rham complex.
Mesh-tying via multiple-control PDE-constrained optimization and GMLS function reconstruction
Abstract not provided.
Towards a scalable multifidelity simulation approach for electrokinetic problems at the mesoscale
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
In this work we present a computational capability featuring a hierarchy of models with different fidelities for the solution of electrokinetics problems at the micro-/nano-scale. A multifidelity approach allows the selection of the most appropriate model, in terms of accuracy and computational cost, for the particular application at hand. We demonstrate the proposed multifidelity approach by studying the mobility of a colloid in a micro-channel as a function of the colloid charge and of the size of the ions dissolved in the fluid.
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.
Improving the Material-Point Method with GMLS
Abstract not provided.
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