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- Finite element method (2)
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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Variational Theory Of Balance Systems, Serge Preston
Variational Theory Of Balance Systems, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constitutive relation C of a balance system is realized as a mapping between a (partial) k-jet bundle and the extended dual bundle similar to the Legendre mapping of the Lagrangian Field Theory. Invariant (variational) form of the balance system corresponding to a constitutive relation C is studied. Special cases of balance systems -Lagrangian systems …
Large-Scale Assembly Of Periodic Nanostructures With Metastable Square Lattices, Chih-Hung Sun, Wei-Lun Min, Nicholas C. Linn, Peng Jiang, Bin Jiang
Large-Scale Assembly Of Periodic Nanostructures With Metastable Square Lattices, Chih-Hung Sun, Wei-Lun Min, Nicholas C. Linn, Peng Jiang, Bin Jiang
Mathematics and Statistics Faculty Publications and Presentations
This article reports a simple and scalable spin-coating technique for assembling non-close-packed colloidal crystals with metastable square lattices over wafer-scale areas. The authors observe the alternate formation of hexagonal and square diffraction patterns when the thickness of the colloidal crystals is gradually reduced during spin coating. No prepatterned templates are needed to induce the formation of the resulting metastable crystals with square arrangement. This bottom-up technology also enables the large-scale production of a variety of squarely ordered nanostructures that are consistent with the industry-standard rectilinear coordinate system for simplified addressing and circuit interconnection. Broadband moth-eye antireflection gratings with square lattices …
Unified Hybridization Of Discontinuous Galerkin, Mixed, And Continuous Galerkin Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan, Raytcho Lazarov
Unified Hybridization Of Discontinuous Galerkin, Mixed, And Continuous Galerkin Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan, Raytcho Lazarov
Mathematics and Statistics Faculty Publications and Presentations
We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element methods including hybridized mixed, continu- ous Galerkin, non-conforming and a new, wide class of hybridizable discontinuous Galerkin methods. The distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements. Since the associated matrix is sparse, symmetric and positive definite, these methods can be efficiently implemented. Moreover, the …
The Derivation Of Hybridizable Discontinuous Galerkin Methods For Stokes Flow, Bernardo Cockburn, Jay Gopalakrishnan
The Derivation Of Hybridizable Discontinuous Galerkin Methods For Stokes Flow, Bernardo Cockburn, Jay Gopalakrishnan
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we introduce a new class of discontinuous Galerkin methods for the Stokes equations. The main feature of these methods is that they can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to certain approximations on the element boundaries. We present four ways of hybridizing the methods, which differ by the choice of the globally coupled unknowns. Classical methods for the Stokes equations can be thought of as limiting cases of these new methods.
A New Elasticity Element Made For Enforcing Weak Stress Symmetry, Bernardo Cockburn, Jay Gopalakrishnan, Johnny Guzmán
A New Elasticity Element Made For Enforcing Weak Stress Symmetry, Bernardo Cockburn, Jay Gopalakrishnan, Johnny Guzmán
Mathematics and Statistics Faculty Publications and Presentations
We introduce a new mixed method for linear elasticity. The novelty is a simplicial element for the approximate stress. For every positive integer k, the row-wise divergence of the element space spans the set of polynomials of total degree k. The degrees of freedom are suited to achieve continuity of the normal stresses. What makes the element distinctive is that its dimension is the smallest required for enforcing a weak symmetry condition on the approximate stress. This is achieved using certain "bubble matrices", which are special divergence-free matrix-valued polynomials. We prove that the approximation error is of order k + …
Polynomial Extension Operators. Part Ii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl
Polynomial Extension Operators. Part Ii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl
Mathematics and Statistics Faculty Publications and Presentations
Consider the tangential trace of a vector polynomial on the surface of a tetrahedron. We construct an extension operator that extends such a trace function into a polynomial on the tetrahedron. This operator can be continuously extended to the trace space of H(curl ). Furthermore, it satisfies a commutativity property with an extension operator we constructed in Part I of this series. Such extensions are a fundamental ingredient of high order finite element analysis.