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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Modeling The Defects That Exists In Crystalline Structures, Kiet A. Tran
Modeling The Defects That Exists In Crystalline Structures, Kiet A. Tran
REU Final Reports
This paper focuses on modeling defects in crystalline materials in one-dimension using field dislocation mechanics (FDM). Predicting plastic deformation in crystalline materials on a microscopic scale allows for the understanding of the mechanical behavior of micron-sized components. Following Das et al (2013), a one dimensional reduction of the FDM model is implemented using Discontinuous Galerkin method and the results are compared with those obtained from the finite difference implementation. Test cases with different initial conditions on the position and distribution of screw dislocations are considered.
Discretization Of The Hellinger-Reissner Variational Form Of Linear Elasticity Equations, Kevin A. Sweet
Discretization Of The Hellinger-Reissner Variational Form Of Linear Elasticity Equations, Kevin A. Sweet
REU Final Reports
This paper addresses the derivation of the Hellinger-Reissner Variational Form from the strong form of a system of linear elasticity equations that are used in relation to geological phenomena. The problem is discretized using finite element discretization. This allowed the creation of a program that was used to run tests on various domains. The resultant displacement vectors for tested domains are shown at the end of the paper.
Trefftz Finite Elements On Curvilinear Polygons, Akash Anand, Jeffrey S. Ovall, Samuel E. Reynolds, Steffen Weisser
Trefftz Finite Elements On Curvilinear Polygons, Akash Anand, Jeffrey S. Ovall, Samuel E. Reynolds, Steffen Weisser
Mathematics and Statistics Faculty Publications and Presentations
We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in the formation of local stiffness matrices. To define our local finite element spaces in the presence of curved edges, we must also properly define what it means for a function defined on a curved edge to be "polynomial" of a given degree on that edge. We consider two natural choices, before settling on the one that yields the inclusion of complete polynomial spaces in our local …
Effects Of Wavelength Variation On Localized Photoemission In Triangular Gold Antennas, Christopher M. Scheffler, Robert Campbell Word, Rolf Könenkamp
Effects Of Wavelength Variation On Localized Photoemission In Triangular Gold Antennas, Christopher M. Scheffler, Robert Campbell Word, Rolf Könenkamp
Student Research Symposium
Exposing metal-dielectric structures to light can result in surface plasmon excitation and propagation along the transition interface, creating a surface plasmon polariton (SPP) response. Photoemission electron microscopy (PEEM) has been used to image nanometer scale plasmonic responses in micron-sized plasmonic devices. With PEEM, optical responses can be characterized in detail, aiding in the development of new types of plasmonic structures and their applications. In thin, triangular gold platelets SPPs can be excited and concentrated within specific regions of the material. In this regard, the platelets act as receiver antennas by converting the incident light into localized excitations in specific regions …
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Quanah Parker
Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Quanah Parker
Mathematics and Statistics Faculty Publications and Presentations
A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of …
Spectral Discretization Errors In Filtered Subspace Iteration, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall
Spectral Discretization Errors In Filtered Subspace Iteration, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall
Mathematics and Statistics Faculty Publications and Presentations
We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space. The algorithm is motivated by a quadrature approximation of an operator-valued contour integral of the resolvent. Resolvents on infinite dimensional spaces are discretized in computable finite-dimensional spaces before the algorithm is applied. This study focuses on how such discretizations result in errors in the eigenspace approximations computed by the algorithm. The computed eigenspace is then used to obtain approximations of the eigenvalue cluster. Bounds for the Hausdorff distance between the computed and exact eigenvalue clusters …