8 citations · 8 across the 10 of their papers we have counts for
13 papers
Adaptive refinement for eigenvalue problems based on an associated source problem
Stefano Giani, Jeffrey Ovall, Gabriel Pinochet-Soto
We introduce an adaptive finite element scheme for the efficient approximation of a (large) collection of eigenpairs of selfadjoint elliptic operators in which the adaptive refinem…
A Canonical Gauge for Computing of Eigenpairs of the Magnetic Schrödinger Operator
Jeffrey S. Ovall, Li Zhu
We consider the eigenvalue problem for the magnetic Schrödinger operator and take advantage of a property called gauge invariance to transform the given problem into an equivalent…
Detecting eigenvectors of an operator that are near a specified subspace
David Darrow, Jeffrey S. Ovall
In modeling quantum systems or wave phenomena, one is often interested in identifying eigenstates that approximately carry a specified property; scattering states approximately ali…
On localization of eigenfunctions of the magnetic Laplacian
Jeffrey S. Ovall, Hadrian Quan, Robyn Reid +1
Let and consider the magnetic Laplace operator given by , where , subject to Dirichlet…
Evaluation of Inner Products of Implicitly-defined Finite Element Functions on Multiply Connected Planar Mesh Cells
Jeffrey S. Ovall, Samuel E. Reynolds
Recent advancements in finite element methods allows for the implementation of mesh cells with curved edges. In the present work, we develop the tools necessary to employ multiply…
Quadrature for Implicitly-defined Finite Element Functions on Curvilinear Polygons
Jeffrey Ovall, Samuel Reynolds
-conforming Galerkin methods on polygonal meshes such as VEM, BEM-FEM and Trefftz-FEM employ local finite element functions that are implicitly defined as solutions of Poisson…
An algorithm for identifying eigenvectors exhibiting strong spatial localization
Jeffrey Ovall, Robyn Reid
We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a target region and a tolerance…
A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques
Stefano Giani, Luka Grubisic, Harri Hakula +1
We propose an a posteriori error estimator for high-order - or -finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for est…
Trefftz Finite Elements on Curvilinear Polygons
Akash Anand, Jeffrey S. Ovall, Samuel Reynolds +1
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 t…
Analysis of FEAST spectral approximations using the DPG discretization
Jay Gopalakrishnan, Luka Grubišić, Jeffrey Ovall +1
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…
Spectral discretization errors in filtered subspace iteration
Jay Gopalakrishnan, Luka Grubišić, Jeffrey Ovall
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…
A Nyström-based finite element method on polygonal elements
Akash Anand, Jeffrey S. Ovall, Steffen Weisser
We consider families of finite elements on polygonal meshes, that are defined implicitly on each mesh cell as solutions of local Poisson problems with polynomial data. Functions in…
Reliable a-posteriori error estimators for -adaptive finite element approximations of eigenvalue/eigenvector problems
Stefano Giani, Luka Grubišić, Jeffrey Ovall
We present reliable a-posteriori error estimates for -adaptive finite element approximations of eigenvalue/eigenvector problems. Starting from our earlier work on adaptive…