90 citations · 179 across the 18 of their papers we have counts for
27 papers
Convergence of Finite Element Methods for Ricci Flow
Guangwei Gao, Evan S. Gawlik, Buyang Li
The convergence of a finite element discretization for the two-dimensional Ricci flow is proved. In this method, the Ricci flow on a two-dimensional surface is formulated into solu…
On the Curvature of Regge Metrics
Evan S. Gawlik, Jack McKee
We use moving frame techniques to derive a notion of curvature for a class of piecewise-smooth Riemannian metrics called Regge metrics, showing that it is a measure that simultaneo…
Structure-preserving and thermodynamically consistent finite element discretization for visco-resistive MHD with thermoelectric effect
Evan S. Gawlik, François Gay-Balmaz, Bastien Manach-Pérennou
We present a structure-preserving and thermodynamically consistent numerical scheme for classical magnetohydrodynamics, incorporating viscosity, magnetic resistivity, heat transfer…
Intrinsic Finite Element Error Analysis on Manifolds with Regge Metrics, with Application to Calculating Connection Forms
Evan S. Gawlik, Jack McKee
We present some aspects of the theory of finite element exterior calculus as applied to partial differential equations on manifolds, especially manifolds endowed with an approximat…
Finite element approximation of the Einstein tensor
Evan S. Gawlik, Michael Neunteufel
We construct and analyze finite element approximations of the Einstein tensor in dimension . We focus on the setting where a smooth Riemannian metric tensor on a polyh…
Finite element approximation of scalar curvature in arbitrary dimension
Evan S. Gawlik, Michael Neunteufel
We analyze finite element discretizations of scalar curvature in dimension . Our analysis focuses on piecewise polynomial interpolants of a smooth Riemannian metric on…
Variational and thermodynamically consistent finite element discretization for heat conducting viscous fluids
Evan S. Gawlik, François Gay-Balmaz
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a str…
Finite element approximation of the Levi-Civita connection and its curvature in two dimensions
Yakov Berchenko-Kogan, Evan S. Gawlik
We construct finite element approximations of the Levi-Civita connection and its curvature on triangulations of oriented two-dimensional manifolds. Our construction relies on the R…
A structure-preserving finite element method for compressible ideal and resistive MHD
Evan S. Gawlik, François Gay-Balmaz
We construct a structure-preserving finite element method and time-stepping scheme for compressible barotropic magnetohydrodynamics (MHD) both in the ideal and resistive cases, and…
A Finite Element Method for MHD that Preserves Energy, Cross-Helicity, Magnetic Helicity, Incompressibility, and
Evan S. Gawlik, François Gay-Balmaz
We construct a structure-preserving finite element method and time-stepping scheme for inhomogeneous, incompressible magnetohydrodynamics (MHD). The method preserves energy, cross-…
Iterations for the Unitary Sign Decomposition and the Unitary Eigendecomposition
Evan S. Gawlik
We construct fast, structure-preserving iterations for computing the sign decomposition of a unitary matrix with no eigenvalues equal to . This decomposition factorizes…
Zolotarev's fifth and sixth problems
Evan S. Gawlik, Yuji Nakatsukasa
In an influential 1877 paper, Zolotarev asked and answered four questions about polynomial and rational approximation. We ask and answer two questions: what are the best rational a…
Local Finite Element Approximation of Sobolev Differential Forms
Evan S. Gawlik, Michael J. Holst, Martin W. Licht
We address fundamental aspects in the approximation theory of vector-valued finite element methods, using finite element exterior calculus as a unifying framework. We generalize th…
A Conservative Finite Element Method for the Incompressible Euler Equations with Variable Density
Evan S. Gawlik, François Gay-Balmaz
We construct a finite element discretization and time-stepping scheme for the incompressible Euler equations with variable density that exactly preserves total mass, total squared…
A Variational Finite Element Discretization of Compressible Flow
Evan S. Gawlik, François Gay-Balmaz
We present a finite element variational integrator for compressible flows. The numerical scheme is derived by discretizing, in a structure preserving way, the Lie group formulation…
Approximating the pth Root by Composite Rational Functions
Evan S. Gawlik, Yuji Nakatsukasa
A landmark result from rational approximation theory states that on can be approximated by a type- rational function with root-exponential accuracy. Motiva…
High-Order Approximation of Gaussian Curvature with Regge Finite Elements
Evan S. Gawlik
A widely used approximation of the Gaussian curvature on a triangulated surface is the angle defect, which measures the deviation between and the sum of the angles between nei…
Rational Minimax Iterations for Computing the Matrix th Root
Evan S. Gawlik
In [E. S. Gawlik, Zolotarev iterations for the matrix square root, arXiv preprint 1804.11000, (2018)], a family of iterations for computing the matrix square root was constructed b…
Zolotarev Iterations for the Matrix Square Root
Evan S. Gawlik
We construct a family of iterations for computing the principal square root of a square matrix using Zolotarev's rational minimax approximants of the square root function. We s…
A Backward Stable Algorithm for Computing the CS Decomposition via the Polar Decomposition
Evan S. Gawlik, Yuji Nakatsukasa, Brian D. Sutton
We introduce a backward stable algorithm for computing the CS decomposition of a partitioned matrix with orthonormal columns, or a rank-deficient partial isometry. Th…
High-Order Retractions on Matrix Manifolds using Projected Polynomials
Evan S. Gawlik, Melvin Leok
We derive a family of high-order, structure-preserving approximations of the Riemannian exponential map on several matrix manifolds, including the group of unitary matrices, the Gr…
Embedding-Based Interpolation on the Special Orthogonal Group
Evan S. Gawlik, Melvin Leok
We study schemes for interpolating functions that take values in the special orthogonal group . Our focus is on interpolation schemes obtained by embedding in a line…
Computing the Fréchet Derivative of the Polar Decomposition
Evan S. Gawlik, Melvin Leok
We derive iterative methods for computing the Fréchet derivative of the map which sends a full-rank matrix to the factor in its polar decomposition , where has or…
Interpolation on Symmetric Spaces via the Generalized Polar Decomposition
Evan Gawlik, Melvin Leok
We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is…