A novel phase field model for Willmore flow is proposed based on a nested variational time discretization. Thereby, the mean curvature in the Willmore functional is replaced by an approximate speed of mean curvature motion, which is computed via a fully implicit variational model for time discrete mean curvature motion. The time discretization of Willmore flow is then performed in a nested fash...

In existing anisotropic diffusion-based semi-supervised learning approaches, anisotropic graph Laplacian is estimated based on (potentially noisy) function evaluations. We propose to regularize the graph Laplacian estimates. We develop a framework that regularizes the Laplace-Beltrami operators on Riemannian manifolds, and discretize it to a regularizer on diffusivity operators on graphs. Isotr...

of a Delay-Di erential Equation Tom a s Gedeon1 Department of Mathematical Sciences, Montana State University, Bozeman,MT 59717 [email protected] Gwendolen Hines2 Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588 [email protected] In this paper, we consider a discrete delay problem with negative feedback _ x(t) = f(x(t); x(t 1)) along with a ce...

We consider geometric biomembranes governed by an L-gradient flow for bending energy subject to area and volume constraints (Helfrich model). We give a concise derivation of a novel vector formulation, based on shape differential calculus, and corresponding discretization via parametric FEM using quadratic isoparametric elements and a semi-implicit Euler method. We document the performance of t...

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, meteorology, electromagnetics, semi-conductor device simulation, models of biological processes and many other engineering areas governed by conservative systems that can be writt...

A novel phase field model for Willmore flow is proposed based on a nested variational time discretization. Thereby, the mean curvature in the Willmore functional is replaced by an approximate speed of mean curvature motion, which is computed via a fully implicit variational model for time discrete mean curvature motion. The time discretization of Willmore flow is then performed in a nested fash...

The Immersed Boundary method is one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to require small time steps to maintain stability when solved with an explicit method. Many implicit or approximately implicit methods have been proposed in the literature to remove this severe time step stability con...

Abstract We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of semi-linear stochastic differential equations (SDEs) where both the drift diffusion are not globally Lipschitz continuous. Numerical instability may arise either from stiffness linear operator or perturbation nonlinear under discretization, both. Typical applications space discretization...

A new method is developed to solve the condensation equation as it relates to air quality models using both semi-Lagrangian and Lagrangian  uxes to increase resolution and perform accurately under stringent conditions that occur in the atmosphere. The new method, partitioned  ux integrated semi-Lagrangian method (PFISLM), can be used with lower-order interpolators and produces highly accurate...