Numerical Solution of Contact Problems using Level Set Methods on Voxel Discretizations

Numerical Solution of Sawada-Kotera equation by using Iterative Methods

Efficient numerical methods for the large-scale, parallel solution of elastoplastic contact problems

Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in ea...

Parametric Level Set Methods for Inverse Problems

In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set parameters. We show that using the appropriate form of parameterizing the level set function results a significantly lower dimensional problem, which bypass...

On multiple level-set regularization methods for inverse problems

We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional Gα based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikh...

Stability Conditions for the Numerical Solution of Convection-Dominated Problems with Skew-Symmetric Discretizations

This paper presents original and close to optimal stability conditions linking the time step and the space step, stronger than the CFL criterion, δt ≤ Cδxα with α = 2r 2r−1 , r an integer for some numerical schemes we produce when solving convection-dominated problems. We test this condition numerically and prove that it applies to nonlinear equations under smoothness assumptions.