6 papers · 1 filter
Moving Mesh Simulations of Pitting Corrosion
Abu Naser Sarker, Ronald D. Haynes, Michael Robertson
Damages due to pitting corrosion of metals cost industry billions of dollars per year and can put human lives at risk. The design and implementation of an adaptive moving mesh meth…
A positivity-preserving unigrid method for elliptic PDEs
Ronald D. Haynes, Scott MacLachlan, Dawei Wang
While constraints arise naturally in many physical models, their treatment in mathematical and numerical models varies widely, depending on the nature of the constraint and the ava…
A Convergence Analysis of the Parallel Schwarz Solution of the Continuous Closest Point Method
Alireza Yazdani, Ronald D. Haynes, Steven J. Ruuth
The discretization of surface intrinsic PDEs has challenges that one might not face in the flat space. The closest point method (CPM) is an embedding method that represents surface…
Domain Decomposition Parabolic Monge-Ampère Approach for Fast Generation of Adaptive Moving Meshes
Mohamed Sulman, Truong Nguyen, Ronald Haynes +1
A fast method is presented for adaptive moving mesh generation in multi-dimensions using a domain decomposition parabolic Monge-Ampère approach. The domain decomposition procedure…
Schwarz solvers and preconditioners for the closest point method
Ian May, Ronald Haynes, Steven Ruuth
The discretization of surface intrinsic elliptic partial differential equations (PDEs) poses interesting challenges not seen in flat space. The discretization of these PDEs typical…
Domain Decomposition for the Closest Point Method
Ian May, Ronald D. Haynes, Steven J. Ruuth
The discretization of elliptic PDEs leads to large coupled systems of equations. Domain decomposition methods (DDMs) are one approach to the solution of these systems, and can spli…