34 citations · 34 across the 3 of their papers we have counts for
6 papers
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…
Linearly Stabilized Schemes for the Time Integration of Stiff Nonlinear PDEs
Kevin Chow, Steven J. Ruuth
In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by…
Boundary treatment of high order Runge-Kutta methods for hyperbolic conservation laws
Weifeng Zhao, Juntao Huang, Steven J. Ruuth
In \cite{ZH2019}, we developed a boundary treatment method for implicit-explicit (IMEX) Runge-Kutta (RK) methods for solving hyperbolic systems with source terms. Since IMEX RK met…
PDEs on moving surfaces via the closest point method and a modified grid based particle method
A. Petras, S. J. Ruuth
Partial differential equations (PDEs) on surfaces arise in a wide range of applications. The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is…
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…