Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
Adaptive local overlapping grid methods for parabolic systems in two space dimensions
Journal of Computational Physics
A scheme for conservative interpolation on overlapping grids
SIAM Journal on Scientific Computing
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
A fully conservative interface algorithm for overlapped grids
Journal of Computational Physics
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
An Algorithm for Assembling Overlapping Grid Systems
SIAM Journal on Scientific Computing
Hole-Cutting for Three-Dimensional Overlapping Grids
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Parallel unsteady turbo-pump simulations for liquid rocket engines
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Overture: An Object-Oriented Framework for Solving Partial Differential Equations
ISCOPE '97 Proceedings of the Scientific Computing in Object-Oriented Parallel Environments
On Coordinate Transformations for Summation-by-Parts Operators
Journal of Scientific Computing
An adaptive numerical scheme for high-speed reactive flow on overlapping grids
Journal of Computational Physics
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
Well-Posed Boundary Conditions for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
A stable hybrid method for hyperbolic problems
Journal of Computational Physics
High-order compact finite-difference methods on general overset grids
Journal of Computational Physics
Journal of Scientific Computing
High order finite difference methods for wave propagation in discontinuous media
Journal of Computational Physics
Journal of Computational Physics
Computations of a Maneuvering Unmanned Combat Air Vehicle Using a High-Order Overset Grid Method
HPCMP-UGC '07 Proceedings of the 2007 DoD High Performance Computing Modernization Program Users Group Conference
A stable high-order finite difference scheme for the compressible Navier-Stokes equations
Journal of Computational Physics
Stable and accurate wave-propagation in discontinuous media
Journal of Computational Physics
Journal of Computational Physics
A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
SIAM Journal on Scientific Computing
A generalized framework for nodal first derivative summation-by-parts operators
Journal of Computational Physics
Hi-index | 31.45 |
Overlapping domain decomposition methods, otherwise known as overset grid or chimera methods, are useful for simplifying the discretization of partial differential equations in or around complex geometries. Though in wide use, such methods are prone to numerical instability unless numerical diffusion or some other form of regularization is used, especially for higher-order methods. To address this shortcoming, high-order, provably energy stable, overlapping domain decomposition methods are derived for hyperbolic initial boundary value problems. The overlap is treated by splitting the domain into pieces and using generalized summation-by-parts derivative operators and polynomial interpolation. New implicit and explicit operators are derived that do not require regularization for stability in the linear limit. Applications to linear and nonlinear problems in one and two dimensions are presented, where it is found the explicit operators are preferred to the implicit ones.