A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Journal of Computational Physics
Adaptive blocks: a high performance data structure
SC '97 Proceedings of the 1997 ACM/IEEE conference on Supercomputing
Interface conditions for wave propagation through mesh refinement boundaries
Journal of Computational Physics
Accurate and stable grid interfaces for finite volume methods
Applied Numerical Mathematics
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
On the order of accuracy for difference approximations of initial-boundary value problems
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
A stable and high-order accurate conjugate heat transfer problem
Journal of Computational Physics
Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators
Journal of Scientific Computing
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
SIAM Journal on Scientific Computing
High Order Stable Finite Difference Methods for the Schrödinger Equation
Journal of Scientific Computing
High-fidelity numerical solution of the time-dependent Dirac equation
Journal of Computational Physics
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In this paper we extend the results from our earlier work on stable boundary closures for the Schrödinger equation using the summation-by-parts-simultaneous approximation term (SBP---SAT) method to include stability and accuracy at nonconforming grid interfaces. Stability at the grid interface is shown by the energy method, and the estimates are generalized to multiple dimensions. The accuracy of the grid interface coupling is investigated using normal mode analysis for operators of 2nd and 4th order formal interior accuracy. We show that full accuracy is retained for the 2nd and 4th order operators. The accuracy results are extended to 6th and 8th order operators by numerical simulations, in which case two orders of accuracy is gained with respect to the lower order approximation close to the interface.