Dispersion-relation-preserving finite difference schemes for computational acoustics
Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Summation by parts, projections, and stability. I
Mathematics of Computation
Summation by parts, projections, and stability. II
Mathematics of Computation
Hybrid Gauss-Trapezoidal Quadrature Rules
SIAM Journal on Scientific Computing
Spatial Finite Difference Approximations for Wave-Type Equations
SIAM Journal on Numerical Analysis
High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates
Journal of Computational Physics
Nodal high-order methods on unstructured grids
Journal of Computational Physics
On Coordinate Transformations for Summation-by-Parts Operators
Journal of Scientific Computing
A family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
Stable and Accurate Artificial Dissipation
Journal of Scientific Computing
Matlab Guide
High-order local absorbing conditions for the wave equation: Extensions and improvements
Journal of Computational Physics
Applied Numerical Mathematics
Grid stabilization of high-order one-sided differencing II: Second-order wave equations
Journal of Computational Physics
Hi-index | 31.46 |
We construct stable, maximal order boundary closures for high order central difference methods. The stability is achieved by adding a small number of additional subcell nodes near the boundaries at experimentally determined locations. We find that methods up through 8th order can be stabilized by the addition of a single node, up through 16th order by the addition of two nodes, and up through 22nd order with three extra nodes. We also consider the application of the technique to dispersion relation preserving methods, and we construct and test artificial dissipation operators.