david/home
Expository notes
A curious upwind implicit scheme for advection
An upwind+RK scheme with stationary unit CFL condition
Chebyshev polynomial of a matrix
Notes on research ideas
Stability optimization of linear multistep methods
A simple proof of the Jeltsch-Nevanlinna disk theorem by means of the CFL condition (A longer version appears on my blog, here)
Absolute stability, disks, and the CFL Theorem
Implicit RK methods with many stages and well-conditioned eigenvectors
Strong stability preservation
Arbitrary order SSP linear multistep methods
More absolute monotonicity conjectures
Reformulation of the 2S conjecture in canonical Shu-Osher form
A formula for the numerator of the stability function for SDIRKs
A heuristic method for splitting RK methods into upwind and downwind parts
New downwind Runge-Kutta methods and some analysis
SSP linear multistep methods with variable step size
Step size strategies for SSP LMMs
Stegotons
See Nonlinear waves in heterogeneous media
Errata
A correction to the stability function formula (4.17)
Plans
Available projects for directed research or MS Thesis students
Some of these have details; others do not yet. For more information, ask me.
- Code generation for Riemann solvers on CPUs and GPUs
- Automated evaluation of hyperbolic PDE discretizations
- Practical Minimum-Storage Runge-Kutta Pairs
- Non-oscillatory Interpolation for Data that is Under-resolved or has Uncertain Smoothness
- Analysis of Scientific Collaboration and Citation Networks
- The Kukulkan Quetzal Chirp
- Smoothed fitted logically quadrilateral grids
- Analysis of extrapolation and deferred correction methods (claimed)
- Orthogonal conditions for high order Runge-Kutta methods
- Wave propagation methods in finite difference and finite element discretizations
- A High order well-balanced wave propagation scheme
