Computational Algorithms and Tools
- Robust Nonlinear Solvers and Nonlinear Preconditioning
- Multigrid and Multiresolution Solvers
- Computational Renormalization
- Mesh Transformation
- Mesh Adaptivity
- Discretizations and Solvers
- Fast Eikonal Solver based on this paper
Nonlinear Solvers and Preconditioning
Function Approximation and Machine Learning
DMPlex: Meshes and Discretizations
Graph Algorithms
Computational Logic
Applications
Aerospace
Biology
Physics
Geophysics
Big Ideas
Verifiable high performance computing
I am thinking of provably correct parallel poset algorithms, like mesh distribution. However, FLAME is already here in some sense, although they have not made any use of good logic tools like Coq.
Computing in the Kolmogorov Basis
What does a composed basis mean? Can we understand how to do the same things we do in linear algebra?
The Multilevel Generalization of Newton
Can a superlinear algebraic iteration be made to operator on only a subset of freqencies? Equivalently, does there exist a superlinear nonlinear smoother?