Simple adaptive grids for 1-d initial value problems
Journal of Computational Physics
Directional control in grid generation
Journal of Computational Physics
Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
An adaptive grid with directional control
Journal of Computational Physics
Moving mesh partial differential equations (MMPDES) based on the equidistribution principle
SIAM Journal on Numerical Analysis
Adaptive grid radiation hydrodynamics with TITAN
13th annual international conference of the center for nonlinear studies on Nonlinear science
Moving mesh methods with upwinding schemes for time-dependent PDEs
Journal of Computational Physics
Multiblock multigrid grid generation algorithms: overcoming multigrid anisotropy
Applied Mathematics and Computation
A multiblock multigrid grid generation method for complex simulations
IMACS Selected papers from the IMACS European conference on Simulation
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
A multilevel iterative field solver for implicit, kinetic, plasma simulation
Journal of Computational Physics
An adaptive finite element method for magnetohydrodynamics
Journal of Computational Physics
A multgrid Newton-Krylov method for multimaterial equilibrium radiation diffusion
Journal of Computational Physics
A Multigrid Preconditioned Newton--Krylov Method
SIAM Journal on Scientific Computing
Full-FAS multigrid grid generation algorithms
Applied Numerical Mathematics - Special issue on numerical grid generation-technologies for advanced simulations
Variational mesh adaptation: isotropy and equidistribution
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
Cost-effectiveness of fully implicit moving mesh adaptation: a practical investigation in 1D
Journal of Computational Physics
Efficient nonlinear solvers for Laplace-Beltrami smoothing of three-dimensional unstructured grids
Computers & Mathematics with Applications
Journal of Computational Physics
Nested Cartesian grid method in incompressible viscous fluid flow
Journal of Computational Physics
Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
Journal of Computational Physics
Hi-index | 31.47 |
We propose an efficient, fully implicit, nonlinear solver for the Beltrami grid generation equation. The Beltrami equation is obtained using Harmonic map theory, and therefore the existence and uniqueness of a solution is guaranteed. The nonlinear solver strategy is based on Newton-Krylov methods, preconditioned here with a multigrid-based method for scalability. Numerical experiments performed for both grid adaptation and grid alignment are presented and demonstrate optimal scaling under grid refinement. We therefore conclude that such a fully nonlinear approach is indeed feasible and efficient.