GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Adaptive remeshing for compressible flow computations
Journal of Computational Physics
An O(n2logn) time algorithm for the minmax angle triangulation
SIAM Journal on Scientific and Statistical Computing
Long and thin triangles can be good for linear interpolation
SIAM Journal on Numerical Analysis
Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems
SIAM Journal on Matrix Analysis and Applications
Delaunay mesh generation governed by metric specifications. Part I algorithms
Finite Elements in Analysis and Design
Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems
SIAM Journal on Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
High-order discontinuous Galerkin methods using an hp-multigrid approach
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
On Mesh Geometry and Stiffness Matrix Conditioning for General Finite Element Spaces
SIAM Journal on Numerical Analysis
Hi-index | 31.45 |
The impact of triangle shapes, including angle sizes and aspect ratios, on accuracy and stiffness is investigated for simulations of highly anisotropic problems. The results indicate that for high-order discretizations, large angles do not have an adverse impact on solution accuracy. However, a correct aspect ratio is critical for accuracy for both linear and high-order discretizations. Large angles are also found to be not problematic for the conditioning of the linear systems arising from the discretizations. Further, when choosing preconditioning strategies, coupling strengths among elements rather than element angle sizes should be taken into account. With an appropriate preconditioner, solutions on meshes with and without large angles can be achieved within a comparable time.