Shuffling Cell Numbers Made LU-SGS 2.8× Slower — RCM Reordering and the Start Cell That Sets Sweep Direction
Shuffling cell numbers on a 576-cell grid pushed LU-SGS from 9 iterations to 25. RCM cuts bandwidth to 24, but the start corner still splits 9 from 21.
One Fewer Quadrature Point and the Solution Blew Up — DG's Integration Floor and the Taylor Basis
For DG-P2 the volume integrand has degree 3, so two Gauss points match three points at 5.989e-3. One point leaves L2 error near 11.7 and order 0.13.
Two Philosophies for Triangulating a Point Cloud — Bowyer–Watson and Advancing Front
Twelve points become 17 triangles. A sliced airfoil edge is not restored by the empty circumcircle; a pipe or the front has to take that edge back.
The Fake Extrema a Second-Order Reconstruction Invents on Unstructured Grids — Barth–Jespersen and Venkatakrishnan Limiters
A second-order face value on an unstructured cell can leave the neighbor range. Barth–Jespersen clips that slope; Venkatakrishnan rounds the clip with K.
When the Mesh Skews, the Laplacian Leaks — Non-Orthogonal Diffusion Correction
The face-area vector splits into an implicit piece and a deferred correction. Minimum correction hits ratio 1 at 45 degrees and stops contracting.
Saving Gradients on Unstructured Grids — Moving Least-Squares Approximation
With h=0.07, order 2 and 25 scattered points, the Taylor MLS derivative of sin(2πx) has RMSE 0.21, about 3% of the 2π amplitude.
Delaunay Triangulation — the Empty-Circumcircle Rule and Bowyer–Watson Insertion
N=60 and 8 hull points fix the triangle count at 2N-2-h=110. Four cocircular corners make the in-circle determinant zero, so either diagonal is legal.
[Paper Review] Beating the Storm Clock — Casulli–Walters (2000) Semi-Implicit Shallow Water on Unstructured Orthogonal Grids
At 28 m depth the explicit limit is 0.2 s. Keeping only the free-surface gradient implicit is what lets a five-minute step survive the estuary.