Scientific Computing
A formulation is a claim about mathematics; a program is a claim about a machine. These articles are about the second one — how a matrix is actually laid out in memory, why the same model can return two different numbers on two machines, what a compiler is permitted to do to an expression, and the discipline that makes a numerical result reproducible rather than merely repeatable.
6 articles
Bloom in linear light, and what sRGB averaging costs
Averaging black and white in sRGB gives code 128 where the physically correct answer is code 188, and every blur, downsample and bloom pays that error
A parallel for over one atomic counter
Splitting an uneven render into eight contiguous blocks reached 2.95x on eight threads. Handing rows out from one atomic counter reached 6.16x, on the same work
The consistent tangent: 7 iterations against 887
Newton converges quadratically only with the exact Jacobian. On one elastoplastic bar the correct tangent needs 7 iterations where the elastic one needs 887.
Sparse direct solvers: ordering, fill-in and the cost
The same matrix, factorised in two different orders, produces 498501 fill entries or none at all. Ordering is not a tuning parameter — it is most of the cost.
Floating point: why two runs of one model disagree
Floating-point addition is not associative. Summing the same thousand contributions in another order moves the answer by 360 units in the last place.
Gauss quadrature in finite elements: how many points
An n-point Gauss rule is exact to degree 2n-1, which decides everything. Under-integrate and the element develops modes that deform at no energy cost at all.
Terms defined
Related topics
Numerical Methods
The numerical machinery underneath engineering analysis: sparse direct solvers, Newton iteration, quadrature, conditioning and floating-point behaviour.
Demoscene
Demos written in C with no assets at all: every pixel and every audio sample computed at runtime, and the techniques that make that possible offline.
Geotechnical FEM
Finite element modelling for geotechnical problems: element families, plane-strain and axisymmetric idealisation, staged construction and solver behaviour.
Constitutive Models
Soil constitutive models: linear elasticity, Mohr-Coulomb, Hardening Soil and small-strain stiffness, including the return-mapping details textbooks omit.