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Simulation and scientific computing
structural-fem
implicit structural finite elements
Abaqus, Code_Aster
System
Techniques · 12
Primitives · 32
structural-fem
Batch checkpoint restart
distributed · medium: Large batch jobs (end-of-day, settlement, payroll runs) that checkpoint and restart idempotently
B rep topology
geometry · medium: Boundary representation: solids as shells, faces, loops, edges and vertices with geometry attached
Graph partitioning
graphs · medium: Split a graph into k balanced parts with few edges between them; multilevel coarsen-partition-refine (METIS, KaHIP) for quality, streaming heuristics (LDG, Fennel) for one-pass scale.
›
Continuation methods
numerics · medium: Homotopy and source or gmin stepping to make Newton converge from a far start
Fill-reducing ordering
numerics · medium: Permute a sparse symmetric matrix before Cholesky/LU so the factor has few new nonzeros; minimum degree, nested dissection and RCM trade quality, speed and parallelism.
›
Finite elements
numerics · medium: Writes the PDE in weak form, approximates it with piecewise polynomials on a mesh and assembles a sparse system; handles any geometry.
›
Incomplete factorization preconditi…
numerics · medium: Sparse approximate LU or Cholesky factors (ILU, IC) that precondition Krylov solvers: fewer iterations than Jacobi, less memory than a direct solve.
›
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Conjugate gradient
numerics · low: Krylov iteration for symmetric positive definite Ax = b using one matrix-vector product and two dot products per step; converges in about √κ iterations.
›
Gaussian quadrature
numerics · low: Approximate an integral by a weighted sum of n function values at roots of orthogonal polynomials; exact for polynomials up to degree 2n-1.
›
Unstructured mesh representation
numerics · low: Cell-face-node connectivity in CSR form for FEM and FVM meshes; partition-friendly ordering
Collective communication
ml-training · low: The family of group exchanges (broadcast, reduce, all-gather, reduce-scatter, all-to-all) and the latency-plus-bytes cost model that picks ring, tree or direct algorithms by message size and topology.
›
Idempotency keys
finance · low: Client-chosen unique key per logical operation, stored with a request fingerprint and the final response, so retries replay the first result instead of acting twice.
›
Write-ahead log
storage · low: Append each change to a checksummed sequential log and fsync it before touching data pages; the basis of crash durability in nearly every database.
›
Cron scheduling
systems · low: Cron expression parsing and next-fire-time computation, with catch-up and time-zone rules
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Half edge mesh
graphics · low: Half-edge mesh connectivity for editable polygon meshes
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Adaptive Runge-Kutta (Dormand-Princ…
numerics · low: An embedded 5(4) Runge-Kutta pair estimates each step's error for free and resizes the step to meet a tolerance; the default non-stiff solver.
›
Rigid-body dynamics
physics · low: Advance one 3D rigid body per step from force and torque: semi-implicit Euler for position, an inertia tensor in the body frame, and quaternion orientation updated by the exponential map.
›
+ 5 more techniques
+ 16 more primitives
System
Techniques · 12
Primitives · 32
structural-fem
Batch checkpoint restart
distributed · medium: Large batch jobs (end-of-day, settlement, payroll runs) that checkpoint and restart idempotently
B rep topology
geometry · medium: Boundary representation: solids as shells, faces, loops, edges and vertices with geometry attached
Graph partitioning
graphs · medium: Split a graph into k balanced parts with few edges between them; multilevel coarsen-partition-refine (METIS, KaHIP) for quality, streaming heuristics (LDG, Fennel) for one-pass scale.
›
Continuation methods
numerics · medium: Homotopy and source or gmin stepping to make Newton converge from a far start
Fill-reducing ordering
numerics · medium: Permute a sparse symmetric matrix before Cholesky/LU so the factor has few new nonzeros; minimum degree, nested dissection and RCM trade quality, speed and parallelism.
›
Finite elements
numerics · medium: Writes the PDE in weak form, approximates it with piecewise polynomials on a mesh and assembles a sparse system; handles any geometry.
›
Incomplete factorization preconditi…
numerics · medium: Sparse approximate LU or Cholesky factors (ILU, IC) that precondition Krylov solvers: fewer iterations than Jacobi, less memory than a direct solve.
›
Sparse direct solver
numerics · medium: Solve sparse Ax = b exactly by reordering, symbolic analysis, numeric LLᵀ/LU and triangular solves; fill-in, not flops per entry, decides the cost.
›
Complementarity contact solver
physics · medium: Contact as LCP or convex optimization (PGS, Newton) with friction cones; soft contacts
Nurbs
geometry · medium: B-splines and NURBS curves and surfaces: knot vectors, de Boor evaluation, knot insertion
Contact manifold generation
physics · medium: Build persistent contact point sets from collision normals by clipping, with feature IDs for warm starts
Polygon clipping
geometry · medium: Polygon intersection/union/difference (Weiler-Atherton, Martinez) for spatial predicates
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Conjugate gradient
numerics · low: Krylov iteration for symmetric positive definite Ax = b using one matrix-vector product and two dot products per step; converges in about √κ iterations.
›
Gaussian quadrature
numerics · low: Approximate an integral by a weighted sum of n function values at roots of orthogonal polynomials; exact for polynomials up to degree 2n-1.
›
Unstructured mesh representation
numerics · low: Cell-face-node connectivity in CSR form for FEM and FVM meshes; partition-friendly ordering
Collective communication
ml-training · low: The family of group exchanges (broadcast, reduce, all-gather, reduce-scatter, all-to-all) and the latency-plus-bytes cost model that picks ring, tree or direct algorithms by message size and topology.
›
Idempotency keys
finance · low: Client-chosen unique key per logical operation, stored with a request fingerprint and the final response, so retries replay the first result instead of acting twice.
›
Write-ahead log
storage · low: Append each change to a checksummed sequential log and fsync it before touching data pages; the basis of crash durability in nearly every database.
›
Cron scheduling
systems · low: Cron expression parsing and next-fire-time computation, with catch-up and time-zone rules
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Half edge mesh
graphics · low: Half-edge mesh connectivity for editable polygon meshes
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Adaptive Runge-Kutta (Dormand-Princ…
numerics · low: An embedded 5(4) Runge-Kutta pair estimates each step's error for free and resizes the step to meet a tolerance; the default non-stiff solver.
›
Rigid-body dynamics
physics · low: Advance one 3D rigid body per step from force and torque: semi-implicit Euler for position, an inertia tensor in the body frame, and quaternion orientation updated by the exponential map.
›
Bézier curves
graphics · low: Smooth curves defined by 3-4 control points, evaluated and split with repeated linear interpolation (de Casteljau) and flattened to lines with a closed-form segment count.
›
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
GJK and EPA
physics · low: GJK decides whether (and how far apart) two convex shapes are from their support functions alone; EPA expands its simplex into penetration depth and normal.
›
Separating axis theorem
physics · low: Convex shapes are disjoint iff some axis separates their projections; testing face normals and edge crosses gives overlap, depth and contact normal.
›
Point in polygon
geometry · low: Ray-casting/winding tests and indexed polygon lookup for reverse geocoding
Fencing tokens
distributed · low: A number that grows with every lock grant and is checked by the protected resource, so a paused ex-holder's late write is rejected.
›
Leases
distributed · low: A lock that expires on its own: bounded-time ownership that survives crashes and partitions, given bounded clock drift and fencing tokens on writes.
›
Quaternion rotations
geometry · low: Unit quaternions as 3D rotations: 4 floats, cheap composition, no gimbal lock, plus the conversions, interpolation choices and numerical care needed in practice.
›
Fixed timestep loop
graphics · low: Fixed simulation dt with accumulator, render interpolation, spiral-of-death guard
CRC32C checksums
hardware-os · low: The Castagnoli CRC-32 with dedicated instructions on x86 (SSE4.2) and ARMv8. It is the standard fast integrity check for storage blocks, logs and network frames.
›
fsync, O_DSYNC and O_DIRECT
hardware-os · low: What fsync, fdatasync, O_DSYNC, O_DIRECT and F_FULLFSYNC really guarantee on Linux and macOS, and the exact call sequences for crash-safe files.
›
SIMD programming
hardware-os · low: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.
›
Runge-Kutta 4
numerics · low: The classic four-stage, fourth-order ODE step; error drops 16× when the step halves, with no derivatives or past steps needed.
›
Semi-implicit Euler
numerics · low: Update velocity from forces first, then position with the new velocity: explicit Euler cost, but symplectic and stable; the default game-physics integrator.
›
Cryptographic hashes (SHA-2, BLAKE3)
security · low: Collision-resistant fingerprints of data; SHA-256 for interoperability, BLAKE3 for speed, HMAC/HKDF for keyed uses.
›
Exponential backoff with jitter
systems · low: Retry after delays that grow geometrically and are randomized, so failed clients spread out instead of hammering a recovering service in synchronized waves.
›
Copy for AI
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