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Simulation and scientific computing
storm-surge
storm surge and tsunami modelling
ADCIRC, GeoClaw
System
Techniques · 10
Primitives · 39
storm-surge
Batch checkpoint restart
distributed · medium: Large batch jobs (end-of-day, settlement, payroll runs) that checkpoint and restart idempotently
Halo exchange
distributed · medium: Each rank stores its block plus a border copy of its neighbours' edge cells, refreshed by small messages every step; communication scales with block surface, not volume.
›
Delaunay triangulation
geometry · medium: Bowyer-Watson and incremental flips; maximizes minimum angles, dual of Voronoi
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.
›
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.
›
Finite volume method
numerics · medium: Conservative cell-averaged discretization with numerical fluxes on structured and unstructured meshes
Flux limiters upwinding
numerics · medium: Upwind schemes, TVD flux limiters, MUSCL and Riemann solvers for shock-capturing advection
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.
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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.
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Unstructured mesh representation
numerics · low: Cell-face-node connectivity in CSR form for FEM and FVM meshes; partition-friendly ordering
Map projections
geometry · low: Web Mercator, UTM and equal-area projections, datums and coordinate transforms
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.
›
Common alerting protocol
networking · low: CAP alert message format: areas as polygons/circles, severity, urgency, multilingual info blocks
Monte Carlo integration
numerics · low: Estimate an expectation by averaging random samples; error falls as σ/√N in any dimension, and variance reduction (antithetic, control variates, importance sampling) shrinks σ.
›
Spherical grids
numerics · low: Lat-lon, cubed-sphere and icosahedral grids for global models; pole and area issues
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.
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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
Eager rendezvous protocol
distributed · low: MPI point-to-point: eager sends for small messages, rendezvous handshake for large ones
Rdma
networking · low: RDMA verbs over InfiniBand/RoCE: queue pairs, memory registration, one-sided ops
Zero-copy I/O
networking · low: Move bytes between files, sockets and NICs by passing page references instead of copying through user space: sendfile, splice, MSG_ZEROCOPY, kTLS.
›
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Space filling curves
geometry · low: Z-order/Morton (geohash) and Hilbert curves mapping multi-dimensional points to sortable keys
+ 3 more techniques
+ 23 more primitives
System
Techniques · 10
Primitives · 39
storm-surge
Batch checkpoint restart
distributed · medium: Large batch jobs (end-of-day, settlement, payroll runs) that checkpoint and restart idempotently
Halo exchange
distributed · medium: Each rank stores its block plus a border copy of its neighbours' edge cells, refreshed by small messages every step; communication scales with block surface, not volume.
›
Delaunay triangulation
geometry · medium: Bowyer-Watson and incremental flips; maximizes minimum angles, dual of Voronoi
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.
›
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.
›
Finite volume method
numerics · medium: Conservative cell-averaged discretization with numerical fluxes on structured and unstructured meshes
Flux limiters upwinding
numerics · medium: Upwind schemes, TVD flux limiters, MUSCL and Riemann solvers for shock-capturing advection
Chunked array storage
storage · medium: Cut an N-dimensional array into a regular grid of independently compressed blocks, so a slice read touches only the overlapping blocks and writers to different blocks run in parallel.
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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.
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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.
›
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.
›
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.
›
Unstructured mesh representation
numerics · low: Cell-face-node connectivity in CSR form for FEM and FVM meshes; partition-friendly ordering
Map projections
geometry · low: Web Mercator, UTM and equal-area projections, datums and coordinate transforms
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.
›
Common alerting protocol
networking · low: CAP alert message format: areas as polygons/circles, severity, urgency, multilingual info blocks
Monte Carlo integration
numerics · low: Estimate an expectation by averaging random samples; error falls as σ/√N in any dimension, and variance reduction (antithetic, control variates, importance sampling) shrinks σ.
›
Spherical grids
numerics · low: Lat-lon, cubed-sphere and icosahedral grids for global models; pole and area issues
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
Eager rendezvous protocol
distributed · low: MPI point-to-point: eager sends for small messages, rendezvous handshake for large ones
Rdma
networking · low: RDMA verbs over InfiniBand/RoCE: queue pairs, memory registration, one-sided ops
Zero-copy I/O
networking · low: Move bytes between files, sockets and NICs by passing page references instead of copying through user space: sendfile, splice, MSG_ZEROCOPY, kTLS.
›
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Space filling curves
geometry · low: Z-order/Morton (geohash) and Hilbert curves mapping multi-dimensional points to sortable keys
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.
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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.
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Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
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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.
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Object storage
cloud · low: S3-compatible blob storage at cents per GB-month with 11 nines durability; pick by egress price, request price and latency, not by storage price alone.
›
Delta encoding
compression · low: Store differences between consecutive values instead of the values, turning sorted IDs, timestamps and counters into small numbers that pack into few bits.
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Zstandard (zstd)
compression · low: LZ77 plus Huffman and FSE entropy coding, with levels from LZ4-like speed to xz-like ratio, all decoding at about 1-2 GB/s.
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HTTP range requests
networking · low: Ask for byte offsets with Range and get a 206 slice back; the standard way to resume, seek and read big remote files piecewise.
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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).
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Bit packing and PFOR
compression · low: Store blocks of integers with exactly b bits each and patch rare outliers separately (PFOR); the fastest integer codec family, billions of values per second.
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Varint (LEB128)
compression · low: Variable-length integers in 7-bit groups with a continuation bit; small numbers take 1 byte, the wire format of Protobuf, WebAssembly and DWARF.
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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.
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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.
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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.
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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.
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Rejection sampling
ml-training · low: Best-of-n and filtered sampling: generate many candidates, keep those passing a verifier or reward threshold
Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
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Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
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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