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Simulation and scientific computing
climate-model
climate model
CESM
System
Techniques · 9
Primitives · 38
climate-model
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.
›
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.
›
Checkpoint and restart
hardware-os · medium: Periodically save enough state to resume a computation after a crash, preemption or move, with an interval that balances save cost against lost work.
›
Conservative regridding
numerics · medium: Remap fields between grids preserving integrals, using overlap areas (first and second order)
Finite volume method
numerics · medium: Conservative cell-averaged discretization with numerical fluxes on structured and unstructured meshes
Semi lagrangian advection
physics · medium: Trace characteristics back and interpolate; unconditionally stable large time steps
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.
›
Spherical grids
numerics · low: Lat-lon, cubed-sphere and icosahedral grids for global models; pole and area issues
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.
›
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.
›
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
›
Reproducible reduction
numerics · low: Order-independent floating-point sums (fixed order, Kahan, binned) for bit-for-bit reproducibility
Spectral methods
numerics · low: Represent the solution by a global Fourier or Chebyshev series; derivatives become multiplications by ik in coefficient space, giving exponential convergence for smooth problems.
›
Stiff solvers (implicit, BDF)
numerics · low: Implicit steps solve a small nonlinear system so fast decaying modes stay stable at any step size; BDF methods are the stiff-ODE workhorse.
›
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.
›
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.
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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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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.
›
Copy-on-write fork
hardware-os · low: fork() gives the child the parent's whole address space by sharing pages read-only and copying one only when someone writes it; vfork and posix_spawn skip even that.
›
Dirty page tracking
hardware-os · low: Write-protection or PML logs of modified guest/process pages
mmap and the page cache
hardware-os · low: How read() and mmap reach file data through the kernel page cache, what readahead and madvise do, and why databases use their own buffer pool instead.
›
+ 2 more techniques
+ 22 more primitives
System
Techniques · 9
Primitives · 38
climate-model
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.
›
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.
›
Checkpoint and restart
hardware-os · medium: Periodically save enough state to resume a computation after a crash, preemption or move, with an interval that balances save cost against lost work.
›
Conservative regridding
numerics · medium: Remap fields between grids preserving integrals, using overlap areas (first and second order)
Finite volume method
numerics · medium: Conservative cell-averaged discretization with numerical fluxes on structured and unstructured meshes
Semi lagrangian advection
physics · medium: Trace characteristics back and interpolate; unconditionally stable large time steps
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.
›
Polygon clipping
geometry · medium: Polygon intersection/union/difference (Weiler-Atherton, Martinez) for spatial predicates
Flux limiters upwinding
numerics · medium: Upwind schemes, TVD flux limiters, MUSCL and Riemann solvers for shock-capturing advection
Spherical grids
numerics · low: Lat-lon, cubed-sphere and icosahedral grids for global models; pole and area issues
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.
›
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.
›
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
›
Reproducible reduction
numerics · low: Order-independent floating-point sums (fixed order, Kahan, binned) for bit-for-bit reproducibility
Spectral methods
numerics · low: Represent the solution by a global Fourier or Chebyshev series; derivatives become multiplications by ik in coefficient space, giving exponential convergence for smooth problems.
›
Stiff solvers (implicit, BDF)
numerics · low: Implicit steps solve a small nonlinear system so fast decaying modes stay stable at any step size; BDF methods are the stiff-ODE workhorse.
›
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.
›
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.
›
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.
›
Copy-on-write fork
hardware-os · low: fork() gives the child the parent's whole address space by sharing pages read-only and copying one only when someone writes it; vfork and posix_spawn skip even that.
›
Dirty page tracking
hardware-os · low: Write-protection or PML logs of modified guest/process pages
mmap and the page cache
hardware-os · low: How read() and mmap reach file data through the kernel page cache, what readahead and madvise do, and why databases use their own buffer pool instead.
›
Ptrace process control
hardware-os · low: Ptrace: attach, read and write registers and memory, single-step, intercept signals
R-tree
geometry · low: A balanced tree of nested bounding boxes that indexes rectangles and points, answering window and nearest-neighbour queries by pruning whole subtrees.
›
Unstructured mesh representation
numerics · low: Cell-face-node connectivity in CSR form for FEM and FVM meshes; partition-friendly ordering
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.
›
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
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.
›
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.
›
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Point in polygon
geometry · low: Ray-casting/winding tests and indexed polygon lookup for reverse geocoding
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.
›
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.
›
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.
›
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.
›
Virtual memory and the TLB
hardware-os · low: How page tables and TLBs translate every address, what TLB reach means, and when 2 MiB or 1 GiB huge pages pay off on Linux.
›
Discrete cosine transform
numerics · low: Fast integer DCT/DST block transforms used by image and video codecs
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.
›
Fast Fourier transform
numerics · low: Computes the DFT in O(n log n) by recursively splitting into even and odd halves; the basis of fast convolution and spectral methods.
›
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.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
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