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ode-dae-solver

ODE/DAE and stiff integration suite

SUNDIALS, DifferentialEquations.jl

SystemTechniques · 6Primitives · 18 ode-dae-solver Fmi co simulationnumerics · medium: Couple simulation units (FMUs) with a master algorithm: step negotiation, rollback, algebraic loopsGmresnumerics · medium: GMRES with restarts: Arnoldi, Givens rotations, for nonsymmetric sparse systemsIncomplete 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 solvernumerics · 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.›Fill-reducing orderingnumerics · 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.›Graph partitioninggraphs · 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.›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.›Spline interpolationnumerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tablesStiff 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.›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 factorizationnumerics · 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).›SIMD programminghardware-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.›CUDA and GPU languageslanguages · low: Programming GPUs: thousands of lockstep threads, bound by memory bandwidth; libraries first, Triton for fused kernels, CUDA C++ for peak speed.›Collective communicationml-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.›Explicit Eulernumerics · 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.›Floating-point errornumerics · 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.›Newton root findingnumerics · 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.›Runge-Kutta 4numerics · 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 Eulernumerics · low: Update velocity from forces first, then position with the new velocity: explicit Euler cost, but symplectic and stable; the default game-physics integrator.›Verlet / leapfrognumerics · low: Half-kick, drift, half-kick: a second-order, time-reversible, symplectic integrator with one force evaluation per step whose energy error stays bounded for millions of steps.›Calling conventions abicompilers · low: System V, Windows x64 and AAPCS64 ABIs: argument registers, stack frames, struct passing, FFId-ary heapdata-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.›+ 2 more primitives

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