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groundwater-model

groundwater flow and transport

MODFLOW

SystemTechniques · 10Primitives · 21 groundwater-model Polygon clippinggeometry · medium: Polygon intersection/union/difference (Weiler-Atherton, Martinez) for spatial predicatesVoronoi diagramsgeometry · medium: Fortune sweep and jump flooding to compute Voronoi regions and distance fieldsEnsemble kalman filternumerics · medium: Kalman update with covariance estimated from an ensemble; localization and inflation for huge statesFinite volume methodnumerics · medium: Conservative cell-averaged discretization with numerical fluxes on structured and unstructured meshesFlux limiters upwindingnumerics · medium: Upwind schemes, TVD flux limiters, MUSCL and Riemann solvers for shock-capturing advectionIncomplete 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.›Levenberg marquardtnumerics · medium: Damped Gauss-Newton nonlinear least squares for model calibrationSparse 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.›Unstructured mesh representationnumerics · low: Cell-face-node connectivity in CSR form for FEM and FVM meshes; partition-friendly orderingFinite differencesnumerics · 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.›Map projectionsgeometry · low: Web Mercator, UTM and equal-area projections, datums and coordinate transformsQuadtree octreegeometry · low: Adaptive spatial subdivision trees for queries and level of detail; loose and linear variantsR-treegeometry · low: A balanced tree of nested bounding boxes that indexes rectangles and points, answering window and nearest-neighbour queries by pruning whole subtrees.›Regularizationmachine-learning · low: Techniques that trade training fit for generalization: weight decay, dropout, early stopping, label smoothing and data mixing, with the exact update rules and defaults.›Conjugate gradientnumerics · 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.›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.›d-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.›Exact geometric predicatesgeometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmeticPoint in polygongeometry · low: Ray-casting/winding tests and indexed polygon lookup for reverse geocodingHalf edge meshgraphics · low: Half-edge mesh connectivity for editable polygon meshesLU 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).›PRNGs (PCG, xoshiro)numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.›Kalman filterrobotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.›+ 3 more techniques+ 5 more primitives

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