numerics — Scientific Computing

A C++ library for numerical analysis, PDE solvers, SPH fluid dynamics, quantum simulation, and stochastic MCMC. Built and optimized over several years of coursework and research.

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Simulations

2D SPH Fluid — dam-break, hot/cold spheres, heat transfer
3D SPH Fluid — dual temperature hoses, free-orbit camera
Navier-Stokes — Kelvin-Helmholtz instability, particle tracers
Electromagnetism — FEM potential solve, B-field, orbiting dipole
Schrödinger Equation — double-slit diffraction, Strang splitting
Quantum Circuits — Bell, GHZ, Grover, teleportation, QFT₃
Ising Nucleation — free-energy barrier crossing (F=0.1, T<Tc)
Ising Ordering — spontaneous symmetry breaking from random init

Library Modules

core

Vector, Matrix, SparseMatrix, BandedMatrix. Backend dispatch: seq, SIMD, BLAS, OpenMP, CUDA.

factorization

LU, QR, Thomas tridiagonal. Direct solvers for dense and structured systems.

solvers

Conjugate gradient, matrix-free CG, restarted GMRES, Jacobi, Gauss-Seidel.

eigen

Power iteration, inverse iteration, Rayleigh quotient, Lanczos, dense Jacobi sweeps.

svd

Full SVD and randomized truncated SVD for large matrices.

spectral

Radix-2 FFT/IFFT, real FFT, precomputed plans. Optional FFTW3 backend.

analysis

Quadrature (trapz, Simpson, Gauss-Legendre, Romberg) and root-finding (bisection, Newton, Brent).

markov

Metropolis sweep, precomputed-probability variant, umbrella sampling with save/restore.

stats

Online Welford mean/variance, histogram with WHAM reweighting, autocorrelation time.

spatial

CellList2D/3D, Verlet list with skin radius. O(N) neighbor search for SPH and MD.

quantum

Statevector simulation, quantum circuit builder, EDMD for unitary evolution.

physics apps

SPH 2D/3D, Navier-Stokes, TDSE, EM fields, Ising MC — full simulation apps.

Status / Last Tested

Generated by cmake --build build --target report. Shows build environment, test results, and benchmark throughput from the most recent run.

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