MatForge — Open Knowledge Hub for Scientific Simulation and Modeling

Reading Time: 10 minutesDeep-dive on Latin Hypercube Sampling, Sobol sequences, and Quasi-Monte Carlo methods for scientific simulations. Learn theory, Python implementation, and when to use each.

Reading Time: 11 minutesPolynomial chaos expansion is a surrogate modeling technique that replaces an expensive simulation with a series of orthogonal polynomials whose coefficients can be used to estimate uncertainty directly. Once fitted, a PCE surrogate gives you analytical access to output means, variances, confidence intervals, and Sobol sensitivity indices without running a single additional simulation. This article […]

Reading Time: 13 minutesLearn why anisotropic mesh adaptation reduces degrees of freedom by 4–30× for advection-dominated flows. Covers metric tensors, error estimators, and practical implementation.

Reading Time: 10 minutesTL;DR — What You Need to Know Domain decomposition splits a simulation grid into overlapping subdomains so each MPI rank can solve its local piece independently. Additive Schwarz (ASM) is the simplest form — you solve locally and add corrections. It works great for small subdomain counts but fails at scale. Restricted Additive Schwarz (RAS) […]

Reading Time: 9 minutesKey Takeaways Seven major funding models exist for open source scientific software, ranging from multi-donor philanthropy (EOSS/OS4S, ~$58M) to government grants (NASA OSTFL, NSF PESOSE, UKRI RSMF, DFG) and EU framework programs (€93.5B Horizon Europe). The “maintenance trap” is the root cause of abandoned research software: academic career systems reward publications, not code maintenance, creating […]

Reading Time: 12 minutesLearn how to make simulation results reproducible using Jupyter notebooks, version control, environment management, Zenodo archiving, and FAIR principles. A practical guide for computational researchers.

Reading Time: 9 minutesLearn when to use spectral methods, discontinuous Galerkin, spectral elements, and hp-FEM. Practical comparison of high-order methods vs traditional FDM, FEM, FVM.

Reading Time: 10 minutesTL;DR Local conservation is guaranteed by FVM flux consistency; FEM and DG must design fluxes carefully. First-order upwind adds artificial viscosity — at CFL = 1, it vanishes, a surprising result most practitioners miss. MOOSE’s RDG(P0P1) with flux limiting reduces numerical diffusion by over 80% compared to full upwinding. Skew-symmetric formulations conserve kinetic energy by […]

Reading Time: 3 minutesAdaptive time stepping dynamically adjusts Δt based on estimated error. Learn embedded RK pairs, BDF error estimation, CFL constraints, and FiPy implementation.

Reading Time: 12 minutesAdvection-dominated partial differential equations are difficult because information moves mainly along a flow direction while physical diffusion provides little smoothing. A numerical method that works well for a diffusion-dominated problem may produce oscillations, excessive smearing, or nonphysical values when advection becomes stronger. The correct response is not simply to select the most diffusive scheme available. […]