Simulation Glossary

A technique that dynamically increases mesh resolution where the solution changes rapidly, improving accuracy efficiently.

A set of states toward which a dynamical system evolves; strange attractors have fractal structure and signal chaos.

A qualitative change in a system's behavior as a parameter crosses a critical value, such as the onset of oscillation or chaos.

A constraint applied at the edges of a domain — such as fixed temperature, pressure, or displacement — that makes a differential equation well-posed.

Computational Fluid Dynamics — the numerical simulation of fluid flow, heat, and mass transfer by discretizing the governing equations.

A stability criterion linking timestep, cell size, and wave speed that explicit schemes must satisfy to remain stable.

Deterministic behavior so sensitive to initial conditions that long-term prediction becomes impossible despite fixed rules.

PolySim's metered unit for cloud computation; local rendering is free, and tokens pay only for cloud-scale solves.

Software that performs symbolic mathematics, such as exact differentiation, integration, and equation solving.

The property that a numerical solution approaches the true solution as the mesh is refined or iterations proceed; failure to converge signals instability or error.

The instantaneous rate of change of a function, central to calculus and to gradient-based simulation methods.

A boundary condition that fixes the value of the solution on the boundary, such as a prescribed temperature.

A system whose state evolves over time according to fixed rules, studied through fixed points, limit cycles, and attractors.

A discretization that approximates derivatives with difference quotients on a structured grid.

A numerical technique that subdivides a body into small elements to approximate the solution of partial differential equations governing stress, heat, and fields.

A discretization that conserves fluxes across control volumes, standard in computational fluid dynamics.

A probabilistic model over functions that yields both predictions and calibrated uncertainty, popular for surrogate modeling.

Using a graphics processor's massive parallelism for general numerical computation, key to fast in-browser simulation.

PolySim's model of running locally by default and bursting to cloud GPUs only when a problem is too large for the device.

The state of a system at the start of a simulation, required to integrate time-dependent equations forward.

Estimating values between known data points, used in meshing, advection, and surrogate modeling.

Smooth, orderly fluid motion in parallel layers, occurring at low Reynolds numbers.

A three-variable ODE model of convection whose solutions form the iconic butterfly-shaped strange attractor.

Coupled equations describing predator–prey population oscillations, foundational to theoretical ecology.

A number quantifying the exponential rate at which nearby trajectories diverge; a positive value indicates chaos.

The subdivision of a simulation domain into discrete cells or elements over which equations are solved; mesh quality strongly affects accuracy and convergence.

A simulation method that integrates Newton's equations for interacting atoms to study material and biomolecular behavior.

A computational technique that uses repeated random sampling to estimate integrals, probabilities, and uncertainty.

The problem of predicting the motion of a group of masses interacting gravitationally, generally unsolvable in closed form for N ≥ 3.

The partial differential equations expressing conservation of momentum for a viscous fluid, underpinning all computational fluid dynamics.

A boundary condition that fixes the derivative (flux) of the solution on the boundary, such as an insulated wall.

The study of the motion of bodies under gravity, from satellites to planetary systems.

An equation relating a function of one variable to its derivatives; the basis of dynamical-system modeling.

An equation involving partial derivatives of a multivariable function, governing fields like heat, waves, and fluid flow.

An elliptic PDE relating a potential field to its source, appearing in electrostatics, gravity, and incompressible flow.

A real-valued function whose value depends only on distance from a center, used to interpolate scattered data and build surrogates.

A class of PDE systems combining local reactions with diffusion, capable of forming self-organizing Turing patterns.

A measure of how far a candidate solution is from satisfying the governing equations; iterative solvers drive the residual toward zero.

A dimensionless ratio of inertial to viscous forces that predicts whether a flow will be laminar or turbulent.

A family of explicit time-integration schemes for ordinary differential equations; the fourth-order variant (RK4) is a widely used standard.

The study of how variation in model outputs can be attributed to different sources of variation in inputs.

A compartmental epidemiology model dividing a population into Susceptible, Infected, and Recovered groups to study outbreaks.

The property that numerical errors do not grow uncontrollably as a simulation proceeds.

The matrix relating nodal displacements to forces in a finite-element model, assembled from element contributions.

A mathematical model of a system evolving with randomness over time, such as Brownian motion.

A fast approximation of an expensive simulation, trained on sampled runs to predict outputs in a fraction of the time.

Manipulation of mathematical expressions in exact symbolic form — differentiation, simplification, and solving — rather than numerically.

A time-integration scheme that conserves the geometric structure of Hamiltonian systems, giving excellent long-term energy behavior.

The process of advancing a time-dependent simulation in discrete increments using an integration scheme.

Chaotic, multi-scale fluid motion characterized by eddies and mixing, requiring statistical or resolved models such as RANS or LES.

A spontaneous spatial pattern arising from a reaction–diffusion instability, explaining stripes and spots in nature.

The discipline of characterizing and propagating uncertainty in model inputs to understand confidence in outputs.

A stable, time-reversible integration method widely used in molecular dynamics and particle physics.

The local spinning motion of a fluid, defined as the curl of the velocity field; a key diagnostic of rotational flow.

A portable binary instruction format that runs near-native code in the browser, powering fast in-browser solvers.

A modern browser API that exposes GPU compute and rendering, enabling near-native simulation performance without installation.