FEATool Multiphysics

Custom Equation Showcase Models

custom-equation
custom-equation
Black-Scholes Equation

Black-Scholes Equation

Black-Scholes Equation

Black-Scholes Equation

This is an example showing how to define a custom parital differential equation (PDE) equation model in the FEATool Multiphysics. In this case the Black-Scholes model equation, which is used in financial analytics to model derivatives and options pricing. The non-linear partial differential equation to be solved reads …

Resonance Frequencies of a Room

Resonance Frequencies of a Room

Resonance Frequencies of a Room

Resonance Frequencies of a Room

This example studies the resonance frequencies of an empty room by using the Helmholz equation for the time-harmonic pressure field Δp + k2 = 0 The resulting eigenmodes can be compared to and validated against the analytical solution for the resonance frequencies of a boxed enclosure, that is f = c/2*√( (i/lx)2 + …

Shallow Water Equations

Shallow Water Equations

Shallow Water Equations

Shallow Water Equations

This example models a moving wave in a pool of shallow water. Although these types of fluid flows are governed by the full three-dimensional Navier-Stokes equations, they can be simplified with a two dimensional approximation, where the z-dimension is replaced with a variable h for the unknown free surface height …

Two Material Wave Guide Interface

Two Material Wave Guide Interface

Two Material Wave Guide Interface

Two Material Wave Guide Interface

This example studies the interface between two different materials in a section of a wave guide. The change in material causes the waves to travel at different speeds. This changing diffraction pattern of the planar time harmonic waves can be investigated by using the Helmholtz equation for the amplitude of the waves A …

Wave Equation on a Circle

Wave Equation on a Circle

Wave Equation on a Circle

Wave Equation on a Circle

This tutorial explains how to set up and solve a generalized wave equation model on a circle, like for example for a drum or membrane, and then tracks how the initial parabolic deformed state will affect the resulting shape. The wave equation is one of the classic hyperbolic partial differential equations (PDE) of the …

Interference and Diffraction

Interference and Diffraction

Interference and Diffraction

Interference and Diffraction

The classic double-slit experiment considers a planar and periodic oscillating wave which hits and passes two narrow slits. Assuming the slits are narrow enough, the passing waves will bend and cause an interference pattern, while diffraction will attenuate the off axis resulting amplitude. In the example the Helmholtz …