|
In [[combustion]], this method is used to describe the instantaneous flame surface, known as the [[G equation]].
== Importance ==
The level set method is a powerful technique for modeling the evolution of interfaces between different regions, such as curves and surfaces. [[Level-set method|It has many applications in physics, engineering, computer graphics, image processing, and more.]]<ref>{{Cite web |last=MIT |first=Math |title=The Level Set Method |url=https://math.mit.edu/classes/18.086/2007/levelsetpres.pdf}}</ref>
The level set method has several advantages over other methods, such as:
* [[Level-set method|It can handle complex shapes and topology changes, such as merging, splitting, or breaking, without requiring reparameterization or remeshing]]
* [[Level-set method|It can use a fixed Cartesian grid to represent the interface implicitly, which simplifies the numerical computations and avoids the need for interpolation or extrapolation]]
* [[Level-set method|It can incorporate various geometric properties, such as normal vector, curvature, or motion, into the level set equation, which is a nonlinear, hyperbolic partial differential equation]]
The level set method is based on the idea of representing an interface as the zero level set of a function, such as a signed distance function. [[Level-set method|The function is then evolved by solving the level set equation, which captures the motion of the interface according to a given speed function.]]<ref name=":0">{{Cite web |title=Level Set Methods: A Fast Introduction ------------------------------------------- Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian Level Set Methods J.A. Sethian |url=https://math.berkeley.edu/~sethian/2006/Semiconductors/ieee_level_set_explain.html |access-date=2023-12-27 |website=math.berkeley.edu}}</ref>
The level set method is a fast and flexible way to track the dynamics of interfaces in various domains and scenarios. [[Level-set method|It is an important tool for numerical analysis and simulation of complex phenomena.]] <ref name=":0" />
==History==
| 