13.1.3 The Level Set Method

In recent years the level set method has received lots of attention in TCAD simulations and in fluid dynamics. It is the newest of the three methods and its basic idea is to represent the surface in question as the set of all zeroes of a certain function, i.e., as its zero level set. Its impact is underlined by the several implementations that have been reported in the realm of TCAD [121,122,53,89,3,10] and the forthcoming commercial process simulator TAURUS by Avant! is wholly based on this technique.

The level set method is not only used in TCAD, but it has also been proposed as a means of tracking moving boundaries in other areas like computational geometry, image enhancement and noise removal [69,70], shape detection and recognition [71,72], electro-migration, and grid generation [118].

The main advantages of the level set method are the relatively fine resolution that can be achieved, the handling of slightly tilted lines and corners, and the precise and easy calculation of surface normals. Furthermore joining surfaces is handled implicitly by the algorithm. On the other hand, efficient level set algorithms that work stably and accurately for many time steps are complicated (cf. Section 13.6).