Abstract: A method for fine decomposition in finite element mesh generation, in which a polygonal boundary of a domain is input into the system by an analyst and the domain is automatically divided into rough elements generally corresponding to Voronoi regions, that is, regions which are closer to respective ones of the polygonal line segments or reflex vertices therebetween. Any arc portion of these regions is converted to a straight line. Additional lines are formed between interior vertices of the rough regions so that all rough regions are either triangles or trapezoids. Adjacent rough regions are then paired across internal boundaries and are classified into four types. The rough regions are then subdivided into fine regions of triangular shape according to rules associated with each of the four types. The degree of fine subdivision can be controlled according to known equations providing the total number of fine elements.

Abstract: A method, amenable to automation, for generating finite elements of a geometric model. The model is first subdivided into coarse subdomains and then the coarse subdomains are further subdivided. The coarse subdivision is performed using a symmetric axis transform which generates axes symmetric to opposing boundaries of the object. The transform also generates a radius function of the axes giving the distance between the axes and the boundaries. A coarse subdomain is created between each single non-branching section of the axes and one of its associated boundaries. The fine subdivisions of the relatively simple coarse subdomains is performed by well known techniques or can beneficially use the radius function.