Fixed Grid (FG) methodology was first introduced by García and Steven as an engine for numerical estimation of two-dimensional elasticity problems. The advantages of using FG are simplicity and speed at a permissible level of accuracy. Two dimensional FG has been proved effective in approximating the strain and stress field with low requirements of time and computational resources. Moreover, FG has been used as the analytical kernel for different structural optimisation methods as Evolutionary Structural Optimisation , Genetic Algorithms (GA), and Evolutionary Strategies . FG consists of dividing the bounding box of the topology of an object into a set of equally sized cubic elements. Elements are assessed to be inside (I), outside (O) or neither inside nor outside (N IO) of the object. Different material properties assigned to the inside and outside medium transform the problem into a multi-material elasticity problem. As a result of the subdivision N IO elements have non-continuous properties. They can be approximated in different ways which range from simple setting of N IO elements as O to complex noncontinuous domain integration. If homogeneously averaged material properties are used to approximate the N IO element, the element stiffness matrix can be computed as a factor of a standard stiffness matrix thus reducing the computational cost of creating the global stiffness matrix. An additional advantage of FG is found when accomplishing re-analysis, since there is no need to recompute the whole stiffness matrix when the geometry changes.This article presents CAD to FG conversion and the stiffness matrix computation based on non-continuous elements. In addition inclusion/exclusion of O elements in the global stiffness matrix is studied. Preliminary results shown that non-continuous N IO elements improve the accuracy of the results with considerable savings in time. Numerical examples are presented to illustrate the possibilities of the method.

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In this paper, a parallel cartesian fixed grid mesh generator for structural and fluid dynamics problems is presented. The method uses the boundary representation of a body and produces a set of equal sized cells which are classified in three different types according to its location with respect to the body. Cells are inside, outside or intersecting the boundary of the body. This classification is made by knowing the number of nodes of a cell that are inside body. That process is accomplished very efficiently as the nodes can be classified in batch. Once boundary cells are identified, its geometry is approximated by the convex hull of the nodes inside the body and the intersection points of the boundary against the cell edges. This paper presents the basics of the Fixed Grid Meshing algorithm, followed by some domain decomposition modifications and the data structures required for its parallel implementation. A set of examples and a brief discussion on the possibility of applying this algorithm together with other approaches is presented.