Computer aided design system

Abstract

In a computer aided design system, a stored geometrical representation of a structure, the material properties thereof, and the loads imposed thereon are converted into a visualization of a mechanical quantity of the structure. A mesh is generated that describes the structure. By application of the finite element method to the mesh, the elements of a stiffness matrix, a loading vector and a vector including an associated degree of freedom index for each row and column of the stiffness matrix is generated. From the stiffness matrix and the loading vector, a matrix A and a right-hand side vector f are generated. A and f are related through the equation Ax=f, wherein the vector x represents the mechanical quantity at points of the mesh. A linear solver of the preconditioned conjugate gradient-type generates the elements of the vector x from A and f using a preconditioning matrix K. The linear solver generates a principal submatrix from the stiffness matrix by setting to zero those elements therein and positioned such that the degree of freedom index associated with their row is not equal to the degree of freedom index associated with their column. The linear solver also generates the preconditioning matrix K from the principal submatrix. The mechanical quantity of the structure is visualized on the computer aided design system as a function of the vector x.