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.