SUMMARYIn the present paper, preconditioning of iterative equation solvers for the Navier-Stokes equations is investigated. The Navier-Stokes equations are solved for the mixed finite element formulation. The linear equation solvers used are the orthomin and the Bi-CGSTAB algorithms. The storage structure of the equation matrix is given special attention in order to avoid swapping and thereby increase the speed of the preconditioner. The preconditioners considered are Jacobian, SSOR and incomplete LU preconditioning of the matrix associated with the velocities. A new incomplete LU preconditioning with fill-in for the pressure matrix at locations in the matrix where the corner nodes are coupled is designed. For all preconditioners, inner iterations are investigated for possible improvement of the preconditioning. Numerical experiments are executed both in two and three dimensions.

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Kjiirnes. M., Svindland A., Wallee L., Wille. S. 0. Localization of early atherosclerotic lesions in an arterial bifurcation in humans. Acta path. microbiol. scand. Sect. A, 89: 35-40, I98 I.The detailed localization of early atherosclerotic lesions in arterial bifurcations was studied in 3 3 brachiocephalic arteries obtained from autopsies of young persons who had suffered a violent and sudden death. Drawings of the sudanophilic lesions in the vessel wall were fed to a computer, scaled to a standardized size and shape, and added together. The results are presented as contour lines connecting points with equal frequency of early lesions. The distribution of the early lesions reveals a distinct pattern: The early lesions start to develop on the outer walls of the bifurcation, while the inner walls downstream from the flow divider are kept free as are also the lateral walls. These results are clearly in conflict with Fry's shear stress hypothesis, while they seem to support Caro's hypothesis of inhibition of local diffusional transport. The results are also at variance with results obtained in most animal models, suggesting that the process which takes place in the vessel wall in these animals may be different from human atherosclerosis.

SUMMARYMixed ÿnite element formulations of incompressible Navier-Stokes Equations leads to non-positive deÿnite algebraic systems inappropriate for iterative solution techniques. However, introducing a suitable preconditioner, the mixed ÿnite element equation system becomes positive deÿnite and solvable by iterative techniques. The present work suggests a priori pivoting sequences for parallel and serial implementations of incomplete Gaussian factorization. Tests are performed for the driven cavity problem in two and three dimensions.

SUMMARYA new method for generating finite element grids in two and three dimensions is developed. The method is based on a new search tree structure. The search tree is built upon triangles in two dimensions and tetrahedra in three dimensions. The density of elements can be varied throughout the computational domain. Efficient search algorithms for finding points in space and for finding the boundary of the domain have been developed. The speed of the grid algorithm will permit adaptive gridding during computation. The grid algorithm is generally applicable to both hydrodynamic as well as aerodynamic finite element computations. The technique has been used with success for gridding the North Sea-Skagerrak area.