Classical and all-floating FETI methods for the simulation of arterial tissues

High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is - as most other biological tissues - characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters.Comment: 29 page

Numerical optimization design of advanced transonic wing configurations

A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure distributions and drag-to-lift ration minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes

A locally adaptive time-stepping algorithm for\ud petroleum reservoir simulations

An algorithm for locally adapting the step-size for large scale finite volume simulations of multi-phase flow in petroleum reservoirs is suggested which allows for an “all-in-one” implicit calculation of behaviour over a very large time scale. Some numerical results for simple two-phase flow in one space dimension illustrate the promise of the algorithm, which has also been applied to very simple 3D cases. A description of the algorithm is presented here along with early results. Further development of the technique is hoped to facilitate useful scaling properties

Nonlinear Finite Element Analysis of Reinforced Concrete Coupled Shear Walls

This thesis is concerned with the development of an inelastic material model to be used in conjunction with the finite element technique to simulate the behaviour of reinforced concrete shear-walls under lateral loads. The proposed computational model is capable of tracing the entire nonlinear response up to ultimate load conditions. The main features of the nonlinear behaviour of concrete and steel are incorporated in the numerical model. These include cracking, nonlinear biaxial stress-strain relationships in concrete up to crushing and yielding of steel. The investigation first considers the linear elastic behaviour of coupled shear-walls then a consistent material model that matches the existing experimental evidence for the behaviour of plain concrete under monotonic biaxial loading is considered. The reinforcing steel is idealized as bilinear uniaxially stressed material. The individual material models are combined with the finite element technique to demonstrate their applicability. To check the validity and accuracy of the numerical model, finite element calculations are compared with experimental results for shallow and deep beams, shear panels subjected to monotonic loading. Finally, various hypothetical coupled shear-walls and tested microconcrete shear walls were analysed highlighting the history of crack propagation, deflections, crushing of concrete and yielding of steel up to failure. The resulting model should prove to be a simple useful research tool for use in the study of any reinforced concrete structure which may be considered to be in a state of plane stress

Modules for Experiments in Stellar Astrophysics (MESA)

Stellar physics and evolution calculations enable a broad range of research in astrophysics. Modules for Experiments in Stellar Astrophysics (MESA) is a suite of open source libraries for a wide range of applications in computational stellar astrophysics. A newly designed 1-D stellar evolution module, MESA star, combines many of the numerical and physics modules for simulations of a wide range of stellar evolution scenarios ranging from very-low mass to massive stars, including advanced evolutionary phases. MESA star solves the fully coupled structure and composition equations simultaneously. It uses adaptive mesh refinement and sophisticated timestep controls, and supports shared memory parallelism based on OpenMP. Independently usable modules provide equation of state, opacity, nuclear reaction rates, and atmosphere boundary conditions. Each module is constructed as a separate Fortran 95 library with its own public interface. Examples include comparisons to other codes and show evolutionary tracks of very low mass stars, brown dwarfs, and gas giant planets; the complete evolution of a 1 Msun star from the pre-main sequence to a cooling white dwarf; the Solar sound speed profile; the evolution of intermediate mass stars through the thermal pulses on the He-shell burning AGB phase; the interior structure of slowly pulsating B Stars and Beta Cepheids; evolutionary tracks of massive stars from the pre-main sequence to the onset of core collapse; stars undergoing Roche lobe overflow; and accretion onto a neutron star. Instructions for downloading and installing MESA can be found on the project web site (http://mesa.sourceforge.net/).Comment: 110 pages, 39 figures; submitted to ApJS; visit the MESA website at http://mesa.sourceforge.ne

The role of non-uniqueness in the development of vortex breakdown in tubes

Numerical solutions of viscous, swirling flows through circular pipes of constant radius and circular pipes with throats have been obtained. Solutions were computed for several values of vortex circulation, Reynolds number and throat/inlet area ratio, under the assumptions of steady flow, rotational symmetry and frictionless flow at the pipe wall. When the Reynolds number is sufficiently large, vortex breakdown occurs abruptly with increased circulation as a result of the existence of non-unique solutions. Solution paths for Reynolds numbers exceeding approximately 1000 are characterized by an ensemble of three inviscid flow types: columnar (for pipes of constant radius), soliton and wavetrain. Flows that are quasi-cylindrical and which do not exhibit vortex breakdown exist below a critical circulation, dependent on the Reynolds number and the throat/inlet area ratio. Wavetrain solutions are observed over a small range of circulation below the critical circulation, while above the critical value, wave solutions with large regions of reversed flow are found that are primarily solitary in nature. The quasi-cylindrical (QC) equations first fail near the critical value, in support of Hall's theory of vortex breakdown (1967). However, the QC equations are not found to be effective in predicting the spatial position of the breakdown structure