Bücher der Reihe Progress in Scientific Computing

In this book, the new and rapidly expanding field of scientific computing is understood in a double sense: as computing for scientific and engineering problems and as the science of doing such computations.

Configurations that have a relatively high ballistic coefficient (such as slender reentry vehicles) and reenter the atmosphere at relatively high angles of attack experience severe heating rates and high dynamic pressures, but only for a short period of time.

These three volumes entitled Advances in Hypersonics contain the Proceedings of the Second and Third Joint US/Europe Short Course in Hypersonics which took place in Colorado Springs and Aachen. The Second Course was organized at the US Air Force Academy, USA in January 1989 and the Third Course at Aachen, Germany in October 1990. The main idea of these Courses was to present to chemists, com- puter scientists, engineers, experimentalists, mathematicians, and physicists state of the art lectures in scientific and technical dis- ciplines including mathematical modeling, computational methods, and experimental measurements necessary to define the aerothermo- dynamic environments for space vehicles such as the US Orbiter or the European Hermes flying at hypersonic speeds. The subjects can be grouped into the following areas: Phys- ical environments, configuration requirements, propulsion systems (including airbreathing systems), experimental methods for external and internal flow, theoretical and numerical methods. Since hyper- sonic flight requires highly integrated systems, the Short Courses not only aimed to give in-depth analysis of hypersonic research and technology but also tried to broaden the view of attendees to give them the ability to understand the complex problem of hypersonic flight. Most of the participants in the Short Courses prepared a docu- ment based on their presentation for reproduction in the three vol- umes. Some authors spent considerable time and energy going well beyond their oral presentation to provide a quality assessment of the state of the art in their area of expertise as of 1989 and 1991.

In the past few years, knowledge about methods for the numerical solution of two-point boundary value problems has increased significantly. Important theoretical and practical advances have been made in a number or fronts, although they are not adequately described in any tt'xt currently available. With this in mind, we organized an international workshop, devoted solely to this topic. Tht' workshop took place in Vancouver, B.C., Canada, in July 1()"e;13, 1984. This volume contains the refereed proceedings of the workshop. Contributions to the workshop were in two formats. There were a small number of invited talks (ten of which are presented in this proceedings); the other contributions were in the rorm or poster sessions, for which there was no parallel activity in the workshop. We had attemptt'd to cover a number of topics and objectives in the talks. As a result, the general review papt'rs of O'Malley and Russell are intended to take a broader perspective, while the other papers are more specific. The contributions in this volume are divided (somewhat arbitrarily) into five groups. The first group concerns fundamental issues like conditioning and decoupling, which have only rect'ntly gained a proper appreciation of their centrality. Understanding of certain aspects or shooting methods ties in with these fundamental concepts. The papers of Russell, dt' Hoog and Mattheij all deal with these issues.

In many scientific or engineering applications, where ordinary differen- tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given meas- ured data and an associated theoretical model, determine unknown para- meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "e;discrepancy"e; between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the sen- sitivity coefficients for the model. may be rather time and storage con- suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inev- itable discretization errors, regularization techniques are necessary.

~his Monograph has two objectives : to analyze a f inite e l e m en t m e th o d useful for solving a large class of t hi n shell prob l e ms, and to show in practice how to use this method to simulate an arch dam prob lem. The first objective is developed in Part I. We record the defi- tion of a general thin shell model corresponding to the W.T. KOlTER linear equations and we show the existence and the uniqueness for a solution. By using a co nform ing fi nite e l e m ent me t hod , we associate a family of discrete problems to the continuous problem ; prove the convergence of the method ; and obtain error estimates between exact and approximate solutions. We then describe the impl em enta t ion of some specific conforming methods. The second objective is developed in Part 2. It consists of applying these finite element methods in the case of a representative practical situation that is an arc h dam pro b le m. This kind of problem is still of great interest, since hydroelectric plants permit the rapid increase of electricity production during the day hours of heavy consumption. This regulation requires construction of new hydroelectric plants on suitable sites, as well as permanent control of existing dams that may be enlightened by numerical stress analysis .