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Dispersive Shallow Water Waves
This monograph presents cutting-edge research on dispersive wave modelling, and the numerical methods used to simulate the propagation and generation of long surface water waves. Including both an overview of existing dispersive models, as well as recent breakthroughs, the authors maintain an ideal balance between theory and applications. From modelling tsunami waves to smaller scale coastal processes, this book will be an indispensable resource for those looking to be brought up-to-date in this active area of scientific research. Beginning with an introduction to various dispersive long wave models on the flat space, the authors establish a foundation on which readers can confidently approa...
Computational Science and High Performance Computing IV
This volume contains 27 contributions to the Forth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing presented in October 2009 in Freiburg, Germany. The workshop was organized jointly by the High Performance Computing Center Stuttgart (HLRS), the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS) and the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg) The contributions range from computer science, mathematics and high performance computing to applications in mechanical and aerospace engineering. They show a wealth of theoretical work and simulation experience with a potential of bringing together theoretical mathematical modelling and usage of high performance computing systems presenting the state of the art of computational technologies.
Subaqueous Mass Movements and Their Consequences
The challenges facing submarine mass movement researchers and engineers are plentiful and exciting. This book follows several high-profile submarine landslide disasters that have reached the world’s attention over the past few years. For decades, researchers have been mapping the world’s mass movements. Their significant impacts on the Earth by distributing sediment on phenomenal scales is undeniable. Their importance in the origins of buried resources has long been understood. Their hazard potential ranges from damaging to apocalyptic, frequently damaging local infrastructure and sometimes devastating whole coastlines. Moving beyond mapping advances, the subaqueous mass movement scientists and practitioners are now also focussed on assessing the consequences of mass movements, and the measurement and modelling of events, hazard analysis and mitigation. Many state-of-the-art examples are provided in this book, which is produced under the auspices of the United Nations Educational, Scientific and Cultural Organisation Program S4SLIDE (Significance of Modern and Ancient Submarine Slope LandSLIDEs).
Numerical Methods for Hyperbolic Equations
Numerical Methods for Hyperbolic Equations is a collection of 49 articles presented at the International Conference on Numerical Methods for Hyperbolic Equations: Theory and Applications (Santiago de Compostela, Spain, 4-8 July 2011). The conference was organized to honour Professor Eleuterio Toro in the month of his 65th birthday. The topics cover
Subaqueous Mass Movements and Their Consequences
Subaqueous landslides are a common slope process in the geological record. In addition to their geological significance, they pose a risk to offshore infrastructure and can trigger destructive tsunamis affecting coastal communities. This volume offers a multi-disciplinary approach to document better the still poorly understood frequency and dynamics of subaqueous landslides.
Numerical Modeling Of Ocean Dynamics
While there are several excellent books dealing with numerical analysis and analytical theory, one has to practically sift through hundreds of references. This monograph is an attempt to partly rectify this situation. It aims to introduce the application of finite-difference methods to ocean dynamics as well as review other complex methods. Systematically presented, the monograph first gives a detailed account of the basics and then go on to discuss the various applications. Recognising the impossibility of covering the entire field of ocean dynamics, the writers have chosen to focus on transport equations (diffusion and advection), shallow water phenomena — tides, storm surges and tsunamis, three-dimensional time dependent oceanic motion, natural oscillations, and steady state phenomena. The many aspects covered by this book makes it an indispensable handbook and reference source to both professionals and students of this field.
Fundamentals of Numerical Reservoir Simulation
The use of numerical reservoir simulation with high-speed electronic computers has gained wide acceptance throughout the petroleum industry for making engineering studies of a wide variety of oil and gas reservoirs throughout the world. These reservoir simulators have been designed for use by reservoir engineers who possess little or no background in the numerical mathematics upon which they are based. In spite of the efforts to improve numerical methods to make reservoir simulators as reliable, efficient, and automatic as possible, the user of a simulator is faced with a myriad of decisions that have nothing to do with the problem to be solved. This book combines a review of some basic reservoir mechanics with the derivation of the differential equations that reservoir simulators are designed to solve.
An Elastic Model for Volcanology
This monograph presents a rigorous mathematical framework for a linear elastic model arising from volcanology that explains deformation effects generated by inflating or deflating magma chambers in the Earth’s interior. From a mathematical perspective, these modeling assumptions manifest as a boundary value problem that has long been known by researchers in volcanology, but has not, until now, been given a thorough mathematical treatment. This mathematical study gives an explicit formula for the solution of the boundary value problem which generalizes the few well-known, explicit solutions found in geophysics literature. Using two distinct analytical approaches—one involving weighted Sobolev spaces, and the other using single and double layer potentials—the well-posedness of the elastic model is proven. An Elastic Model for Volcanology will be of particular interest to mathematicians researching inverse problems, as well as geophysicists studying volcanology.
The Water Waves Problem
This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.
Inverse Problems
The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B. A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography. The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level.
