This book presents the first survey of the Localized Orthogonal Decomposition (LOD) method, a pioneering approach for the numerical homogenization of partial differential equations with multiscale data beyond periodicity and scale separation. The authors provide a careful error analysis, including previously unpublished results, and a complete implementation of the method in MATLAB. They also reveal how the LOD method relates to classical homogenization and domain decomposition. Illustrated with numerical experiments that demonstrate the significance of the method, the book is enhanced by a survey of applications including eigenvalue problems and evolution problems. Numerical Homogenization by Localized Orthogonal Decomposition is appropriate for graduate students in applied mathematics, numerical analysis, and scientific computing. Researchers in the field of computational partial differential equations will find this self-contained book of interest, as will applied scientists and engineers interested in multiscale simulation.
Inside the 3rd edition of this esteemed masterwork, hundreds of the most distinguished authorities from around the world provide today's best answers to every question that arises in your practice. They deliver in-depth guidance on new diagnostic approaches, operative technique, and treatment option, as well as cogent explanations of every new scientific concept and its clinical importance. With its new streamlined, more user-friendly, full-color format, this 3rd edition makes reference much faster, easier, and more versatile. More than ever, it's the source you need to efficiently and confidently overcome any clinical challenge you may face. Comprehensive, authoritative, and richly illustrated coverage of every scientific and clinical principle in ophthalmology ensures that you will always be able to find the guidance you need to diagnose and manage your patients' ocular problems and meet today's standards of care. Updates include completely new sections on "Refractive Surgery" and "Ethics and Professionalism"... an updated and expanded "Geneitcs" section... an updated "Retina" section featuring OCT imaging and new drug therapies for macular degeneration... and many other important new developments that affect your patient care. A streamlined format and a new, more user-friendly full-color design - with many at-a-glance summary tables, algorithms, boxes, diagrams, and thousands of phenomenal color illustrations - allows you to locate the assistance you need more rapidly than ever.
Thoroughly updated, this state-of-the-art text covers the diagnosis and treatment of all major diseases and disorders of the eye. Generously illustrated with high quality clinical photographs and excellent drawings. Includes high-tech diagnostic and therapeutic information as well as a comprehensive glossary and hands, easy-to-use tables. (Midwest).
This book presents the first survey of the Localized Orthogonal Decomposition (LOD) method, a pioneering approach for the numerical homogenization of partial differential equations with multiscale data beyond periodicity and scale separation. The authors provide a careful error analysis, including previously unpublished results, and a complete implementation of the method in MATLAB. They also reveal how the LOD method relates to classical homogenization and domain decomposition. Illustrated with numerical experiments that demonstrate the significance of the method, the book is enhanced by a survey of applications including eigenvalue problems and evolution problems. Numerical Homogenization by Localized Orthogonal Decomposition is appropriate for graduate students in applied mathematics, numerical analysis, and scientific computing. Researchers in the field of computational partial differential equations will find this self-contained book of interest, as will applied scientists and engineers interested in multiscale simulation.
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