Boris N. Khoromskij

Gabriel Wittum

During the last decade essential progress has been achieved in the analysis and implementation of multilevel/rnultigrid and domain decomposition methods to explore a variety of real world applications. An important trend in mod ern numerical simulations is the quick improvement of computer technology that leads to the well known paradigm (see, e. g. , [78,179]): high-performance computers make it indispensable to use numerical methods of almost linear complexity in the problem size N, to maintain an adequate scaling between the computing time and improved computer facilities as N increases. In the h-version of the finite element method (FEM), the multigrid iteration real izes an O(N) solver for elliptic differential equations in a domain n c IRd d with N = O(h- ) , where h is the mesh parameter. In the boundary ele ment method (BEM) , the traditional panel clustering, fast multi-pole and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the boundary. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.

Numerical Solution of Elliptic Differential Equations by Reduction to the Interface

Andreas Dengel

Olga Zlatkin-Troitschanskaia

While information and communication technology has a vast influence on our lives, little is understood about its effects on the way we learn. In the Age of Information, students – consciously or not – are learning in diverse formal and informal environments from a broad variety of sources, with scientific knowledge competing against unfounded assertions, and misinformation and biased data spreading through social and mass media. The Positive Learning in the Age of Information (PLATO) program illustrated by the contributions in this book unites outstanding and highly innovative expertise on the fundamentals of information processing and human learning to investigate a new paradigm of positive learning as a vital, morally and ethically oriented approach, which is of existential importance to maintaining the civilization standards of a modern society in the digital age.

A Blessing or a Curse?

Positive Learning in the Age of Information

C.A. Brebbia

Alexander Peters

Bruno Herrling

Udo Meissner

William G. Gray

George F. Pinder

This two-volume work constitutes the edited proceedings of the Tenth International Conference on Computational Methods in Water Resources (formerly Finite Elements in Water Resources), held at Heidelberg University, Germany in July 1994, organized jointly by Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (Interdisciplinary Center for Scientific Computing) and Sonderforschungsbereich 359 of Heidelberg University and the Institute of Supercomputing and Applied Mathematics of IBM Heidelberg. The 1994 proceedings present the work of authors from 23 countries. Numerical methods, mathematical modeling and applications to subsurface and surface hydrology are covered by a wide variety of papers. Issues of formation description and modeling, including parameter estimation, heterogeneity, and scaling up continue to attract the attention of a large number of researchers. Several papers edited in this book concern the solution of the Navier--Stokes equations. For applied mathematicians, engineers and geoscientists working in the fields of numerical methods, hydrology, ecology, water resources planning and management, remediation design, porous media research, petroleum engineering and coastal engineering.

Computational Methods in Water Resources X

Gabriel Wittum

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