During the early 1960s, scientists began to envision problem-solving computing environments not only powerful enough to solve complex problems but also able to interact with users on human terms. While many tried to create PSEs over the next few years, by the early 1970s they had abandoned almost all of these attempts. Technology could not yet support PSEs in computational science. But the dream of the 1960s can be the reality of the 1990s: high-performance computers combined with better understanding of computing and computational science have put PSEs well within our reach. The term 'problem-solving environment' means different things to different people. A PSE is a computer system that provides all the computational facilities necessary to solve a target class of problems. These features include advanced solution methods, automatic or semi-automatic selection of solution methods, and ways to easily incorporate novel solution methods. Simple PSEs appeared early in computing without being recognized as such. Some of the capabilities of future problem-solving environments seem like science fiction, but whatever form they eventually take, their scientific and economic impact will be enormous.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
A population of seven non-overlapping domain decomposition methods for solving elliptic differential equations are viewed and formulated as iterated interface relaxation procedures. A comprehensive review of the underlying mathematical ideas and the computational characteristics is given. The existing theoretical results are also reviewed and high level descriptions of the various algorithms are presented. The effectiveness of these methods on various differential problems is investigated by presenting and discussing preliminary performance evaluation data.
ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTMagnetic Resonance Spectroscopy. The Configurational Stability of Primary Grignard Reagents. 3,3-Dimethylbutylmagnesium Chloride1George M. Whitesides, Michal Witanowski, and John D. RobertsCite this: J. Am. Chem. Soc. 1965, 87, 13, 2854–2862Publication Date (Print):July 1, 1965Publication History Published online1 May 2002Published inissue 1 July 1965https://doi.org/10.1021/ja01091a014RIGHTS & PERMISSIONSArticle Views232Altmetric-Citations56LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1023 KB) Get e-Alertsclose Get e-Alerts
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Two distinct mechanisms of crack initiation and advance by void growth have been identified in the literature on the mechanics of ductile fracture. One is the interaction a single void with the crack tip characterizing initiation and the subsequent void by void advance of the tip. This mechanism is represented by the early model of Rice and Johnson and the subsequent more detailed numerical computations of McMeeking and coworkers on a single void interacting with a crack tip. The second mechanism involves the simultaneous interaction of multiple voids on the plane ahead of the crack tip both during initiation and in subsequent crack growth. This mechanism is revealed by models with an embedded fracture process zone, such as those developed by Tvergaard and Hutchinson. While both mechanisms are based on void nucleation, growth and coalescence, the inferences from them with regard to crack growth initiation and growth are quantitatively different. The present paper provides a formulation and numerical analysis of a two-dimensional plane strain model with multiple discrete voids located ahead of a pre-existing crack tip. At initial void volume fractions that are sufficiently low, initiation and growth is approximately represented by the void by void mechanism. At somewhat higher initial void volume fractions, a transition in behavior occurs whereby many voids ahead of the tip grow at comparable rates and their interaction determines initiation toughness and crack growth resistance. The study demonstrates that improvements to be expected in fracture toughness by reducing the population of second phase particles responsible for nucleating voids cannot be understood in terms of trends of one mechanism alone. The transition from one mechanism to the other must be taken into account.