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This special issue collects papers which develop and update methodologies and results illustrated at the International Workshop MASCOT01--1st Meeting on Applied Scientific Computing and Tools-- Grid Generation, Approximated Solutions and Visualization, held in Rome, October 22-24, 2001 at the Istituto per le Applicazioni del Calcolo (IAC). The meeting was supported by IMACS, the International Association for Mathematics and Computers in Simulation and ISGG, the International Society of Grid Generation and co-sponsored by the Italian National Group of Scientific Computing (GNCS-- Gruppo Nazionale di Calcolo Scientifico) and the Italian Society for Applied and Industrial Mathematics (SIMAI--Societa' Italiana per la Matematica Applicata e Industriale). Publication of the MASCOT01 Proceedings followed the Workshop, and in this issue, extensions and new results are presented. MASCOT meetings are intended to become a forum to discuss a wide spectrum of topics concerning scientific computing as applied to the effective solution of complex application problems. Thus topics range from theoretical to application inquiries and results, and include investigation in approximation and interpolation, advances in numerical grid generation, development of effective solvers of partial differential equations (PDEs) and the design of user-friendly and effective software tools. Modern and innovative modeling and simulation environments combine a large amount of expertise to handle complex and multidisciplinary application problems.