numerical solution of partial differential equations iliev et al 2013 06 18 Cấu trúc dữ liệu và giải thuật

Springer Proceedings in Mathematics & Statistics Oleg P Iliev · Svetozar D Margenov Peter D Minev · Panayot S Vassilevski Ludmil T Zikatanov Editors Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications In Honor of Professor Raytcho Lazarov’s 40 Years of Research in Computational Methods and Applied Mathematics CuuDuongThanCong.com Springer Proceedings in Mathematics & Statistics Volume 45 For further volumes: http://www.springer.com/series/10533 CuuDuongThanCong.com Springer Proceedings in Mathematics & Statistics This book series features volumes composed of select contributions from workshops and conferences in all areas of current research in mathematics and statistics, including OR and optimization In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematical and statistical research today CuuDuongThanCong.com Oleg P Iliev • Svetozar D Margenov Peter D Minev • Panayot S Vassilevski Ludmil T Zikatanov Editors Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications In Honor of Professor Raytcho Lazarov’s 40 Years of Research in Computational Methods and Applied Mathematics 123 CuuDuongThanCong.com Editors Oleg P Iliev Department of Flow and Material Simulation Fraunhofer Institute for Industrial Mathematics Kaiserslautern, Germany Peter D Minev Department of Mathematical and Statistical Sciences University of Alberta Edmonton, AB, Canada Svetozar D Margenov Institute for Parallel Processing Bulgarian Academy of Sciences Sofia, Bulgaria Panayot S Vassilevski Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore, CA, USA Ludmil T Zikatanov Department of Mathematics The Pennsylvania State University University Park, PA, USA ISSN 2194-1009 ISSN 2194-1017 (electronic) ISBN 978-1-4614-7171-4 ISBN 978-1-4614-7172-1 (eBook) DOI 10.1007/978-1-4614-7172-1 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013939589 © Springer Science+Business Media New York 2013 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer Permissions for use may be obtained through RightsLink at the Copyright Clearance Center Violations are liable to prosecution under the respective Copyright Law The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made The publisher makes no warranty, express or implied, with respect to the material contained herein Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) CuuDuongThanCong.com Preface The design and implementation of numerical models that accurately capture the appropriate model features of complex physical systems described by time-dependent coupled systems of nonlinear PDEs present one of the main challenges in today’s scientific computing This volume integrates works by experts in computational mathematics, and its applications focused on the modern algorithms which are in the core of accurate modeling: adaptive finite-element methods, conservative finite-difference and finite-volume methods, and multilevel solution techniques Fundamental theoretical results are revisited in several survey articles, and new techniques in numerical analysis are introduced Applications showing the efficiency, reliability, and robustness of the algorithms in porous media, structural mechanics, and electromagnetism are presented The volume consists of papers prepared in the context of the International Symposium “Numerical Solution of Partial Differential Equations: Theory, Algorithms and their Applications” in honor of Professor Raytcho Lazarov’s 40 years of research in computational methods and applied mathematics and on the occasion of his 70th birthday The symposium was organized and sponsored by the Institute of Information and Communication Technologies (IICT), Bulgarian Academy of Sciences (BAS), Lawrence Livermore National Laboratory (USA), and Department of Mathematics, The Pennsylvania State University (USA) Members of the program committee are Oleg Iliev (ITWM Fraunhofer, Kaiserslautern, Germany), Peter Minev (University of Alberta, Canada), Svetozar Margenov (Institute of Information and Communication Technologies, BAS), Panayot Vassilevski (Lawrence Livermore National Laboratory, USA), and Ludmil Zikatanov (The Pennsylvania State University, USA) The list of participants who were invited to contribute and authored or coauthored a paper included in this volume is: Owe Axelsson (Uppsala University, Sweden; KAU, Saudi Arabia; Academy of Sciences, Czech Republic) Carsten Carstensen (Humboldt University of Berlin, Germany) v CuuDuongThanCong.com vi Preface Panagiotis Chatzipantelidis (University of Crete, Greece) Ivan Dimov (IICT, Bulgarian Academy of Sciences, Bulgaria) Stefka Dimova (Sofia University, Bulgaria) Oleg Iliev (ITWM Fraunhofer, Germany) Ulrich Langer (Johannes Kepler University and RICAM, Austria) Svetozar Margenov (IICT, Bulgarian Academy of Sciences, Bulgaria) Peter Minev (University of Alberta, Canada) Joseph Pasciak (Texas A&M, USA) Petr Vabishchevich (IMM, Russian Academy of Sciences, Russia) Panayot Vassilevski (Lawrence Livermore National Laboratory, USA) Junping Wang (National Science Foundation, USA) Joerg Willems (RICAM, Austrian Academy of Sciences, Austria) Ludmil Zikatanov (The Pennsylvania State University, USA) The editors are grateful to the Institute of Information and Communication Technologies (IICT), Bulgarian Academy of Sciences, the Lawrence Livermore National Laboratory, and the Department of Mathematics at Penn State for the support of the symposium On behalf of all the contributors, we dedicate this volume to our teacher, friend, and colleague Raytcho Lazarov Kaiserslautern, Germany Sofia, Bulgaria Edmonton, AB, Canada Livermore, CA, USA University Park, PA, USA CuuDuongThanCong.com Oleg P Iliev Svetozar D Margenov Peter D Minev Panayot S Vassilevski Ludmil T Zikatanov Preface vii On the Occasion of the 70th Anniversary of Raytcho Lazarov With great pleasure we introduce this collection of papers in honor of Raytcho Lazarov, professor at the Texas A&M University and Doctor of Sciences and Doctor Honoris Causa of the “St Kliment Ohridski” University of Sofia, Bulgaria Raytcho Lazarov is a computational mathematician of extraordinary depth and breadth whose work has had and continues to have exceptional impact on computational and applied mathematics He has authored or coauthored more than 200 journal publications and books spanning all major areas in computational mathematics and bridging mathematical theory and scientific computing with sciences and engineering Raytcho Lazarov was born in Kardzhali (Ã Ö Ð ), Bulgaria, on January 23, 1943 He graduated from “St Antim I” High School in Zlatograd ( Ð ØĨ Ư ) and in 1961 went to Sofia University “St Kliment Ohridski” to continue his studies in the Department of Mathematics (industrial profile) During his first year as a college student, Raytcho demonstrated his talent for mathematics, and his dedication to study it, and he was selected to continue his education at the University of Wroclaw in Poland in 1963 In Wroclaw Raytcho was able to interact with many distinguished mathematicians from the Polish mathematical school and received first-rate mathematical training In 1968 Raytcho Lazarov was admitted to the PhD program of the Moscow State University As a graduate student in Moscow, he studied and worked under the supervision of Academician A A Samarskii who was one of the best contemporary computational mathematicians in the world Lazarov’s thesis work was on “Finite difference schemes for elasticity problems in curvilinear domains,” among the first rigorous studies of numerical approximations of problems in structural mechanics After receiving his PhD degree in 1972, Raytcho Lazarov worked as a research associate and senior research associate in the Institute of Mathematics (IM) of the Bulgarian Academy of Sciences (BAS) until 1987 During this time he established himself as one of the leading experts in numerical analysis In 1976 Raytcho Lazarov visited the Rutherford Laboratory in Didcot, UK, for one year, and this visit had notable impact on his future research His focus shifted to the theory and applications of the finite element method (FEM) which remains to be his primary field of research to this day Lazarov earned the degree of doctor of sciences in June 1982 with a thesis on “Error estimates of the difference schemes for some problems of mathematical physics having generalized solutions.” This thesis contained several breakthrough results, which were published in more than 10 papers and formed the basis for a research monograph that he coauthored with A A Samarskii and V Makarov, Difference Schemes for Differential Equations Having Generalized Solutions, which was published in 1987 In 1986 Lazarov’s superb scientific achievements earned him the title of a professor of mathematics at the Institute of Mathematics of the Bulgarian Academy of Sciences, a position that he continues to hold to this day His leadership ability CuuDuongThanCong.com viii Preface was also recognized by his colleagues, and in 1985 he became the head of the Laboratory on Numerical Analysis, BAS, and a deputy-director of the Laboratory on Parallel Algorithms and High Performance Computer Systems, BAS In 1986 Lazarov became deputy-director of the newly established Center for Informatics and Computer Technology (CICT) at BAS This was one of the first interdisciplinary centers worldwide for mathematical research on advanced algorithms for the emerging parallel computer systems He played a crucial role in hiring a cohort of the best young applied mathematicians in Bulgaria—Djidjev, Vassilevski, Margenov, Dimov, Bochev, and many more In fact, Raytcho Lazarov’s leadership was the key in making CICT one of the best places for large-scale scientific computing and parallel algorithms In 1984 Raytcho initiated a series of international conferences on numerical methods and applications in Sofia, Bulgaria, which helped to publicize the results and achievements of the Bulgarian numerical analysts and to integrate them into the international community Such accomplishments were noticed by his colleagues around the world Vidar Thom´ee helped Raytcho to get a visiting position at the University of Wyoming in 1987 This turned out to be a critical point in Lazarov’s career In Wyoming he met and befriended Richard Ewing who at that time was a director of the Enhanced Oil Recovery Institute (EORI) and the Institute of Scientific Computation (ISC) at the University of Wyoming During his stay in Laramie in 1988–1992, Lazarov worked on superconvergence and local refinement techniques for mixed FE methods During that time Raytcho initiated many collaborations and friendships with prominent mathematicians such as Jim Bramble, Joe Pasciak, Panayot Vassilevski, Junping Wang, Tom Russell, Yuri Kuznetsov, Steve McCormick, Tom Manteuffel, and Owe Axelsson At that time Raytcho Lazarov led the development of algorithms based on the Bramble–Ewing–Pasciak–Schatz (BEPS) preconditioner and locally refined mixed FE and finite-volume methods that were also implemented in the EORI proprietary codes The friendship and collaboration with Dick Ewing initiated another change in Raytcho’s career, and in 1992 he moved to Texas A&M University as a professor of mathematics, a position that he continues to hold now This coincided with the establishment of the Institute of Scientific Computation (ISC) at Texas A&M under the directorship of Richard Ewing, which quickly attracted a team of worldrenowned experts in this area like J Bramble, J Pasciak, R Lazarov, and, more recently, Y Efendiev, J.-L Guermond, G Petrova, B Popov, W Bangerth, and A Bonito The work they did in the last 20 years on computational mathematics and its applications in flows in porous media, multiphysics problems, modeling of fluids, structures and their interactions, etc had a significant impact on these and in other research areas Raytcho’s pivotal role in this research is well known from his results on least-squares FEM; discontinuous Galerkin methods; multigrid, multilevel, and multiscale methods, mixed FEM, and more recently fractional order partial differential equations In recognition of his achievements Raytcho Lazarov has been awarded several honorary titles and degrees: the medal “St Kl Ohridski” with blue ribbon (2003– the highest honors given by Sofia University, Bulgaria, to scientists); Doctor Honoris CuuDuongThanCong.com Preface ix Causa of Sofia University “St Kl Ohridski” (2006); the medal of the Institute of Mathematics, Bulgarian Academy of Sciences 2008; Pichoridis Distinguished Lectureship, University of Crete, Greece (2008); and Erasmus Mundus Visiting Scholar Award, University of Kaiserslautern (2008) Most recently he was named a recipient of the medal of the Bulgarian Academy of Sciences “Marin Drinov” with ribbon (2013), which is given to scholars for outstanding contributions in the advancement of science During his career Lazarov has held visiting positions and contributed to advancement of research in many institutions around the globe: Joint Institute for Nuclear Research in Dubna, Russia (1980); Australian National University, Canberra (1990); Mittag Leffler Institute of Mathematics, Stockholm, Sweden (1998); University of Linz and RICAM, Austria (2005); Fraunhofer Institute of Industrial Mathematics, Kaiserslautern, Germany (2006); Lawrence Livermore National Laboratory (regularly from 1998 to 2010); and KAUST in Saudi Arabia (2008–2013) He is a member of the editorial board of five international journals and a number of conference proceedings, and he is also serving on the scientific committees of several international conferences Raytcho Lazarov is an outstanding scholar, and his work has had a profound impact on mathematics and other fields of science and engineering during the last four decades His extraordinary personality, with strict academic integrity requirements for himself and his collaborators complemented by truly compassionate care about their needs, has influenced the professional and personal development of those who have had a chance to work with him The teams which he has created over the years combined research interests, philosophy, and personal friendship, and they withstood the test of time We congratulate Raytcho on the occasion of his 70th birthday and wish him the best of health and enjoyment in his personal life and in continuing and expanding his successful research achievements Kaiserslautern, Germany Sofia, Bulgaria Edmonton, AB, Canada Livermore, CA, USA University Park, PA, USA CuuDuongThanCong.com Oleg P Iliev Svetozar D Margenov Peter D Minev Panayot S Vassilevski Ludmil T Zikatanov ... oleg .iliev@ itwm.fraunhofer.de; heiko.andrae@itwm.fraunhofer.de O.P Iliev et al (eds.), Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications, Springer Proceedings... Livermore, CA 94551, USA e-mail: panayot@llnl.gov O.P Iliev et al (eds.), Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications, Springer Proceedings... ? ?Numerical Solution of Partial Differential Equations: Theory, Algorithms and their Applications” in honor of Professor Raytcho Lazarov’s 40 years of research in computational methods and applied