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 Diff erential Equations: Theory, Algorithms, and Their Applications In Honor of Professor Raytcho Lazarov’s 40 Years of Research in Computational Methods and Applied Mathematics Springer Proceedings in Mathematics & Statistics Volume 45 Forfurthervolumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, 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 mathematicalandstatisticalresearchtoday. 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 Editors OlegP.Iliev SvetozarD.Margenov DepartmentofFlowandMaterial InstituteforParallelProcessing Simulation BulgarianAcademyofSciences FraunhoferInstitute Sofia,Bulgaria forIndustrialMathematics Kaiserslautern,Germany PanayotS.Vassilevski CenterforAppliedScientific PeterD.Minev Computing DepartmentofMathematicaland LawrenceLivermoreNational StatisticalSciences Laboratory UniversityofAlberta Livermore,CA,USA Edmonton,AB,Canada LudmilT.Zikatanov DepartmentofMathematics ThePennsylvaniaStateUniversity UniversityPark,PA,USA ISSN2194-1009 ISSN2194-1017(electronic) ISBN978-1-4614-7171-4 ISBN978-1-4614-7172-1(eBook) DOI10.1007/978-1-4614-7172-1 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2013939589 ©SpringerScience+BusinessMediaNewYork2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection 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’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface Thedesignandimplementationofnumericalmodelsthataccuratelycapturetheap- propriatemodelfeaturesofcomplexphysicalsystemsdescribedbytime-dependent coupledsystems of nonlinearPDEs presentone of the main challengesin 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. Fundamentaltheoreticalresultsarerevisitedinseveralsurveyarticles,andnewtech- niques in numerical analysis are introduced. Applications showing the efficiency, reliability,androbustnessofthealgorithmsinporousmedia,structuralmechanics, andelectromagnetismarepresented. The volume consists of papers prepared in the context of the International Symposium “Numerical Solution of Partial Differential Equations: Theory, Algo- rithmsandtheirApplications”inhonorofProfessorRaytchoLazarov’s40yearsof researchincomputationalmethodsandappliedmathematicsandontheoccasionof his70thbirthday. The symposium was organized and sponsored by the Institute of Information andCommunicationTechnologies(IICT),BulgarianAcademyofSciences(BAS), LawrenceLivermoreNationalLaboratory(USA),andDepartmentofMathematics, ThePennsylvaniaStateUniversity(USA).Membersoftheprogramcommitteeare OlegIliev(ITWMFraunhofer,Kaiserslautern,Germany),PeterMinev(University of Alberta, Canada), Svetozar Margenov (Institute of Information and Commu- nication Technologies, BAS), Panayot Vassilevski (Lawrence Livermore National Laboratory, USA), and Ludmil Zikatanov (The Pennsylvania State University, USA). Thelistofparticipantswhowereinvitedtocontributeandauthoredorcoauthored apaperincludedinthisvolumeis: Owe Axelsson(UppsalaUniversity,Sweden;KAU, SaudiArabia;Academyof Sciences,CzechRepublic) CarstenCarstensen(HumboldtUniversityofBerlin,Germany) v vi Preface PanagiotisChatzipantelidis(UniversityofCrete,Greece) IvanDimov(IICT,BulgarianAcademyofSciences,Bulgaria) StefkaDimova(SofiaUniversity,Bulgaria) OlegIliev(ITWMFraunhofer,Germany) UlrichLanger(JohannesKeplerUniversityandRICAM,Austria) SvetozarMargenov(IICT,BulgarianAcademyofSciences,Bulgaria) PeterMinev(UniversityofAlberta,Canada) JosephPasciak(TexasA&M,USA) PetrVabishchevich(IMM,RussianAcademyofSciences,Russia) PanayotVassilevski(LawrenceLivermoreNationalLaboratory,USA) JunpingWang(NationalScienceFoundation,USA) JoergWillems(RICAM,AustrianAcademyofSciences,Austria) LudmilZikatanov(ThePennsylvaniaStateUniversity,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 supportofthesymposium. Onbehalfofallthecontributors,wededicatethisvolumetoourteacher,friend, andcolleagueRaytchoLazarov. Kaiserslautern,Germany OlegP.Iliev Sofia,Bulgaria SvetozarD.Margenov Edmonton,AB,Canada PeterD.Minev Livermore,CA,USA PanayotS.Vassilevski UniversityPark,PA,USA LudmilT.Zikatanov Preface vii Onthe Occasionof the70th Anniversaryof RaytchoLazarov With great pleasure we introduce this collection of papers in honor of Raytcho Lazarov,professorattheTexasA&MUniversityandDoctorofSciencesandDoctor HonorisCausaofthe“St.KlimentOhridski”UniversityofSofia,Bulgaria. Raytcho Lazarov is a computational mathematician of extraordinary depth and breadth whose work has had and continues to have exceptional impact on computationalandappliedmathematics.Hehasauthoredorcoauthoredmorethan 200 journal publications and 4 books spanning all major areas in computational mathematics and bridging mathematical theory and scientific computing with sciencesandengineering. RaytchoLazarovwasborninKardzhali( ),Bulgaria,onJanuary23, 1943.Hegraduatedfrom“St.AntimI”High(cid:0)S(cid:2)ch(cid:3)o(cid:4)o(cid:5)l(cid:6)in(cid:7)Z(cid:8)latograd( )and in 1961 went to Sofia University “St. Kliment Ohridski” to con(cid:9)tin(cid:7)u(cid:6)e(cid:10)(cid:11)h(cid:12)i(cid:3)s(cid:6)s(cid:4)tudies in the Department of Mathematics (industrial profile). During his first year as a collegestudent,Raytchodemonstratedhistalentformathematics,andhisdedication 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-ratemathematicaltraining. In1968RaytchoLazarovwasadmittedtothePhDprogramoftheMoscowState University. As a graduate student in Moscow, he studied and worked under the supervisionofAcademicianA.A.Samarskiiwhowasoneofthebestcontemporary computationalmathematiciansin the world. Lazarov’sthesis workwas on “Finite differenceschemesforelasticityproblemsincurvilineardomains,”amongthefirst rigorousstudiesofnumericalapproximationsofproblemsinstructuralmechanics. AfterreceivinghisPhDdegreein1972,RaytchoLazarovworkedasaresearch associate andseniorresearchassociate in theInstitute ofMathematics(IM)ofthe BulgarianAcademyofSciences(BAS)until1987.Duringthistimeheestablished 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 visithadnotableimpactonhisfutureresearch.Hisfocusshiftedtothetheoryand applicationsof the finite elementmethod (FEM) which remainsto be his primary fieldofresearchtothisday. 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, whichwaspublishedin1987. In 1986 Lazarov’s superb scientific achievements earned him the title of a professorofmathematicsattheInstituteofMathematicsoftheBulgarianAcademy ofSciences, a positionthathe continuesto hold to thisday.His leadershipability viii Preface was also recognized by his colleagues, and in 1985 he became the head of the Laboratoryon NumericalAnalysis, BAS, and a deputy-directorof the Laboratory on Parallel Algorithms and High Performance Computer Systems, BAS. In 1986 Lazarov became deputy-director of the newly established Center for Informatics andComputerTechnology(CICT)atBAS.Thiswasoneofthefirstinterdisciplinary centersworldwideformathematicalresearchonadvancedalgorithmsfortheemerg- ing 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 keyinmakingCICToneofthebestplacesforlarge-scalescientificcomputingand parallelalgorithms.In1984Raytchoinitiatedaseriesofinternationalconferences onnumericalmethodsandapplicationsinSofia,Bulgaria,whichhelpedtopublicize the results and achievements of the Bulgarian numerical analysts and to integrate themintotheinternationalcommunity. Such accomplishmentswere noticedby hiscolleaguesaroundthe world. Vidar Thome´ehelpedRaytchotogetavisitingpositionattheUniversityofWyomingin 1987.ThisturnedouttobeacriticalpointinLazarov’scareer.InWyominghemet andbefriendedRichardEwingwhoatthattimewasadirectoroftheEnhancedOil RecoveryInstitute(EORI)andtheInstituteofScientificComputation(ISC) atthe UniversityofWyoming.DuringhisstayinLaramiein1988–1992,Lazarovworked onsuperconvergenceandlocalrefinementtechniquesformixedFEmethods.During that time Raytcho initiated many collaborations and friendships with prominent mathematicians such as Jim Bramble, Joe Pasciak, Panayot Vassilevski, Junping Wang,TomRussell,YuriKuznetsov,SteveMcCormick,TomManteuffel,andOwe Axelsson. At that time Raytcho Lazarov led the developmentof algorithmsbased ontheBramble–Ewing–Pasciak–Schatz(BEPS)preconditionerandlocallyrefined mixed FE and finite-volume methods that were also implemented in the EORI proprietarycodes. The friendship and collaboration with Dick Ewing initiated another change in Raytcho’scareer, and in 1992he movedto 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 underthedirectorshipofRichardEwing,whichquicklyattractedateamofworld- renowned 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 fromhisresultsonleast-squaresFEM;discontinuousGalerkinmethods;multigrid, multilevel,andmultiscalemethods,mixedFEM,andmorerecentlyfractionalorder partialdifferentialequations. In recognition of his achievements Raytcho Lazarov has been awarded several honorarytitlesanddegrees:the medal“St. Kl.Ohridski”with blueribbon(2003– thehighesthonorsgivenbySofiaUniversity,Bulgaria,toscientists);DoctorHonoris 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” withribbon(2013),whichisgiventoscholarsforoutstandingcontributionsinthe advancementofscience. DuringhiscareerLazarovhasheldvisitingpositionsandcontributedtoadvance- mentofresearchin manyinstitutionsaroundthe globe:JointInstitute forNuclear ResearchinDubna,Russia(1980);AustralianNationalUniversity,Canberra(1990); Mittag Leffler Institute of Mathematics, Stockholm, Sweden (1998); University of Linz and RICAM, Austria (2005); Fraunhofer Institute of Industrial Mathe- matics,Kaiserslautern,Germany(2006);LawrenceLivermoreNationalLaboratory (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 severalinternationalconferences. RaytchoLazarovisanoutstandingscholar,andhisworkhashadaprofoundim- pactonmathematicsandotherfieldsofscienceandengineeringduringthelastfour decades.Hisextraordinarypersonality,withstrictacademicintegrityrequirements forhimselfandhiscollaboratorscomplementedbytrulycompassionatecareabout theirneeds,hasinfluencedtheprofessionalandpersonaldevelopmentofthosewho 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 withstoodthetestoftime. WecongratulateRaytchoontheoccasionofhis70thbirthdayandwishhimthe bestof healthandenjoymentin his personallife andin continuingandexpanding hissuccessfulresearchachievements. Kaiserslautern,Germany OlegP.Iliev Sofia,Bulgaria SvetozarD.Margenov Edmonton,AB,Canada PeterD.Minev Livermore,CA,USA PanayotS.Vassilevski UniversityPark,PA,USA LudmilT.Zikatanov