Finite Difference Methods,Theory and Applications: 6th International Conference, FDM 2014, Lozenetz, Bulgaria, June 18-23, 2014, Revised Selected Papers PDF
Preview Finite Difference Methods,Theory and Applications: 6th International Conference, FDM 2014, Lozenetz, Bulgaria, June 18-23, 2014, Revised Selected Papers
Ivan Dimov István Faragó Lubin Vulkov (Eds.) 5 4 0 Finite Difference Methods, 9 S C Theory and Applications N L 6th International Conference, FDM 2014 Lozenetz, Bulgaria, June 18–23, 2014 Revised Selected Papers 123 Lecture Notes in Computer Science 9045 Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, Lancaster, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Zürich, Switzerland John C. Mitchell Stanford University, Stanford, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Dortmund, Germany Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbrücken, Germany More information about this series at http://www.springer.com/series/7407 á ó Ivan Dimov Istv n Farag (cid:129) Lubin Vulkov (Eds.) Finite Difference Methods, Theory and Applications 6th International Conference, FDM 2014 – Lozenetz, Bulgaria, June 18 23, 2014 Revised Selected Papers 123 Editors IvanDimov LubinVulkov InstituteofInformationandCommunication University of Rousse Technologies Rousse BulgarianAcademy of Sciences Bulgaria Sofia Bulgaria István Faragó Institute of Mathematics andMTA-ELTE Numerical Analysis andLarge Networks Research Group EötvösLorándUniversity Budapest Hungary ISSN 0302-9743 ISSN 1611-3349 (electronic) Lecture Notesin Computer Science ISBN 978-3-319-20238-9 ISBN978-3-319-20239-6 (eBook) DOI 10.1007/978-3-319-20239-6 LibraryofCongressControlNumber:2015941871 LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe 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 storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynow knownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbookare believedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsortheeditors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia (www.springer.com) Preface The International Conference on Finite Difference Methods is a traditional forum for scientists from all over the world, providing opportunities to share ideas and establish fruitful cooperation. The papers in this volume were presented at the 6th International Conference on Finite Difference Methods: Theory and Applications. FDM: T&A was heldinLozenetz,Bulgaria,inJune2014.Theconferencewasorganizedandsponsored by Rousse University. This conference continued the tradition offour previous meet- ings:1997inRousse(Bulgaria),organizedbytheDivisionofNumericalAnalysisand Statistics;1998inMinsk(Belarus),organizedbytheInstituteofMathematics,Belarus Academy of Science; 2000 in Palanga, (Lithuania), organized by the Institute of Mathematics and Informatics (Vilnus); and 2006 and 2010 in Lozenetz (Bulgaria), organized by the Division of Numerical Analysis and Statistics, Rousse University. Thepurposeofthefirstthreeconferences(heldinBulgaria,Belarus,andLithuania) wastobringtogetherscientistsfromtheEastandWesttoexchangeideasandestablish research cooperation. We have observed that the contacts among scientists have become more regular and we are proud of our contribution in this respect. The general topic for FDM: T&A 2014 was finite difference and combined finite difference methods as well as finite element methods and their various applications in physics,chemistry,engineering,biology,andfinance.Anumberofmodernnumerical techniques were discussed and presented during the conference: splitting techniques, Green’s function method, multigrid methods, and immersed interface method, among others. Some contemporary topics were the focus of the following minisymposia: (1) Financial Mathematics; (2) Asymptotic-Numerical Treatment of Problems with Boundary and Internal Layer; (3) Numerical Methods for Fractional Differential Equations; (4) Computational Methods in Geophysics. Thesuccessoftheconferenceandthepresentvolumeareduetothejointeffortsof manycolleaguesfromvariousinstitutionsandorganizations.Wethankourcolleagues fortheirhelpintheorganizationofthisconference.WeespeciallythankM.Kolevafor herhelpinthepreparationofthisvolume.Wearealsogratefultotheorganizersofthe minisymposia. The 7th International FDM:T&A Conference will be organized in June 2018. March 2015 Ivan Dimov István Faragó Lubin Vulkov Organization FDM:T&A2014was organizedbytheUniversity ofRousse AngelKanchev,Rousse, Bulgaria. Scientific Committee Ivan Dimov, Bulgaria Matthias Ehrhardt, Germany István Faragó, Hungary Martin Gander, Switzerland Bosko Jovanovic, Serbia Abdul Khaliq, USA Raytcho Lazarov, USA Piotr Matus, Belarus Peter Minev, Canada Nikolay Nefedof, Russia Grigorii Shishkin, Russia Vladimir Shidurov, Russia Petr Vabishchevich, Russia Song Wang, Australia Ivan Yotov, USA Zlotnik Zlotnik, Russia Local Organizers Chair Luben Vulkov Tatiana Chernogorova Jury Dimitrov Miglena Koleva Walter Mudzimbabwe Radoslav Valkov Contents Invited Papers Simulation of Flow in Fractured Poroelastic Media: A Comparison of Different Discretization Approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 I. Ambartsumyan, E. Khattatov, I. Yotov, and P. Zunino A Transparent Boundary Condition for an Elastic Bottom in Underwater Acoustics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Anton Arnold and Matthias Ehrhardt Well-Posedness in Hölder Spaces of Elliptic Differential and Difference Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Allaberen Ashyralyev Operator Semigroups for Convergence Analysis . . . . . . . . . . . . . . . . . . . . . 38 Petra Csomós, István Faragó, and Imre Fekete The Power of Trefftz Approximations: Finite Difference, Boundary DifferenceandDiscontinuousGalerkinMethods;NonreflectingConditions and Non-Asymptotic Homogenization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 FritzKretzschmar,SaschaM.Schnepp,HerbertEgger,FarzadAhmadi, Nabil Nowak, Vadim A. Markel, and Igor Tsukerman On Extension of Asymptotic Comparison Principle for Time Periodic Reaction-Diffusion-Advection Systems with Boundary and Internal Layers. . . 62 Nikolay Nefedov and Aleksei Yagremtsev The Finite Difference Method for Boundary Value Problem with Singularity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Viktor A. Rukavishnikov and Elena I. Rukavishnikova Superconvergence of Some Linear and Quadratic Functionals for Higher-Order Finite Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Vladimir Shaydurov and Tianshi Xu Time Step for Numerically Solving Parabolic Problems. . . . . . . . . . . . . . . . 96 Petr N. Vabishchevich Recent Advances in Numerical Solution of HJB Equations Arising in Option Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Song Wang and Wen Li VIII Contents Applications of Numerical Methods for Stochastic Controlled Switching Diffusions with a Hidden Markov Chain: Case Studies on Distributed Power Management and Communication Resource Allocation . . . . . . . . . . . 117 ZhixinYang,LeYiWang,GeorgeYin,QingZhang,andHongweiZhang Error Estimates of the Crank-Nicolson-Polylinear FEM with the Discrete TBC for the Generalized Schrödinger Equation in an Unbounded Parallelepiped. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Alexander Zlotnik Contributed Papers DifferenceSchemesforDelayParabolicEquationswithPeriodicBoundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Allaberen Ashyralyev and Deniz Agirseven Some Results of FEM Schemes Analysis by Finite Difference Method . . . . . 153 Dmitry T. Chekmarev Application of Finite Difference TVD Methods in Hypersonic Aerodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Yury Dimitrienko, Mikhail Koryakov, and Andrey Zakharov Finite Difference Equations for Neutron Flux and Importance Distribution in 3D Heterogeneous Reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 A. Elshin Matrix-Free Iterative Processes for Implementation of Implicit Runge–Kutta Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Boris Faleichik and Ivan Bondar Simulation of Technogenic and Climatic Influences in Permafrost for Northern Oil Fields Exploitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 M.Yu. Filimonov and N.A. Vaganova Iterative Implicit Methods for Solving Nonlinear Dynamical Systems: Application of the Levitron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Jürgen Geiser, Karl Felix Lüskow, and Ralf Schneider Modeling Textile Fabric Used in Pest Control with a 3 Scale Domain Decomposition Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Tineke Goessens, Benny Malengier, and Lieva Van Langenhove The Theory and Applications of the SMIF Method for Correct Mathematical Modeling of the Incompressible Fluid Flows. . . . . . . . . . . . . . 209 Valentin Gushchin and Pavel Matyushin Contents IX Determination of the Time-Dependent Thermal Conductivity in the Heat Equation with Spacewise Dependent Heat Capacity. . . . . . . . . . . . . . . . . . . 217 M.S. Hussein and D. Lesnic Inverse Problems of Simultaneous Determination of the Time-Dependent Right-Hand Side Term and the Coefficient in a Parabolic Equation. . . . . . . . 225 Vitaly L. Kamynin Effectiveness of the Parallel Implementation of the FEM for the Problem of the Surface Waves Propagation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Evgeniya Karepova and Ekaterina Dementyeva Splitting Scheme for Poroelasticity and Thermoelasticity Problems . . . . . . . . 241 Alexandr E. Kolesov, Petr N. Vabishchevich, Maria V. Vasilyeva, and Victor F. Gornov Numerical Investigation of Adaptive Immune Response to Viral Infection . . . 249 Mikhail Kolev, Ana Markovska, and Boiana Garkova Efficient Application of the Two-Grid Technique for Solving Time-Fractional Non-linear Parabolic Problem . . . . . . . . . . . . . . . . . . . . . . 257 Miglena N. Koleva Error Estimates of Four Level Conservative Finite Difference Schemes for Multidimensional Boussinesq Equation. . . . . . . . . . . . . . . . . . . . . . . . . 266 Natalia Kolkovska Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator . . . . . . . . . . . . . . . . . . . . . 274 Hongling Lu, Zhenlai Han, Chao Zhang, and Yan Zhao Finite-Difference Simulation of Wave Propagation Through Prestressed Elastic Media. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 Egor Lys, Evgeniy Romenski, Vladimir Tcheverda, and Mikhail Epov Modeling the Wind Influence on Acoustic-Gravity Propagation Waves in a Heterogeneous Earth-Atmosphere Model. . . . . . . . . . . . . . . . . . . . . . . 290 B. Mikhailenko, A.A. Mikhailov, and G.V. Reshetova Numerical Solutions of Fractional Differential Equations by Extrapolation . . . 299 Kamal Pal, Fang Liu, and Yubin Yan Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Kamal Pal, Fang Liu, Yubin Yan, and Graham Roberts Spline Collocation for Fractional Integro-Differential Equations . . . . . . . . . . 315 Arvet Pedas, Enn Tamme, and Mikk Vikerpuur
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