Numerical Methods And Applications
INSTITUTE OF MATHEMATICS AND INFORMATICSBULGARIAN ACADEMY OF SCIENCESNumerical Methodsand ApplicationsSeventh International Conference,August 20‐24, 2010, Borovets, BulgariaScientific ProgramAbstractsList of Participants
Seventh International Conference onNumerical Methods and ApplicationsNM&Aʹ10Organizer:Institute of Mathematics and Informatics, Bulgarian Academy of SciencesOrganizing committee:Chairperson: N. KolkovskaI. Bazhlekov, T. Chernogorova, I. Hristov, M. Dimova, I. Georgiev,S. Stoilova, D. Vasilevain cooperation with Institute of Information and Communication Technologies, BulgarianAcademy of Sciences, Faculty of Mathematics and Informatics, Sofia UniversityʺSt. Kliment Ohridskiʺ, Society for Industrial and Applied Mathematics (SIAM), Lecture Notes in Computer Science, Springer.Invited Speakers: M. Feistauer (Charles University Prague, Czech Republic), J.‐L. Guermond (Texas A&M University, USA), K. Sabelfeld (Institute of Computational Mathematics and ComputationalPhysics, Russia), J. Schöeberl (Vienna University of Technology, Austria), Bl. Sendov (Institute of Information and Communication Technologies,Bulgaria), P. Vabishchevich (Institute for Mathematical Modelling, Russia), I. Yotov (University of Pittsburgh, USA).Keynote Speakers: A. Ern (University Paris‐Est, France), R. Lazarov (Texas A&M University, USA), S. Parter (University of Wisconsin, USA).August 20 ‐ 24, 2010, Borovets, Bulgaria
Part AScientific Program
Friday, August 20Plenary SessionLecture Hall A08:30 – 09:15RegistrationChairperson: I. Dimov09:15 – 09:3009:30 – 10:10OpeningBl. Sendov,New Conjectures in the Hausdorff Geometry of PolynomialsB-5310:10 – 10:5010:50 – 11:20K. Sabelfeld,Stochastic Algorithms in Linear Algebra - Beyond the Markov Chains and Neumann - Ulam SchemeB-52Coffee BreakChairperson: R. Lazarov11:20 – 12:00J.-L. Guermond, M. Nazarov, R. Pasquetti, B. Popov,Entropy Viscosity for Nonlinear Conservation LawsB-2912:00 – 12:30S. Parter,Revisiting Preconditioning: An Interesting Result and the Lessons Learned from ItB-4412:30 – 14:3013:30 – 14:30LUNCHRegistrationParallel SessionsLecture Hall A“Monte Carlo and Quasi-Monte Carlo Methods”Lecture Hall BContributed Talks“Approximation Techniques in Numerical Analysis”Chairperson: M. NedjalkovChairperson: Bl. Sendov14:30 – 15:0014:30 – 14:50A. Asenov,G. P. Nikolov, P. B. Nikolov,Advanced Monte Carlo Techniques in the Simulation ofQuadrature Formulae Based on Interpolation by ParabolicCMOS Devices and CircuitsSplinesB-2B-4314:50 – 15:10N. Naidenov, S. Kostadinova,Bicubic Spline Recovering of Smooth Surfaces on the Basis15:00 – 15:30I. Dimov, R. Georgieva,of Irregular DataB-42Monte Carlo Method for Numerical Integration Based onSobol' Sequences15:10 – 15:30V. H. Hristov, N. V. Kyurkchiev, A. I. Iliev,Global Convergence Properties of the SOR-WeierstrassMethodB-31B-1815:30 – 15:5015:30 – 15:50S. Stefanov,I. Markovsky,Particle Monte Carlo Algorithms with Small Number ofAffine Data Modeling by Low-Rank ApproximationPartilces in Grid CellsB-56A-1B-40
15:50 – 16:1015:50 – 16:10C. Meszaros,I. Lirkov, S. Stoilova,The b-adic Diaphony as a Tool to Study Pseudo-randomness On Some Properties of the Augmented Systems Arising inof NetsInterior Point MethodsB-41B-3816:10 – 16:40Coffee BreakParallel SessionsLecture Hall ALecture Hall B“Environmental Modelling”Contributed Talks “ Numerical Methods for Differential andIntegral Equations”Chairperson: A. StrunkChairperson: I. Yotov16:40 – 16:5016:40 – 17:00M. Grote, T. Mitkova,OpeningHigh-Order Explicit Local Time-Stepping for DampedWave EquationsB-2816:50 – 17:2017:00 – 17:20K. Georgiev, Z. Zlatev,A. Bradji, J. Fuhrmann,Specialized Sparse Matrices Solver in the Chemical Part ofSome Error Estimates for the Discretization of Parabolican Environmental ModelEquations on General Multidimensional NonconformingSpatial MeshesB-10B-2717:20 – 17:4017:20 – 17:40M. C. Vila, J. Soeiro de Carvalho, A. Fiúza,N. Kolkovska,Advanced Numerical Tools Applied to Geo-EnvironmentalConvergence of Finite Difference Schemes for aEngineering - Soils Contaminated by PetroleumMultidimensional Boussinesq EquationHydrocarbons, A Case StudyB-60B-3517:40 – 18:0017:40 – 18:00J. Březina, P. Rálek, M. Hokr,S. C. S. Rao, S. Kumar,Parallel Simulator of Multidimensional Fracture Flow andAn Efficient Numerical Method for a System of SingularlyTransportPerturbed Semilinear Reaction-Diffusion EquationsB-49B-1118:00 – 18:2018:00 – 18:20K. Liolios, S. Radev, V. Tsihrintzis,C. Hofreither,A Numerical Investigation for the Optimal ContaminantA Non-Standard Finite Element Method Based onInlet Positions in Horizontal Subsurface Fllow WetlandsBoundary Integral OperatorsB-37B-3019:30RECEPTIONSaturday, August 21Parallel SessionsLecture Hall ALecture Hall B“Metaheuristics for Optimization Problems”“Environmental Modelling”Chairperson: S. FidanovaChairperson: K. Georgiev09:00 – 09:3009:00 – 09:20C. Cotta,A. Strunk, H. Elbern, A. Ebel,Future Generation Memetic AlgorithmsUsing Satellite Observations for Air Quality Assessmentwith an Inverse Model SystemB-57B-1309:30 – 09:5009:20 – 09:40F. Zamfirache, M. Frîncu, D. Zaharie,K. Ganev, G. Gadzhev, N. Miloshev, G. Jordanov, A.Population-based Metaheuristics for Tasks Scheduling inTodorova, D. Syrakov, M. Prodanova,Atmospheric Composition Studies for the Balkan RegionHeterogeneous Distributed SystemsB-24B-61A-2
09:50 – 10:10D. Simian, F. Stoica, C. Simian,Evaluation of the Co-mutation Operators in Optimization ofMultiple SVM Kernels09:40 – 10:00I. Etropolska, M. Prodanova, D. Syrakov, K. Ganev, N.Miloshev, K. Slavov,Bulgarian Operative System for Chemical WeatherForecastB-55B-2010:00 – 10:20A. Terziyski, N, Kochev,Distributed Software System for Data Evaluation andNumerical Simulations of Atmospheric ProcessesB-5810:20 – 10:50Coffee BreakParallel SessionsLecture Hall A“Metaheuristics for Optimization Problems”Chairperson: C. Cotta10:50 – 11:10S. Fidanova, P. Marinov, K. Atanassov,Start Strategies of ACO Applied on Subset ProblemsLecture Hall B“Monte Carlo and Quasi-Monte Carlo Methods”Chairperson: A. Penzov10:50 – 11:20M. Magdics, L. Szirmay-Kalos, B. Tóth, Á. Csendesi, A.Penzov,B-21 Scatter Estimation for PET ReconstructionB-3811:10 – 11:3011:20 – 11:40S. Fidanova, P. Marinov, K. Atanassov,K. Sabelfeld, N. Mozartova,Sensityvity Analysis of ACO Start Strategies for SubsetSparsified Randomization Algorithms for the SVD basedProblemsLow Rank ApproximationsB-22B-5211:30 – 11:5011:40 – 12:00A. Băutu, H. Luchian,M. L. Dinis, A. Fiúza,Protein Structure Prediction in the 2D HP Model UsingUsing Monte-Carlo Simulation for Risk Assessment:Particle Swarm OptimizationApplication to Occupational Exposure During RemediationWorksB-7B-1911:50 – 12:1012:00 – 12:20J. P. Pedroso,T. Averina,Metaheuristics for the Asymmetric Hamiltonian PathMonte Carlo Simulation of Inhomogeneous PoissonB-45 EnsemblesB-512:20 – 14:30LUNCH14:00 – 14:30RegistrationParallel SessionsLecture Hall AContributed Talks“Hierarchical and Domain Decomposition Methods”Lecture Hall BContributed Talks“Computational Physics, Chemistry, Biology and Engineering”Chairperson: S. MargenovChairperson: St. Radev14:30 – 14:50E. Karer, J. Kraus, L. Zikatanov,Auxiliary Space Preconditioner for a Locking-free FiniteElement Approximation of the Linear Elasticity ProblemB-3414:30 – 14:50M. Hokr, J. Kopal, J. Březina, P. Rálek,Sensitivity of Results of the Water Flow Problem in aDiscrete Fracture Network with Large CoefficientDifferences14:50 – 15:10B. Ayuso, I. Georgiev, J. Kraus, L. Zikatanov,Preconditioning of DG FEM Elasticity Systems14:50 – 15:10C. I. Christov, N. T. Kolkovska, D. P. Vasileva,On the Numerical Simulation of Unsteady Solutions for the 2DBoussinesq Paradigm EquationB-30B-615:10 – 15:3015:10 – 15:30P. Boyanova, S. Margenov,I. Hristov, S. Dimova,Optimal Order Multilevel Solvers in a Projection Scheme for Fluxon Dynamics in Stacked Josephson JunctionsNavier-Stokes EquationsB-9A-3B-12B-31
15:30 – 15:50P. Popov, Y. Efendiev, Y. Gorb,Multsacle Modeling of Poroelasticity in Highly DeformableFractured ReservoirsB-4615:50 – 16:10I. Georgiev, M. Lymbery, S. Margenov,Analysis of the Constant in the Strengthened CauchyBunyakowski-Schwarz Inequality for Quadratic FiniteElementsB-2716:10 – 16:4015:30 – 15:50T. L. Boyadjiev, H. T. Melemov,Merger Bound States in 0-π Josephson StructuresB-915:50 – 16:10M. Dimova, S. Dimova,Numerical Investigation of Self-Similar Solutions of aReaction Diffusion Equation in a Vicinity of CriticalParametersB-18Coffee BreakParallel SessionsLecture Hall AContributed Talks“Computational Mechanics”Lecture Hall BContributed Talks“Computational Physics, Chemistry, Biology and Engineering”Chairperson: P. Vabishchevich16:40 – 17:00J.-L. Guermond, P. D. Minev,A New Class of Fractional Step Techniques for theIncompressible Navier-Stokes Equations Using DirectionSplittingB-2917:00 – 17:20A. S. Shamaev, A. A. Gavrikov, D. U. Knyazkov,Some Spectral Problems of Porous Media AcousticsChairperson: S. Dimova16:40 – 17:00N. N. Elkin, A. P. Napartovich, D. V. Vysotsky,Bidirectorial Beam Propagation Method Applied for Laserswith Multilayer Active MediumB-2017:00 – 17:20A. Liolios, S. Radev,A Numerical Approach for Obtaining Fragility Curves inSeismic Structural Mechanics: A Bridge Case of EgnatiaMotorway in Northern GreeceB-54B-3617:20 – 17:4017:20 – 17:40S. Radev, N. K. Vitanov,G. Bencheva,Application of Spectral Method for Investigation of theOn the Numerical Solution of a Chemotaxis System inProfiles of the Optimum Fields for Variational ProblemsHaematologyConnected to the Turbulent Thermal ConvectionB-47B-817:40 – 18:0017:40 – 18:00N. K. Vitanov,P. Kh. Atanasova, T. L. Boyadjiev, E. V. Zemlyanaya,Numerical Investigation of the Upper Bounds on theYu. M. Shukrinov,Convective Heat Trasport in a Heated From Below Rotating Stability Analysis of Magnetic Flux in the LJJ Model withFluid LayerDouble Sine-Gordon EquationB-61B-218:00 – 18:20S. Stoykov, P. Ribeiro,Forced Vibrations of 3D Beams with Large AmplitudesB-57Sunday, August 22Plenary SessionLecture Hall A08:45 – 09:2509:25 – 10:05Chairperson: J.-L. GuermondM. Feistauer,Discontinuous Galerkin Finite Element Method for Convection-Diffusion Problems and CompressibleFlowB-21J. Schöberl,Hybrid Discontinuous Galerkin Methods with Vector Valued Finite ElementsB-5310:05 – 10:20Coffee BreakA-4
10:20 – 11:00Chairperson: K. SabelfeldB. Ganis, D. Vassilev, I. Yotov, M. Zhong,A Multiscale Stochastic Framework for Stokes-Darcy Flow and Transport11:00 – 11:30O. P. Iliev, R. Lazarov, J. WillemsNumerical Upscaling of Flows in Highly Heterogeneous Porous MediaB-25B-3211:30 – 12:30LUNCH12:30EXCURSIONMonday, August 23Plenary SessionLecture Hall AChairperson: M. Feistauer09:00 – 9:4009:40 – 10:10P. Vabishchevich, SM Stability for Time-Dependent ProblemsB-59E. Burman, A. Ern, M. A. Fernández,Explicit Runge - Kutta Schemes and Finite Elements with Symmetric Stabilization for First-OrderLinear PDE SystemsB-1210:10 – 10:40Coffee BreakParallel SessionsLecture Hall ALecture Hall B“Monte Carlo and Quasi-Monte Carlo Methods”“Environmental Modelling”Chairperson: K. SabelfeldChairperson: K. Georgiev10:35 – 11:0010:40 – 11:00D. Vasileska, A. Hossain, K. Raleva, S. M. GoodnickT. Brechet, C. Camacho, V. Veliov,Global Warming and Economic BehaviourIs Self-Heating Important in Nanowire FETs?B-10B-5911:00 – 11:2011:00 – 11:20K. Raleva, D. Vasileska, S. M. GoodnickTz. Ostromsky, I. Dimov, Havasi, I. Farago, Z. Zlatev,Modeling Thermal Effects in Fully-Depleted SOI DevicesRichardson Extrapolated Numerical Methods for Onewith Arbitrary Crystallographic OrientationDimensional Advection SchemesB-48B-4411:20 – 11:4011:20 – 11:40M. Nedjalkov, S. Selberherr, I. Dimov,E. Băutu, A. Bărbulescu,Stochastic Algorithm for Solving the Wigner-BoltzmannMining Temperature Trends with GEP EnsemblesCorrection EquationB-43B-811:40 – 12:0011:40 – 12:00A. Makarov, V. Sverdlov, S. Selberherr,N. Dobrinkova, G. Jordanov, J. Mandel, WRF-FireModeling of the SET and RESET Process in BipolarApplied in BulgariaResistive Oxide-Based Memory using Monte CarloB-19SimulationsB-3912:00 – 12:2012:00 – 12:20V. Baláž, V. Grozdanov, V. Ristovska-Dimitrieva, O.G. Dimitriu, R.ŞtefănescuComparative Numerical Results in 4D-Var DataStrauch, S. Stoilova,On the Mean Square Worst-Case Error of the Quasi-MonteAssimilation Problems Using POD TechniquesCarlo Integration in Weighted Sobolev SpacesB-6B-6212:20 – 14:30LUNCH14:00 – 14:30RegistrationA-5
Parallel SessionsLecture Hall A“Metaheuristics for Optimization Problems”Chairperson: K. Penev14:30 – 14:50O. Roeva, T. Slavov,Fed-batch Cultivation Control based on Genetic AlgorithmPID Controller TuningLecture Hall B“Modelling and Simulation of Electrochemical Processes”Chairperson: O. Iliev14:30 – 15:00J. Fuhrmann, K. Gärtner, M. Ehrhardt, A. Linke, H.Langmach, H. Zhao,Numerical Modeling in Electrochemistry by Voronoi FiniteVolume MethodsB-50B-2314:50 – 15:1015:00 – 15:20F. Torrecilla-Pinero, J. A. Torrecilla-Pinero, J. A. Gomez- O. Iliev, A. Latz, J. Zausch,Modeling of Species and Charge Transport in Li-IonPulido, M. A. Vega-Rodriguez, J. M. Sanchez-Perez,Parameter Estimation for a Logistic Curve. An Example ofBatteriesUse in an Engineering ProblemB-58B-3315:10 – 15:3015:20 – 15:40I. Skalna, J. Duda,O. Iliev, S. Margenov, P. Popov, Y. Vutov,A Comparison of Metaheurisitics for the Problem of Solving Finite Volume Discretization of Nonlinear Diffusion in LiParametric Interval Linear SystemsIon BatteriesB-55B-3315:30 – 15:5015:40 – 16:00M. Angelova, S. Tzonkov, T. Pencheva,K. Bartkowski, O. Iliev, A. Latz,Genetic Algorithms Based Parameter Identification of Yeast On Numerical Simulation of 1D Problems DescribingFed-Batch CultivationTransport Processes in Li-Ion BatteriesB-1B-715:50 – 16:10M. Seredynski, P. Bouvry,Perspectives of a Selfish Behavior in Self-Policing WirelessMobile Ad Hoc NetworkB-5316:10 – 16:40Coffee BreakParallel SessionsLecture Hall ALecture Hall B“Grid Computing and Applications”Chairperson: E. Atanassov16:40 – 17:10E. Atanassov, T. Gurov, A. Karaivanova, S. Ivanovska, D.Slavov,Efficient Gridification of Environmental ModelingApplicationsB-317:10 – 17:30V. Spiridonov, D. Syrakov, M. Prodanova, A. Bogachev, K.Ganev, N. Miloshev, G. Jordanov, K. Slavov,First results of See-Grid-Sci VO "Environment" ApplicationCCIAQB-5617:30 – 17:50C. Resteanu, R. Trandafir,Programming Problems with a Large Number of ObjectiveFunctionsB-5017:50 – 18:10R. Goranova,An Approach of Modeling ROOT Processes in GridContributed Talks“Numerical Linear Algebra”Chairperson: J. Schöberl16:40 – 17:00J. Buša, J. Buša, jr., E. Hayryan,OpenCL Implementation of the Analytical Method for theComputation of the Accessible Surface Area and ExcludedVolume of Overlapping SpheresB-1117:00 – 17:20M. Manguoglu, E. Cox, F. Saied, A. Sameh,Parallel Computation of the Fiedler Vector and Solution ofLarge Sparse Linear Systems via Banded PreconditionersB-4017:20 – 17:40P. D. Michailidis, K. G. Margaritis,Experimental Study of Matrix Multiplication on MultiCoreProcessorsB-4117:40 – 18:00I. Skalna,Interval Dependency and the Problem of SolvingParametric Linear SystemsB-28B-5518:10 – 18:3018:00 – 18:20E. Atanassov, M. Durchova,P. Hr. Petkov, M. M. Konstantinov, N. D. Christov,Efficient GPU-based Generation of the Scrambled HaltonCondition and Error Estimates in Kalman Filter DesignB-46SequenceB-319:30CONFERENCE DINNERA-6
Tuesday, August 24Parallel SessionsLecture Hall ALecture Hall B“Metaheuristics for Optimization Problems”Contributed Talks“Numerical Methods for Differential and IntegralEquations”Chairperson: S. FidanovaChairperson: N. Kolkovska09:30 – 09:5009:30 – 09:50N. Fujimoto, S. Tsutsui,J. D. Kandilarov, R. L. Vulkov,A Highly-Parallel TSP Solver for a GPU ComputingA Numerical Approach for the American Call OptionPlatformPricing ModelB-24B-3409:50 – 10:1009:50 – 10:10K. Penev, A. Ruzhekov,T. Chernogorova, R. Valkov,Adaptive Intelligence Applied to Numerical OptimisationFinite-Volume Difference Schemes for the Black-SholesB-46 Equation in Stochastic Volatility ModelsB-1210:10 – 10:3010:10 – 10:30A. Ruzhekov, K. Penev,M. N. Koleva, L. G. Vulkov,Tool for Observation, Comparison and Analysis ofA Numerical Study of a Parabolic Monge-Ampere EquationAdvanced Search Algorithmsin Mathematical FinanceB-51B-3510:30 – 10:5010:30 – 10:50V. Atanassova, K. Atanassov,N. Ishimura, M. N. Koleva, L. G. Vulkov,Ant Colony Optimization Approach to Tokens' MovementNumerical Solution of a Nonlinear Evolution Equation forwithin Generalized Netsthe Risk PreferenceB-5B-3410:50 – 11:1010:50 – 11:10L. Atanassova, K. Atanassov,A. Andreev, M. Racheva,Intuitionistic Fuzzy Interpretation of Conway’s Game of Life On the Integral Type Crouzeix-Raviart NonconformingB-4 Finite ElementsB-111:10 – 11:3011:10 – 11:30M. Hernández, J. J. Cáceres, M. Pérez,A. Andreev, M. Racheva,Forecasting the Composition of Demand for HigherPostprocessing Techniques Using a Linear NonconformingEducation Degrees by Genetic AlgorithmsFinite ElementsB-29B-1DEPARTUREA-7
Part BAbstracts
On the Integral Type Crouzeix-Raviart NonconformingFinite ElementsA. Andreev, M. RachevaWe analyze some approximation properties of nonconforming piecewise linear finiteelements. These elements use integral degrees of freedom which yield supercloseproperties and that is why they are more appropriate for postprocessing procedures.The approximate eigenvalues obtained with this method dive asymptotically lowerbounds of the exact eigenvalues. Finally, computational aspects are discussed andnumerical examples are presented.Postprocessing Techniques Using a Linear NonconformingFinite ElementsA. Andreev, M. RachevaTwo different a-posteriori techniques which improve the order of convergence of finiteelement solutions are presented. These methods are realized by means of an integraltype Crouzeix-Raviart nonconforming finite element. Superconvergence rate is established to a second order elliptic problem by introducing nonstandard interpolatedelements. We also analyze a simple postprocessing method applied to second ordereigenvalue problems. Both approaches are illustrated and discussed by appropriatenumerical examples.Genetic Algorithms Based Parameter Identification of YeastFed-Batch CultivationM. Angelova, S. Tzonkov, T. PenchevaDifferent kinds of genetic algorithms have been investigated for a parameter identification of a fermentation process. Altogether eight realizations of genetic algorithmshave been presented four of simple genetic algorithms and four of multi-populationones. Each of them is characterized with a different sequence of implementation ofmain genetic operators, namely selection, crossover and mutation. A comparison ofconsidered eight types of genetic algorithms is presented for a parameter identificationof a fed-batch cultivation of S. cerevisiae. All kinds of multi-population algorithmslead to considerable improvement of the optimization criterion value but for morecomputational time. Among the considered multi-population algorithms the best onehas an operators sequence of crossover, mutation and selection. Different kinds ofconsidered simple genetic algorithms lead to similar values of the optimization criterion but the genetic algorithm with an operators sequence of mutation, crossover andselection is significantly faster than the others.B-1
Advanced Monte Carlo Techniques in the Simulation ofCMOS Devices and CircuitsA. AsenovIn this paper we describe advanced Monte Carlo simulation techniques that are usedto study statistical variability in contemporary and future CMOS technology generations at the levels of physical transistor simulation, compact model and circuitsimulation. First we will review the major sources of statistical variability in nanoCMOS transistors focusing at the 45nm technology generation and beyond and willintroduced the advanced 3D statistical physical statistical simulation technology andtools used to fo
Distributed Software System for Data Evaluation and Numerical Simulations of Atmospheric Processes B-58 10:20 – 10:50 Coffee Break Parallel Sessions Lecture Hall A “Metaheuristics for Optimization Problems” Lecture Hall B “Monte Carlo and Quasi-Monte Carlo Methods” C
numerical solutions. Emphasis will be placed on standing the under basic concepts behind the various numerical methods studied, implementing basic numerical methods using the MATLAB structured programming environment, and utilizing more sophisticated numerical methods provided as built-in
1. To be an advanced level course in numerical methods and their applications; 2. To (introduce and) develop confidence in MATLAB (and UNIX); 3. To teach mathematical methods through computation; 4. To develop numerical methods in the context of case studies. Objectives 1. To learn numerical methods for data analysis, optimisation,linear .
the numerical solution of second-order optimization methods. Next step development of Numerical Multilinear Algebra for the statistical analysis of multi-way data, the numerical solution of partial di erential equations arising from tensor elds, the numerical solution of higher-order optimization methods.
General formulation of conventional numerical methods A.1 Introduction The general formulation of continuum and discontinuum methods, as well as the simula-tion of fracture process using different numerical tecniques, described in this appendix, is based on the previous work made by Jing (2003). A.2 Numerical methods in rock engineering
Fenton, J.D. (1999) Numerical Methods for Nonlinear Waves, in Advances in Coastal and Ocean Engineering, Vol. 5, ed. P.L.-F. Liu, pp241-324, World Scientific: Singapore. Numerical methods for nonlinear waves John D. Fenton . Introduction The first statement that should be made about the use of fully-nonlinear numerical methods for waves
The sixth edition of Numerical Methods for Engineers offers an innovative and accessible presentation of numerical methods; the book has earned the Meriam-Wiley award, which is given by the American Society for Engineering Education for the best textbook. Because soft-ware packages are now regularly used for numerical analysis, this eagerly .
A SURVEY OF NUMERICAL METHODS FOR OPTIMAL CONTROL Anil V. Rao A survey of numerical methods for optimal control is given. The objective of the article is to describe the major methods that have been developed over the years for solving general optimal control problems. In particular, the two broad classes of indirect and direct methods
2. Numerical approximation of PDEs. Both the mathematical analysis of the PDEs and the numerical analysis of methods rely heavily on the strong tools of functional analysis. Numerical approximation of PDEs is a cornerstone of the mathematical modeling since almost all modeled real world problems fail to have analytic solutions or they are not
