Download or read book High Order Accuracy Computational Methods for Long Time Integration of Nonlinear PDEs in Complex Domains written by and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The overarching goal of this research was to construct stable, robust and efficient high order accurate computational methods for long time integration of nonlinear partial differential equations. High order accuracy methods (Spectral, Finite Difference and Finite Elements) for the numerical simulations of flows with discontinuities, in complex geometries were developed. In particular applications in supersonic combustion were emphasized. Specific research subjects included: Robust high order compact difference schemes, ENO and WENO schemes, discontinuous Galerkin methods, the resolution of the Gibbs phenomenon, parallel computing and high order accurate boundary conditions. In order to overcome the difficulties stemming from complicated geometries, we have developed multidomain techniques as well as spectral methods on arbitrary grids. Several multidimensional codes for supersonic reactive flows had been constructed as well as a library of spectral codes (Pseudopack).
Download or read book High Order Accuracy Computational Methods for Long Time Integration of Nonlinear PDEs in Complex Domains written by David Gottlieb and published by . This book was released on 1999 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 written by Robert M. Kirby and published by Springer. This book was released on 2015-11-26 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.
Download or read book Developments in Isogeometric Analysis and Application to High Order Phase Field Models of Biomembranes written by Navid Valizadeh and published by . This book was released on 2021* with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Isogeometric analysis (IGA) is a numerical method for solving partial differential equations (PDEs), which was introduced with the aim of integrating finite element analysis with computer-aided design systems. The main idea of the method is to use the same spline basis functions which describe the geometry in CAD systems for the approximation of solution fields in the finite element method (FEM). Originally, NURBS which is a standard technology employed in CAD systems was adopted as basis functions in IGA but there were several variants of IGA using other technologies such as T-splines, PHT splines, and subdivision surfaces as basis functions. In general, IGA offers two key advantages over classical FEM: (i) by describing the CAD geometry exactly using smooth, high-order spline functions, the mesh generation process is simplified and the interoperability between CAD and FEM is improved, (ii) IGA can be viewed as a high-order finite element method which offers basis functions with high inter-element continuity and therefore can provide a primal variational formulation of high-order PDEs in a straightforward fashion. The main goal of this thesis is to further advance isogeometric analysis by exploiting these major advantages, namely precise geometric modeling and the use of smooth high-order splines as basis functions, and develop robust computational methods for problems with complex geometry and/or complex multi-physics. As the first contribution of this thesis, we leverage the precise geometric modeling of isogeometric analysis and propose a new method for its coupling with meshfree discretizations. We exploit the strengths of both methods by using IGA to provide a smooth, geometrically-exact surface discretization of the problem domain boundary, while the Reproducing Kernel Particle Method (RKPM) discretization is used to provide the volumetric discretization of the domain interior. The coupling strategy is based upon the higher-order consistency or reproducing conditions that are directly imposed in the physical domain. The resulting coupled method enjoys several favorable features: (i) it preserves the geometric exactness of IGA, (ii) it circumvents the need for global volumetric parameterization of the problem domain, (iii) it achieves arbitrary-order approximation accuracy while preserving higher-order smoothness of the discretization. Several numerical examples are solved to show the optimal convergence properties of the coupled IGA-RKPM formulation, and to demonstrate its effectiveness in constructing volumetric discretizations for complex-geometry objects. As for the next contribution, we exploit the use of smooth, high-order spline basis functions in IGA to solve high-order surface PDEs governing the morphological evolution of vesicles. These governing equations are often consisted of geometric PDEs, high-order PDEs on stationary or evolving surfaces, or a combination of them. We propose an isogeometric formulation for solving these PDEs. In the context of geometric PDEs, we consider phase-field approximations of mean curvature flow and Willmore flow problems and numerically study the convergence behavior of isogeometric analysis for these problems. As a model problem for high-order PDEs on stationary surfaces, we consider the Cahn-Hilliard equation on a sphere, where the surface is modeled using a phase-field approach. As for the high-order PDEs on evolving surfaces, a phase-field model of a deforming multi-component vesicle, which consists of two fourth-order nonlinear PDEs, is solved using the isogeometric analysis in a primal variational framework. Through several numerical examples in 2D, 3D and axisymmetric 3D settings, we show the robustness of IGA for solving the considered phase-field models. Finally, we present a monolithic, implicit formulation based on isogeometric analysis and generalized-alpha time integration for simulating hydrodynamics of vesicles according to a phase-field model. Compared to earlier works, the number of equations of the phase-field model which need to be solved is reduced by leveraging high continuity of NURBS functions, and the algorithm is extended to 3D settings. We use residual-based variational multi-scale method (RBVMS) for solving Navier-Stokes equations, while the rest of PDEs in the phase-field model are treated using a standard Galerkin-based IGA. We introduce the resistive immersed surface (RIS) method into the formulation which can be employed for an implicit description of complex geometries using a diffuse-interface approach. The implementation highlights the robustness of the RBVMS method for Navier-Stokes equations of incompressible flows with non-trivial localized forcing terms including bending and tension forces of the vesicle. The potential of the phase-field model and isogeometric analysis for accurate simulation of a variety of fluid-vesicle interaction problems in 2D and 3D is demonstrated.
Download or read book Efficient Numerical Methods For Chemotaxis and Plasma Modulation Instability Studies written by Truong B. Nguyen and published by . This book was released on 2019 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we develop efficient numerical solvers for nonlinear systems of partial differential equations (PDEs). These systems of PDEs concern two different sets of physical problems. The first set includes chemotaxis models such as Keller-Segel models and cancer cell invasion models. Solutions of these models are observed to experience the blow-up phenomenon or the development of sharp and spiky features. Therefore, efficient and accurate numerical techniques must be employed in order to capture the solutions' behaviors. For this research, we design efficient solvers for these systems in the one and two spatial dimensions. In particular, we plan to apply adaptive moving mesh methods in which the mesh points are continuously redistributed by a coordinate transformation from the computational domain to the physical domain so that the grid nodes are concentrated in regions of large solution variations in the physical domain. The second system is the system of nonlinear PDEs that govern the plasma modulation instability of wave collapse. It is known that the nonlinear interaction of lower-hybrid wave with a much lower frequency plasma perturbation leads to the development of modulation instability which causes oscillations of electric field and formations of cavitons. Cavitons, which are regions where plasma's density is observed to be decreased, collapse in finite time and during this period, the trapped energy of electric field oscillations is dissipated and electrons are heated up. Direct experiment observations of collapse phenomenon of cavitons can be difficult. Therefore, numerical simulations are desired. To overcome the above challenges and achieve the thesis' goals, we first study the basic mechanisms of the adaptive moving mesh methods by implementing adaptive grid methods using finite difference and finite element discretization. We then apply them for well known toy problems e.g., Burgers' equations. On the other hand, we re-implement the pseudo-spectral method and we also apply the method to compute solutions to simple problems e.g., solving Poisson problems with periodic boundary conditions. Once the methods are tested with toy examples, we are ready to apply them to obtain numerical solutions to the nonlinear diffusion-reaction-chemotaxis models (cancer invasion models and Keller-Segel models) and the system of nonlinear equations that govern the modulation instability. In particular, we apply adaptive moving mesh methods for nonlinear diffusion-reaction-chemotaxis models. These model equations are discretized using finite difference (FD) and/or finite element (FE) methods. Positivity preserving schemes are used for the spatial discretization of these chemotaxis models to ensure that the physical solutions remain positive at all time levels. Numerical experiments are performed to demonstrate the performance of the adaptive mesh methods. Our numerical results show that the proposed moving mesh methods reduce the computational cost while improving the accuracy of the computed solutions when comparing to uniform grid methods. Meanwhile, we follow Shapiro's approach in his 1993 paper to further test our pseudo-spectral solver for solving the governing system of plasma modulation instability in two and three spatial dimensions. The pseudo-spectral method utilizes the computation of the fast Fourier transform (FFT) which is done by using FFTW library. High order time integration techniques are applied to calculate solutions at the a time. We further extend the pseudo-spectral method to a highly scalable solver by implementing it in parallel using Message Passing Interface (MPI). Our MPI code allows us to speed up the computations especially in the three dimensional problem. Next, we use our solvers to numerically study the effect of plasma's shear velocity on the wave collapse phenomenon. Finally, we implement a solver that uses adaptive moving mesh finite difference method for the system of PDEs that govern the modulation instability phenomenon in the two dimensional case.
Download or read book Computational Partial Differential Equations written by Hans Petter Langtangen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1973 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020 1 written by Jens M. Melenk and published by Springer Nature. This book was released on 2023-06-30 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.
Download or read book Peridynamic Differential Operator for Numerical Analysis written by Erdogan Madenci and published by Springer. This book was released on 2019-01-17 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities. PD also serves as a natural filter to smooth noisy data and to recover missing data. This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson’s and Navier’s equations for direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization. Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.
Download or read book Wave and Tidal Energy written by Deborah Greaves and published by John Wiley & Sons. This book was released on 2018-03-28 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eine umfassende Publikation zu sämtlichen Aspekten der Wellen- und Gezeitenenergie. Wave and Tidal Energy gibt einen ausführlichen Überblick über die Entwicklung erneuerbarer Energie aus dem Meer, bezieht sich auf die neueste Forschung und Erfahrungen aus Anlagentests. Das Buch verfolgt zwei Ziele, zum einen vermittelt es Einsteigern in das Fachgebiet eine Überblick über die Wellen- und Gezeitenenergie, zum anderen ist es ein Referenzwerk für komplexere Studien und die Praxis. Es vermittelt Detailwissen zu wichtigen Themen wie Ressourcencharakterisierung, Technologie für Wellen- und Gezeitenanlagen, Stromversorgungssysteme, numerische und physikalische Modellierung, Umwelteffekte und Politik. Zusätzlich enthält es eine aktuelle Übersicht über Entwicklungen in der ganzen Welt sowie Fallstudien zu ausgewählten Projekten. Hauptmerkmale: - Ausführliches Referenzwerk zu allen Aspekten der interdisziplinären Fachrichten Wellen- und Gezeitenenergie. - Greift auf die neuesten Forschungsergebnisse und die Erfahrung führender Experten in der numerischen und laborgestützten Modellierung zurück. - Gibt einen Überblick über regionale Entwicklungen in aller Welt, repräsentative Projekte werden in Fallstudien vorgestellt. Wave and Tidal Energy ist ein wertvolles Referenzwerk für eine breite Leserschaft, von Studenten der Ingenieurwissenschaften und technischen Managern über politische Entscheidungsträger bis hin zu Studienabsolventen und Forschern.
Download or read book High Order Methods for Computational Physics written by Timothy J. Barth and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.
Download or read book Advanced Numerical Methods in Applied Sciences written by Luigi Brugnano and published by MDPI. This book was released on 2019-06-20 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
Download or read book High Order Nonlinear Numerical Schemes for Evolutionary PDEs written by Rémi Abgrall and published by Springer. This book was released on 2014-05-19 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.
Download or read book Fractional Order Processes written by Seshu Kumar Damarla and published by CRC Press. This book was released on 2018-09-03 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estimate parameters of a mathematical model under consideration from experimental or simulated data. A simple tuning technique, which aims to produce a robust FO PID controller exhibiting iso-damping property during re-parameterization of a plant, is devised in the book. A new numerical method to find an equivalent finite dimensional integer order system for an infinite dimensional FO system is developed in the book. The book also introduces a numerical method to solve FO optimal control problems. Key features Proposes generalized triangular function operational matrices. Shows significant applications of triangular orthogonal functions as well as triangular strip operational matrices in simulation, identification and control of fractional order processes. Provides numerical methods for simulation of physical problems involving different types of weakly singular integral equations, Abel’s integral equation, fractional order integro-differential equations, fractional order differential and differential-algebraic equations, and fractional order partial differential equations. Suggests alternative way to do numerical computation of fractional order signals and systems and control. Provides source codes developed in MATLAB for each chapter, allowing the interested reader to take advantage of these codes for broadening and enhancing the scope of the book itself and developing new results.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nano and Micro Electromechanical Systems written by Sergey Edward Lyshevski and published by CRC Press. This book was released on 2018-10-03 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: Society is approaching and advancing nano- and microtechnology from various angles of science and engineering. The need for further fundamental, applied, and experimental research is matched by the demand for quality references that capture the multidisciplinary and multifaceted nature of the science. Presenting cutting-edge information that is applicable to many fields, Nano- and Micro-Electromechanical Systems: Fundamentals of Nano and Microengineering, Second Edition builds the theoretical foundation for understanding, modeling, controlling, simulating, and designing nano- and microsystems. The book focuses on the fundamentals of nano- and microengineering and nano- and microtechnology. It emphasizes the multidisciplinary principles of NEMS and MEMS and practical applications of the basic theory in engineering practice and technology development. Significantly revised to reflect both fundamental and technological aspects, this second edition introduces the concepts, methods, techniques, and technologies needed to solve a wide variety of problems related to high-performance nano- and microsystems. The book is written in a textbook style and now includes homework problems, examples, and reference lists in every chapter, as well as a separate solutions manual. It is designed to satisfy the growing demands of undergraduate and graduate students, researchers, and professionals in the fields of nano- and microengineering, and to enable them to contribute to the nanotechnology revolution.
Download or read book Non standard Discretisation Methods in Solid Mechanics written by Jörg Schröder and published by Springer Nature. This book was released on 2022-04-14 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume summarizes research being pursued within the DFG Priority Programme 1748: "Reliable Simulation Methods in Solid Mechanics. Development of non-standard discretisation methods, mechanical and mathematical analysis", the aim of which was to develop novel discretisation methods based e.g. on mixed finite element methods, isogeometric approaches as well as discontinuous Galerkin formulations, including a sound mathematical analysis for geometrically as well as physically nonlinear problems. The Priority Programme has established an international framework for mechanical and applied mathematical research to pursue open challenges on an inter-disciplinary level. The compiled results can be understood as state of the art in the research field and show promising ways of further research in the respective areas. The book is intended for doctoral and post-doctoral students in civil engineering, mechanical engineering, applied mathematics and physics, as well as industrial researchers interested in the field.
