Solution Of Fluid Structure Interaction Problems Using A Discontinuous Galerkin Technique

Download Solution Of Fluid Structure Interaction Problems Using A Discontinuous Galerkin Technique full books in PDF, epub, and Kindle. Read online Solution Of Fluid Structure Interaction Problems Using A Discontinuous Galerkin Technique ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Solution of Fluid-structure Interaction Problems Using a Discontinuous Galerkin Technique

Author : Anshul Mohnot
Publisher :
ISBN 13 :
Total Pages : 58 pages
Book Rating : 4.:/5 (261 download)

DOWNLOAD NOW!

Book Synopsis Solution of Fluid-structure Interaction Problems Using a Discontinuous Galerkin Technique by : Anshul Mohnot

Download or read book Solution of Fluid-structure Interaction Problems Using a Discontinuous Galerkin Technique written by Anshul Mohnot and published by . This book was released on 2008 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work aims to address the problem of fluid-structure interaction using a discontinuous Galerkin approach. Starting from the Navier-Stokes equations on a fixed domain, an arbitrary Lagrangian Eulerian (ALE) approach is used to derive the equations for the deforming domain. A geometric conservation law (GCL) is then introduced, which guarantees freestream preservation of the numerical scheme. The space discretization is performed using a discontinuous Galerkin method and time integration is performed using either an explicit four stage Runge-Kutta scheme or an implicit BDF2 scheme. The mapping parameters for the ALE formulation are then obtained using algorithms based on radial basis functions (RBF) or linear elasticity. These strategies are robust and can be applied to bodies with arbitrary shapes and undergoing arbitrary motions. The robustness and accuracy of the ALE scheme coupled with these mapping strategies is then demonstrated by solving some model problems. The ability of the scheme to handle complex flow problems is demonstrated by analyzing the low Reynolds number flow over an oscillating circular cylinder.

High-Order Discontinuous Galerkin Fluid-Structure Interaction Methods

Author : Bradley M. Froehle
Publisher :
ISBN 13 :
Total Pages : 89 pages
Book Rating : 4.:/5 (94 download)

DOWNLOAD NOW!

Book Synopsis High-Order Discontinuous Galerkin Fluid-Structure Interaction Methods by : Bradley M. Froehle

Download or read book High-Order Discontinuous Galerkin Fluid-Structure Interaction Methods written by Bradley M. Froehle and published by . This book was released on 2013 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a high-order accurate scheme for fully coupled fluid-structure interaction problems. The fluid is discretized using a discontinuous Galerkin method on unstructured tetrahedral meshes, and the structure uses a high-order volumetric continuous Galerkin finite element method. Standard radial basis functions are used for the mesh deformation. The time integration is performed using a partitioned approach based on implicit-explicit Runge-Kutta methods. The resulting scheme fully decouples the implicit solution procedures for the fluid and the solid parts, which we perform using two separate efficient parallel solvers. We demonstrate up to fifth order accuracy in time on a non-trivial test problem, on which we also show that additional subiterations are not required. We solve a benchmark problem of a cantilever beam in a shedding flow, and show good agreement with other results in the literature. In addition, we create several simulations which are motivated by real-world phenomena. First, we investigate flow around a thin membrane at high-angle of attack, demonstrating the ability of the leading edge of the membrane to align with the incident flow. Examples are provided in both two and three dimensions. Next, we consider biologically inspired flight, by investigating wing-like structures driven in a flapping motion in both two and three dimensions. Finally, we demonstrate how the method may be used in acoustics problems, simulating a tuning fork in three dimensions. Here we accurately capture decay rates purely from the fluid-structure interaction and without any damping coefficients built into the structure model.

A Hybridizable Discontinuous Galerkin Method For Modeling Fluid--structure Interaction

Author : Jason Sheldon
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (951 download)

DOWNLOAD NOW!

Book Synopsis A Hybridizable Discontinuous Galerkin Method For Modeling Fluid--structure Interaction by : Jason Sheldon

Download or read book A Hybridizable Discontinuous Galerkin Method For Modeling Fluid--structure Interaction written by Jason Sheldon and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: As computational methods have matured and computing power has increased over the years, simulations have grown in complexity by attempting to accurately model both larger and more involved physical systems. Although the computational demand of these simulations has increased, the required accuracy of the solution has not decreased, resulting in simulations that can become prohibitively computationally expensive. New computational tools need to be developed that both maintain solution accuracy while minimizing the ever increasing computational cost in time and resources. This dissertation presents a novel application of the recently developed hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid-structure interaction (FSI) problems. Current applications of the HDG method are reviewed and shown to be limited in scope to single-physics scenarios; however, they do include both solid and fluid problems, which are necessary for FSI modeling. Utilizing these established models, HDG formulations for linear elastostatics, linear elastodynamics, nonlinear elastodynamics, Eulerian Navier-Stokes, and arbitrary Lagrangian-Eulerian Navier-Stokes are derived. The elasticity formulations are all written in a Lagrangian reference frame, with the nonlinear formulation restricted to hyperelastic materials. With these individual solid and fluid formulations, the remaining challenge in FSI modeling is coupling together their disparate mathematics on the fluid-solid interface. In past work (Sheldon, 2012; Sheldon et al., 2014), a continuous Galerkin FSI model with a variety of coupling strategies was implemented, which greatly facilitated the process of creating a novel HDG FSI model. HDG FSI modeling comes with its own unique challenges, however, which are discussed and then addressed by modifications to the established component formulations. The resultant HDG FSI model is then presented. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then numerically validated against benchmark problems proposed by Turek and Hron (Turek and Hron, 2006). The HDG results show increasing accuracy compared to the benchmark's measured quantities as simulations are refined. Finally, concluding remarks are presented and the future work necessary to turn this HDG FSI model into a production level tool is outlined.

Discontinuous Galerkin Method

Author : Vít Dolejší
Publisher : Springer
ISBN 13 : 3319192671
Total Pages : 575 pages
Book Rating : 4.3/5 (191 download)

DOWNLOAD NOW!

Book Synopsis Discontinuous Galerkin Method by : Vít Dolejší

Download or read book Discontinuous Galerkin Method written by Vít Dolejší and published by Springer. This book was released on 2015-07-17 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.

Discontinuous Galerkin Methods

Author : Bernardo Cockburn
Publisher : Springer Science & Business Media
ISBN 13 : 3642597211
Total Pages : 468 pages
Book Rating : 4.6/5 (425 download)

DOWNLOAD NOW!

Book Synopsis Discontinuous Galerkin Methods by : Bernardo Cockburn

Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.

Proceedings of the 14th International Conference on Vibration Problems

Author : Evangelos J. Sapountzakis
Publisher : Springer Nature
ISBN 13 : 9811580499
Total Pages : 1203 pages
Book Rating : 4.8/5 (115 download)

DOWNLOAD NOW!

Book Synopsis Proceedings of the 14th International Conference on Vibration Problems by : Evangelos J. Sapountzakis

Download or read book Proceedings of the 14th International Conference on Vibration Problems written by Evangelos J. Sapountzakis and published by Springer Nature. This book was released on 2020-12-23 with total page 1203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the select proceedings of the 14th International Conference on Vibration Problems (ICOVP 2019) held in Crete, Greece. The volume brings together contributions from researchers working on vibration related problems in a wide variety of engineering disciplines such as mechanical engineering, wind and earthquake engineering, nuclear engineering, aeronautics, robotics, and transport systems. The focus is on latest developments and cutting-edge methods in wave mechanics and vibrations, and includes theoretical, experimental, as well as applied studies. The range of topics and the up-to-date results covered in this volume make this interesting for students, researchers, and professionals alike.

Design and Analysis of Space-time and Galerkin/least-squares Finite Element Methods for Fluid-structure Interaction in Exterior Domains

Download Design and Analysis of Space-time and Galerkin/least-squares Finite Element Methods for Fluid-structure Interaction in Exterior Domains PDF Online Free

Author : Stanford University. Division of Applied Mechanics. Division of Applied Mechanics
Publisher :
ISBN 13 :
Total Pages : 332 pages
Book Rating : 4.F/5 ( download)

DOWNLOAD NOW!

Book Synopsis Design and Analysis of Space-time and Galerkin/least-squares Finite Element Methods for Fluid-structure Interaction in Exterior Domains by : Stanford University. Division of Applied Mechanics. Division of Applied Mechanics

Download or read book Design and Analysis of Space-time and Galerkin/least-squares Finite Element Methods for Fluid-structure Interaction in Exterior Domains written by Stanford University. Division of Applied Mechanics. Division of Applied Mechanics and published by . This book was released on 1994 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Efficient High-Order Discretizations for Computational Fluid Dynamics

Author : Martin Kronbichler
Publisher : Springer Nature
ISBN 13 : 3030606104
Total Pages : 314 pages
Book Rating : 4.0/5 (36 download)

DOWNLOAD NOW!

Book Synopsis Efficient High-Order Discretizations for Computational Fluid Dynamics by : Martin Kronbichler

Download or read book Efficient High-Order Discretizations for Computational Fluid Dynamics written by Martin Kronbichler and published by Springer Nature. This book was released on 2021-01-04 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to teach the basics of the discontinuous Galerkin (DG) method in terms of its finite volume and finite element ingredients. It also discusses the computational efficiency of high-order methods versus state-of-the-art low order methods in the finite difference context, given that accuracy requirements in engineering are often not overly strict. The book mainly addresses researchers and doctoral students in engineering, applied mathematics, physics and high-performance computing with a strong interest in the interdisciplinary aspects of computational fluid dynamics. It is also well-suited for practicing computational engineers who would like to gain an overview of discontinuous Galerkin methods, modern algorithmic realizations, and high-performance implementations.

Fluid-structure Interactions

Author : Thomas Richter
Publisher : Springer
ISBN 13 : 3319639706
Total Pages : 452 pages
Book Rating : 4.3/5 (196 download)

DOWNLOAD NOW!

Book Synopsis Fluid-structure Interactions by : Thomas Richter

Download or read book Fluid-structure Interactions written by Thomas Richter and published by Springer. This book was released on 2017-08-26 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts by introducing the fundamental concepts of mathematical continuum mechanics for fluids and solids and their coupling. Special attention is given to the derivation of variational formulations for the subproblems describing fluid- and solid-mechanics as well as the coupled fluid-structure interaction problem. Two monolithic formulations for fluid-structure interactions are described in detail: the well-established ALE formulation and the modern Fully Eulerian formulation, which can effectively deal with problems featuring large deformation and contact. Further, the book provides details on state-of-the-art discretization schemes for fluid- and solid-mechanics and considers the special needs of coupled problems with interface-tracking and interface-capturing techniques. Lastly, advanced topics like goal-oriented error estimation, multigrid solution and gradient-based optimization schemes are discussed in the context of fluid-structure interaction problems.

An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method

Author : Justin Kauffman
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)

DOWNLOAD NOW!

Book Synopsis An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method by : Justin Kauffman

Download or read book An Overset Mesh Framework for the Hybridizable Discontinuous Galerkin Finite Element Method written by Justin Kauffman and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational simulations contain discretizations of both a physical domain and a mathematical model. In this dissertation, an overset mesh framework is used to discretize the physical domain, and the hybridizable discontinuous Galerkin (HDG) finite element method is used to discretize the mathematical model. It is proposed that using an overset mesh framework for the HDG method enables stable solutions to be computed for complex geometries and dynamic meshes. Overset mesh methods are chosen because they are efficient at decomposing geometrically complex domains. The HDG method was chosen because it provides solutions that are arbitrarily high-order accurate, reduces the size of the global discrete problem, and has the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. An overset mesh method can utilize an inherent property of the HDG method, the decomposition of the solution into global (face) and local (volume) parts. The global solution exists only on the cell boundaries; while, the local solution exists in the interior of each cell and is decoupled between neighboring cells. This decomposition introduces face-volume coupling in the weak form for degrees of freedom on cell boundaries, which is used as the foundation for the overset communication between subdomains.Ultimately, the goal of this work is to simulate full-scale hydrodynamic and fluid-structure interaction (FSI) problems. To achieve these simulations, the necessary building blocks must first be verified and validated in the overset-HDG framework. The building blocks demonstrated in this dissertation are steady convection-diffusion, linear elasticostatics, and pseudo-compressible Navier-Stokes in both Eulerian and arbitrary Lagrangian-Eulerian frames. Computational simulations are performed to demonstrate the applicability and accuracy of the overset-HDG algorithm.

Fluid-Structure Interaction

Author : Stefan Frei
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311049258X
Total Pages : 442 pages
Book Rating : 4.1/5 (14 download)

DOWNLOAD NOW!

Book Synopsis Fluid-Structure Interaction by : Stefan Frei

Download or read book Fluid-Structure Interaction written by Stefan Frei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-20 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph discusses modeling, adaptive discretisation techniques and the numerical solution of fluid structure interaction. An emphasis in part I lies on innovative discretisation and advanced interface resolution techniques. The second part covers the efficient and robust numerical solution of fluid-structure interaction. In part III, recent advances in the application fields vascular flows, binary-fluid-solid interaction, and coupling to fractures in the solid part are presented. Moreover each chapter provides a comprehensive overview in the respective topics including many references to concurring state-of-the art work. Contents Part I: Modeling and discretization On the implementation and benchmarking of an extended ALE method for FSI problems The locally adapted parametric finite element method for interface problems on triangular meshes An accurate Eulerian approach for fluid-structure interactions Part II: Solvers Numerical methods for unsteady thermal fluid structure interaction Recent development of robust monolithic fluid-structure interaction solvers A monolithic FSI solver applied to the FSI 1,2,3 benchmarks Part III: Applications Fluid-structure interaction for vascular flows: From supercomputers to laptops Binary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard Equations Coupling fluid-structure interaction with phase-field fracture: Algorithmic details

Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations

Author : Xiaobing Feng
Publisher : Springer Science & Business Media
ISBN 13 : 3319018183
Total Pages : 289 pages
Book Rating : 4.3/5 (19 download)

DOWNLOAD NOW!

Book Synopsis Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations by : Xiaobing Feng

Download or read book Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations written by Xiaobing Feng and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.

Computational Mechanics of Fluid-Structure Interaction

Author : Rajeev Kumar Jaiman
Publisher : Springer Nature
ISBN 13 : 9811653550
Total Pages : 337 pages
Book Rating : 4.8/5 (116 download)

DOWNLOAD NOW!

Book Synopsis Computational Mechanics of Fluid-Structure Interaction by : Rajeev Kumar Jaiman

Download or read book Computational Mechanics of Fluid-Structure Interaction written by Rajeev Kumar Jaiman and published by Springer Nature. This book was released on 2021-11-29 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide a compilation of the state-of-the-art numerical methods for nonlinear fluid-structure interaction using the moving boundary Lagrangian-Eulerian formulation. Single and two-phase viscous incompressible fluid flows are considered with the increasing complexity of structures ranging from rigid-body, linear elastic and nonlinear large deformation to fully-coupled flexible multibody system. This book is unique with regard to computational modeling of such complex fluid-structure interaction problems at high Reynolds numbers, whereby various coupling techniques are introduced and systematically discussed. The techniques are demonstrated for large-scale practical problems in aerospace and marine/offshore engineering. This book also provides a comprehensive understanding of underlying unsteady physics and coupled mechanical aspects of the fluid-structure interaction from a computational point of view. Using the body-fitted and moving mesh formulations, the physical insights associated with structure-to-fluid mass ratios (i.e., added mass effects), Reynolds number, large structural deformation, free surface, and other interacting physical fields are covered. The book includes the basic tools necessary to build the concepts required for modeling such coupled fluid-structure interaction problems, thus exposing the reader to advanced topics of multiphysics and multiscale phenomena.

International Workshop on Fluid-Structure Interaction. Theory, Numerics and Applications

Author : Stefan Hartmann
Publisher : kassel university press GmbH
ISBN 13 : 3899586670
Total Pages : 278 pages
Book Rating : 4.8/5 (995 download)

DOWNLOAD NOW!

Book Synopsis International Workshop on Fluid-Structure Interaction. Theory, Numerics and Applications by : Stefan Hartmann

Download or read book International Workshop on Fluid-Structure Interaction. Theory, Numerics and Applications written by Stefan Hartmann and published by kassel university press GmbH. This book was released on 2009 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finite Element Methods and Their Applications

Author : Mahboub Baccouch
Publisher : BoD – Books on Demand
ISBN 13 : 1839623411
Total Pages : 318 pages
Book Rating : 4.8/5 (396 download)

DOWNLOAD NOW!

Book Synopsis Finite Element Methods and Their Applications by : Mahboub Baccouch

Download or read book Finite Element Methods and Their Applications written by Mahboub Baccouch and published by BoD – Books on Demand. This book was released on 2021-11-17 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides several applications of the finite element method (FEM) for solving real-world problems. FEM is a widely used technique for numerical simulations in many areas of physics and engineering. It has gained increased popularity over recent years for the solution of complex engineering and science problems. FEM is now a powerful and popular numerical method for solving differential equations, with flexibility in dealing with complex geometric domains and various boundary conditions. The method has a wide range of applications in various branches of engineering such as mechanical engineering, thermal and fluid flows, electromagnetics, business management, and many others. This book describes the development of FEM and discusses and illustrates its specific applications.

Mathematical Analysis and Applications

Author : Themistocles M. Rassias
Publisher : Springer Nature
ISBN 13 : 3030313395
Total Pages : 694 pages
Book Rating : 4.0/5 (33 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Analysis and Applications by : Themistocles M. Rassias

Download or read book Mathematical Analysis and Applications written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2019-12-12 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: An international community of experts scientists comprise the research and survey contributions in this volume which covers a broad spectrum of areas in which analysis plays a central role. Contributions discuss theory and problems in real and complex analysis, functional analysis, approximation theory, operator theory, analytic inequalities, the Radon transform, nonlinear analysis, and various applications of interdisciplinary research; some are also devoted to specific applications such as the three-body problem, finite element analysis in fluid mechanics, algorithms for difference of monotone operators, a vibrational approach to a financial problem, and more. This volume is useful to graduate students and researchers working in mathematics, physics, engineering, and economics.

Numerical Mathematics and Advanced Applications 2011

Author : Andrea Cangiani
Publisher : Springer Science & Business Media
ISBN 13 : 3642331343
Total Pages : 811 pages
Book Rating : 4.6/5 (423 download)

DOWNLOAD NOW!

Book Synopsis Numerical Mathematics and Advanced Applications 2011 by : Andrea Cangiani

Download or read book Numerical Mathematics and Advanced Applications 2011 written by Andrea Cangiani and published by Springer Science & Business Media. This book was released on 2013-01-20 with total page 811 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.