Download or read book A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces written by and published by . This book was released on 2007 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: The isotropic elastic wave equation governs the propagation of seismic waves caused by earthquakes and other seismic events. It also governs the propagation of waves in solid material structures and devices, such as gas pipes, wave guides, railroad rails and disc brakes. In the vast majority of wave propagation problems arising in seismology and solid mechanics there are free surfaces. These free surfaces have, in general, complicated shapes and are rarely flat. Another feature, characterizing problems arising in these areas, is the strong heterogeneity of the media, in which the problems are posed. For example, on the characteristic length scales of seismological problems, the geological structures of the earth can be considered piecewise constant, leading to models where the values of the elastic properties are also piecewise constant. Large spatial contrasts are also found in solid mechanics devices composed of different materials welded together. The presence of curved free surfaces, together with the typical strong material heterogeneity, makes the design of stable, efficient and accurate numerical methods for the elastic wave equation challenging. Today, many different classes of numerical methods are used for the simulation of elastic waves. Early on, most of the methods were based on finite difference approximations of space and time derivatives of the equations in second order differential form (displacement formulation), see for example [1, 2]. The main problem with these early discretizations were their inability to approximate free surface boundary conditions in a stable and fully explicit manner, see e.g. [10, 11, 18, 20]. The instabilities of these early methods were especially bad for problems with materials with high ratios between the P-wave (C{sub p}) and S-wave (C{sub s}) velocities. For rectangular domains, a stable and explicit discretization of the free surface boundary conditions is presented in the paper [17] by Nilsson et al. In summary, they introduce a discretization, that use boundary-modified difference operators for the mixed derivatives in the governing equations. Nilsson et al. show that the method is second order accurate for problems with smoothly varying material properties and stable under standard CFL constraints, for arbitrarily varying material properties. In this paper we generalize the results of Nilsson et al. to curvilinear coordinate systems, allowing for simulations on non-rectangular domains. Using summation by parts techniques, we show that there exists a corresponding stable discretization of the free surface boundary condition on curvilinear grids. We also prove that the discretization is stable and energy conserving both in semi-discrete and fully discrete form. As for the Cartesian method in, [17], the stability and conservation results holds for arbitrarily varying material properties. By numerical experiments it is established that the method is second order accurate.
Download or read book The Finite Difference Modelling of Earthquake Motions written by Peter Moczo and published by Cambridge University Press. This book was released on 2014-04-24 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.
Download or read book Earthquake Engineering written by Halil Sezen and published by BoD – Books on Demand. This book was released on 2012-08-08 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent major earthquakes around the world have shown the vulnerability of infrastructure and the need for research to better understand the nature of seismic events and their effects on structures. As a result, earthquake engineering research has been expanding as more and more data become available from a large array of seismic instruments, large scale experiments and numerical simulations. The first part of this book presents results from some of the current seismic research work including three-dimensional wave propagation in different soil media, seismic loss assessment, probabilistic hazard analysis, geotechnical problems including soil-structure interaction. The second part of the book focuses on the seismic behavior of structures including historical and monumental structures, bridge embankments, and different types of bridges and bearings.
Download or read book Differential Quadrature and Differential Quadrature Based Element Methods written by Xinwei Wang and published by Butterworth-Heinemann. This book was released on 2015-03-24 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Quadrature and Differential Quadrature Based Element Methods: Theory and Applications is a comprehensive guide to these methods and their various applications in recent years. Due to the attractive features of rapid convergence, high accuracy, and computational efficiency, the differential quadrature method and its based element methods are increasingly being used to study problems in the area of structural mechanics, such as static, buckling and vibration problems of composite structures and functional material structures. This book covers new developments and their applications in detail, with accompanying FORTRAN and MATLAB programs to help you overcome difficult programming challenges. It summarises the variety of different quadrature formulations that can be found by varying the degree of polynomials, the treatment of boundary conditions and employing regular or irregular grid points, to help you choose the correct method for solving practical problems. - Offers a clear explanation of both the theory and many applications of DQM to structural analyses - Discusses and illustrates reliable ways to apply multiple boundary conditions and develop reliable grid distributions - Supported by FORTRAN and MATLAB programs, including subroutines to compute grid distributions and weighting coefficients
Download or read book Supercomputing written by Vladimir Voevodin and published by Springer Nature. This book was released on 2019-12-09 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-conference proceedings of the 5th Russian Supercomputing Days, RuSCDays 2019, held in Moscow, Russia, in September 2019. The 60 revised full papers presented were carefully reviewed and selected from 127 submissions. The papers are organized in the following topical sections: parallel algorithms; supercomputer simulation; HPC, BigData, AI: architectures, technologies, tools; and distributed and cloud computing.
Download or read book High Performance Computing written by Julian M. Kunkel and published by Springer. This book was released on 2017-06-09 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 32nd International Conference, ISC High Performance 2017, held in Frankfurt, Germany, in June 2017. The 22 revised full papers presented in this book were carefully reviewed and selected from 66 submissions. The papers cover the following topics: applications and algorithms; proxy applications; architecture and system optimization; and energy-aware computing.
Download or read book High Performance Computing on Vector Systems 2009 written by Sabine Roller and published by Springer Science & Business Media. This book was released on 2009-10-07 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the results of the Tera op Workbench, other projects related to High Performance Computing, and the usage of HPC installations at HLRS. The Tera op Workbench project is a collaboration between the High Performance C- puting Center Stuttgart (HLRS) and NEC Deutschland GmbH (NEC-HPCE) to s- port users in achieving their research goals using High Performance Computing. The rst stage of the Tera op Workbench project (2004–2008) concentrated on user’s applications and their optimization for the former ag ship of HLRS, a - node NEC SX-8 installation. During this stage, numerous individual codes, dev- oped and maintained by researchers or commercial organizations, have been a- lyzed and optimized. Within the project, several of the codes have shown the ability to outreach the TFlop/s threshold of sustained performance. This created the pos- bility for new science and a deeper understanding of the underlying physics. The second stage of the Tera op Workbench project (2008–2012) focuses on c- rent and future trends of hardware and software developments. We observe a strong tendency to heterogeneous environments on the hardware level, while at the same time, applications become increasingly heterogeneous by including multi-physics or multi-scale effects. The goal of the current studies of the Tera op Workbench is to gain insight in the developments of both components. The overall target is to help scientists to run their application in the most ef cient and most convenient way on the hardware best suited for their purposes.
Download or read book Parallel Computing Technologies written by Victor Malyshkin and published by Springer. This book was released on 2017-08-17 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 14th International Conference on Parallel Computing Technologies, PaCT 2017, held in Nizhny Novgorod, Russia, in September 2017. The 25 full papers and 24 short papers presented were carefully reviewed and selected from 93 submissions. The papers are organized in topical sections on mainstream parallel computing, parallel models and algorithms in numerical computation, cellular automata and discrete event systems, organization of parallel computation, parallel computing applications.
Download or read book Research and Education Traditions and Innovations written by Sergei Khakhomov and published by Springer Nature. This book was released on 2022-03-31 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains selected articles presented at the 19th International Conference on Global Research and Education, organized by the Francisk Skorina Gomel State University in Gomel, Belarus, Octoter 20–22, 2021. The areas of focus of the book are modern areas of physics and technology, as well as methods and materials of e-learning and online education. It covers areas as plasma physics, bioengineering, solid state physics, nanoelectronics, photonics, environmental design, compositional structures and metamaterials, robotics and metrology, computer physics, online education and e-learning.
Download or read book Computational Methods in Geosciences written by William Edward Fitzgibbon and published by SIAM. This book was released on 1992-01-01 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses a dozen topics related to mathematical and computational issues in geophysical fluid and solid mechanics, including local grid refinement for reservoir simulation, a method of factoring long z-transform polynomials, and the finite element modelling of surface flow problems. See entry QC155
Download or read book Nodal Discontinuous Galerkin Methods written by Jan S. Hesthaven and published by Springer Science & Business Media. This book was released on 2007-12-18 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE’s, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE’s: Maxwell’s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.
Download or read book Hypercube Multiprocessors 1987 written by Michael T. Heath and published by SIAM. This book was released on 1987-01-01 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Parallel Computing.
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computational Seismology written by Heiner Igel and published by Oxford University Press. This book was released on 2017 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text to a range of numerical methods used today to simulate time-dependent processes in Earth science, physics, engineering and many other fields. It looks under the hood of current simulation technology and provides guidelines on what to look out for when carrying out sophisticated simulation tasks.
Download or read book Stability Analysis of Finite Difference Schemes for the Viscoelastic Wave Equation written by and published by . This book was released on 1994 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is difficult to predict stability properties of a finite difference scheme. It has to be investigated through the roots of the Z-transformed and Fourier transformed difference scheme (modal equation). To simultaneously investigate several schemes for the viscoelastic wave equation, it is possible to derive the modal equation with parameterized coefficients. Several conditionally stable schemes were found, where the most efficient is a staggered scheme with a stability condition closely resembling that of an elastic scheme.
Download or read book Finite Element and Discontinuous Galerkin Methods for Transient Wave Equations written by Gary Cohen and published by Springer. This book was released on 2016-08-05 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulationof waves.
Download or read book Numerical Grid Generation written by J. F. Thompson and published by Appleton & Lange. This book was released on 1985-06-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
