Download or read book Research on Parallel Adaptive Finite Element Methods written by and published by . This book was released on 2000 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this project we studied several fundamental issues arising in the parallel adaptive solution of linear and nonlinear elliptic and parabolic PDEs using multilevel algorithms. We focused our attention on a new approach described in the paper ''A New Paradigm for Parallel Adaptive Mesh Refinement'' by Bank and Hoist. The new approach requires almost no communication to solve an elliptic equation in parallel, and therefore has the potential to scale much more efficiently on massively parallel computers than do more traditional algorithms. The algorithm described in the Bank and Hoist paper has an inherently multilevel structure, in that a sequence of problems on a refinement hierarchy of meshes is solved during the course of the calculation. In particular, the algorithm has three main components: (1) We solve a small problem on a coarse mesh, and use a posteriori error estimates to partition the mesh. (2) Each processor is provided the complete coarse mesh and instructed to solve the entire problem, but with its adaptive refinement largely limited to its own assigned mesh partition. (3) A final mesh is computed using the union of the refined partitions provided by each processor. The mesh is regularized into a global conformal mesh, and a final solution is computed using a standard overlapping domain decomposition method or a parallel multigrid method. In certain circumstances the third step can be avoided, leading to an algorithm with no communication beyond that required to synchronize the processors at the beginning of the calculation. We looked at the algorithm closely during the LLNL project in Summer 1999, and we examined algorithms for performing the third step of the algorithm efficiently on massively parallel computers, including parallel multilevel methods and mortar element methods. One result of the summer work at LLNL was a scheme for producing a global conforming mesh in the 3D case through the use of a consistent tie-breaking approach in conjunction with longest-edge simplex bisection. This result completely removes some of the implementation complexity that normally makes the 3D case much more difficult that the 2D case. We presented our work on the parallel algorithm at the Workshop on Iterative Methods held in Livermore in Summer 1999.
Download or read book Parallel Adaptive Finite Element Analysis written by David Kok Hong Leong and published by . This book was released on 2000 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Key Based Parallel Adaptive Refinement Technique for Finite Element Methods written by and published by . This book was released on 1997 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Massively Parallel Adaptive Finite Element Method with Dynamic Load Balancing written by and published by . This book was released on 1993 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct massively parallel, adaptive finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. We also present results using adaptive p-refinement to reduce the computational cost of the method. We describe tiling, a dynamic, element-based data migration system. Tiling dynamically maintains global load balance in the adaptive method by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. We demonstrate the effectiveness of the dynamic load balancing with adaptive p-refinement examples.
Download or read book Parallel Adaptive Finite Element Methods for Problems in Natural Convection written by and published by . This book was released on 2008 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulations of combined buoyant and surface tension driven flow, also known as Rayleigh-Bénard-Marangoni (RBM) convection are conducted for heated fluid layers of small aspect ratio (defined as the ratio of the horizontal extent of the domain divided by the depth of the fluid) in square cross-section containers. A particular non-dimensionalization of the governing equations is developed in which the aspect ratio of the domain appears as a continuous parameter. The simulations extend and enhance existing experimental studies of the RBM convection phenomenon by mapping continuous solution branches in aspect ratio and Marangoni number parameter space. Key implementation aspects of the development of the adaptive mesh refinement (AMR) library libMesh are discussed, and a series of simulations of the RBM problem with a stick-slip boundary condition demonstrate the suitability of AMR for computing these flows.
Download or read book Adaptive Finite and Boundary Element Methods written by C. A. Brebbia and published by . This book was released on 1993-01 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallel Multigrid on Unstructured Grids Using Adaptive Finite Element Methods written by Linda Stals and published by . This book was released on 1995 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Finite Element Methods with Applications written by Thomas Apel and published by Springer. This book was released on 2019-06-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.
Download or read book Parallel hp adaptive finite element analysis for viscous incompressible flow problems written by Abani Kumar Patra and published by . This book was released on 1995 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A New Parallel Domain Decomposition Method for the Adaptive Finite Element Solution of Elliptic Parallel Differential Equations written by R. E. Bank and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Birkhäuser. This book was released on 2013-11-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Springer Science & Business Media. This book was released on 2003-01-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix.
Download or read book Parallel Finite Element Computations written by B. H. V. Topping and published by . This book was released on 1996 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describing the main procedures for the parallelization of the finite element method for distributed memory architectures, this book is for engineers, computer scientists and mathematicians working on the application of high performance computing to finite element methods. Its procedures are applicable to distributed memory computer architectures.
Download or read book Finite Elements written by Sashikumaar Ganesan and published by Cambridge University Press. This book was released on 2017-05-11 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: An easy-to-understand guide covering the key principles of finite element methods and its applications to differential equations.
Download or read book A Parallel Goal oriented Adaptive Finite Element Method for 2 5D Electromagnetic Modeling written by Kerry Key and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a parallel goal-oriented adaptive finite element algorithm that can be used to rapidly compute highly accurate solutions for 2.5D controlled-source electromagnetic (CSEM) and 2D magnetotelluric (MT) modeling problems. We employ unstructured triangular grids to permit efficient discretization of complex modeling domains such as those containing topography, dipping layers and multiple scale structures. Iterative mesh refinement is guided by a goal-oriented error estimator based on a form of dual residual weighting, which is carried out using hierarchical basis computations. Our formulation of the error estimator considers the relative error in the strike aligned fields and their spatial gradients, and therefore results in a more efficient use of mesh vertices than previous error estimators based on absolute field errors. This algorithm is parallelized over frequencies, transmitters, receivers and wave-numbers, where adaptive refinement can be performed in parallel on subsets of these parameters while nearby parameters are able to share the refined grid, thus enabling our algorithm to achieve accurate solutions in run-times of seconds to tens of seconds for realistic models and data parameters when run on cluster computers containing about a thousand processors. Application of this new algorithm to a complex model that includes strong seafloor topography variations and multiple thin stacked reservoirs demonstrates the performance and scalability on a large cluster computer.
Download or read book A parallel infrastructure for scalable adaptive finite element methods and its application to least squares C infinity supercsript collocation written by Harold Carter Edwards and published by . This book was released on 1997 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parallel Multilevel Methods written by Gerhard Zumbusch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Main aspects of the efficient treatment of partial differential equations are discretisation, multilevel/multigrid solution and parallelisation. These distinct topics are covered from the historical background to modern developments. It is demonstrated how the ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic boundary value problems. Error estimators and adaptive grid refinement techniques for ordinary and for sparse grid discretisations are presented. Different types of additive and multiplicative multilevel solvers are discussed with respect to parallel implementation and application to adaptive refined grids. Efficiency issues are treated both for the sequential multilevel methods and for the parallel version by hash table storage techniques. Finally, space-filling curve enumeration for parallel load balancing and processor cache efficiency are discussed.
