Computing with HP-Adaptive Finite Elements: Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications Volume 2
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Computing with HP-Adaptive Finite Elements: Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications Volume 2

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Description

With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts and logic governing 3D code and implementation. Taking the next step in hp technology, Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the 3D hp algorithm and provides numerical results using the 3Dhp code developed by the authors and their colleagues. The first part of the book focuses on fundamentals of the 3D theory of hp methods as well as issues that arise when the code is implemented. After a review of boundary-value problems, the book examines exact hp sequences, projection-based interpolation, and De Rham diagrams. It also presents the 3D version of the automatic hp-adaptivity package, a two-grid solver for highly anisotropic hp meshes and goal-oriented Krylov iterations, and a parallel implementation of the 3D code. The second part explores several recent projects in which the 3Dhp code was used and illustrates how these applications have greatly driven the development of 3D hp technology. It encompasses acoustic and electromagnetic (EM) scattering problems, an analysis of complex structures with thin-walled components, and challenging simulations of logging tools. The book concludes with a look at the future of hp methods. Spearheaded by a key developer of this technology with more than 20 years of research in the field, this self-contained, comprehensive resource will help readers overcome the difficulties in coding hp-adaptive elements.show more

Product details

  • Hardback | 440 pages
  • 166.9 x 231.9 x 28.2mm | 716.68g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • United States
  • English
  • 250 black & white illustrations, 7 black & white tables
  • 1584886722
  • 9781584886723

About Leszek Demkowicz

The University of Texas at Austin, USA The University of Texas at Austin, USA The University of Texas at Austin, USA The University of Texas at Austin, USA The University of Texas at Austin, USA The University of Texas at Austin, USAshow more

Table of contents

PREFACE THEORY AND CODE DEVELOPMENT BOUNDARY-VALUE PROBLEMS Single Elliptic Equation Linear Elasticity Maxwell Equations Elasticity Coupled with Acoustics EXACT HP SEQUENCES, PROJECTION-BASED INTERPOLATION, DE RHAM DIAGRAMS Exact Polynomial Sequences H1-, H(curl)-, and H(div)-Conforming Projection-Based Interpolation Shape Functions 3D HP FINITE ELEMENT METHOD Construction of FE Basis Functions on Regular Meshes Supported h-Refinements p-Refinements and the Minimum Rule Constrained Approximation 3DHP CODE Organization of the 3Dhp Code Data Structure in FORTRAN 90 Data Structure Supporting Algorithms GEOMETRY MODELING GMP Manifold: Compatible Parametrizations Transfinite Interpolation Interfacing with CUBIT Exact Geometry and Parametric Elements: Mesh Generation AUTOMATIC HP ADAPTIVITY IN THREE SPACE DIMENSIONS The hp Algorithm Goal-Oriented hp Adaptivity Examples HIGH-PERFORMANCE COMPUTATION Fast Integration Algorithm Telescopic Solver Linear Solvers TWO-GRID HP SOLVER Formulation Elementary Convergence Theory Implementation Details Numerical Examples A DOMAIN DECOMPOSITION-BASED PARALLEL IMPLEMENTATION Mesh Repartitioning. Interfacing with Zoltan A Nested-Dissections Parallel Multi-Frontal Solver Parallel Mesh Refinements and Mesh Reconciliation Numerical Examples APPLICATIONS ACOUSTIC SCATTERING PROBLEMS Infinite Element Examples ELECTROMAGNETIC SCATTERING PROBLEMS Formulation of Scattering Problems EM Infinite Element A Domain Decomposition Approach Calculation of Radar Cross Section Adaptivity Examples 3D ELASTICITY AND THIN-WALLED STRUCTURES Introduction Classical Shell Theory-Comparison Solutions of Complex Thin-Walled Structures SIMULATION OF RESISTIVITY LOGGING DEVICES Description and Finite Element Modeling of Resistivity Logging Measurements 2D Numerical Simulations of Axisymmetric Problems 3D Numerical Simulations CONCLUSIONS AND FUTURE WORK APPENDICES REFERENCES INDEXshow more

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