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.

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.

Preface. Boundary-Value Problems. Exact hp Sequences, Projection-Based Interpolation, De Rham Diagrams. 3D hp Finite Element Method. 3Dhp Code. Geometry Modeling. Automatic hp Adaptivity in Three Space Dimensions. High-Performance Computation. Two-Grid hp Solver. A Domain Decomposition-Based Parallel Implementation. Acoustic Scattering Problems. Electromagnetic Scattering Problems. 3D Elasticity and Thin-Walled Structures. Simulation of Resistivity Logging Devices. Conclusions and Future Work. Appendices. References. Index.

This book presents the theoretical foundations of the 3D hp algorithm and provides numerical results using the 3Dhp code developed by the authors and their colleagues. Focusing on the 3D theory of hp methods as well as coding issues, the first part 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 applications in which the 3Dhp code was used, including acoustic and electromagnetic scattering problems, thin-walled structures, and challenging simulations of logging tools.

"Together with the first volume, the second volume forms a unique, up-to-date, and self-contained presentation of the current status of hp-adaptive finite elements ...This two-volume book is therefore strongly recommended to all mathematicians as well as engineers working on hp-adaptive finite element methods."
—Journal of Applied Mathematics and Mechanics

"This is an elegant framework for the hp element with generalize classical elements of Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini . . . The authors provide here such a useful survey within 400 pages." – Dietrich Braess, in Mathematical Reviews, 2009e

Presents the theoretical foundations of the 3D hp algorithm and provides numerical results using the 3Dhp code. Focusing on the 3D theory of hp methods as well as coding issues, this book also presents the 3D version of the automatic hp-adaptivity package, and a two-grid solver for highly anisotropic hp meshes and goal-oriented Krylov iterations.

Über den Autor

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, USA

Inhaltsverzeichnis

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 Deillegalscription and Finite Element Modeling of Resistivity Logging Measurements 2D Numerical Simulations of Axisymmetric Problems 3D Numerical Simulations CONCLUSIONS AND FUTURE WORK APPENDICES REFERENCES INDEX

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