Computing with hp-ADAPTIVE FINITE ELEMENTS

by Leszek Demkowicz; Jason Kurtz; David Pardo; Maciek Paszenski; Waldemar Rachowicz; Adam Zdunek

• ISBN13: 9781420011692
• ISBN10: 1420011693
• Format: Nonspecific Binding
• Copyright: 2007-11-02
• Publisher: Taylor & Francis

Summary

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.

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

Index

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