Advanced Finite Element Methods and Applications

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Thomas Apel, Olaf Steinbach
Springer Science & Business Media, Jul 16, 2012 - Technology & Engineering - 376 pages
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This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods.

Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.

 

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Contents

A Brief History of the Parallel Dawn in KarlMarxStadtChemnitz
1
Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes
27
Fast Domain Decomposition Algorithms for Elliptic Problems with Piecewise Variable Orthotropism
57
Inexact Additive Schwarz Solvers for hpFEM Discretizations in Three Dimensions
90
A Rigorous Error Analysis of Coupled FEMBEM Problems with Arbitrary Many Subdomains
109
A Review of Anisotropic Refinement Methods for Triangular Meshes in FEM
133
Computing the Stress Intensity Factors
153
Multilevel Preconditioners for TemporalDifference Learning Methods Related to Recommendation Engines
175
Convergence Orders of Iterative Methods for Nonlinear Eigenvalue Problems
217
Sensitivity Analysis for Maxwell Eigenvalue Problems in Industrial Applications
239
Nonsequential Optical Field Tracing
257
Boundary Element Method for Linear Elasticity with Conservative Body Forces
274
Towards the Direct and Inverse Adaptive Mixed Finite Element Formulations for Nearly Incompressible Elasticity at Large Strains
299
Application of the Reciprocity Principle for the Determination of Planar Cracks in Piezoelectric Material
324
A Software for Simulating ThreeDimensional Fatigue Crack Growth
355
Copyright

Efficient Solvers for Saddle Point Problems with Applications to PDEConstrained Optimization
196

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