Computing with HP-Adaptive Finite Elements: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications (Hardcover)

PREFACETHEORY AND CODE DEVELOPMENTBOUNDARY-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 Functions3D HP FINITE ELEMENT METHOD Construction of FE Basis Functions on Regular MeshesSupported h-Refinementsp-Refinements and the Minimum Rule Constrained Approximation3DHP CODEOrganization of the 3Dhp Code Data Structure in FORTRAN 90 Data Structure Supporting AlgorithmsGEOMETRY MODELINGGMP Manifold: Compatible Parametrizations Transfinite Interpolation Interfacing with CUBITExact Geometry and Parametric Elements: Mesh GenerationAUTOMATIC HP ADAPTIVITY IN THREE SPACE DIMENSIONSThe hp AlgorithmGoal-Oriented hp AdaptivityExamplesHIGH-PERFORMANCE COMPUTATIONFast Integration AlgorithmTelescopic Solver Linear SolversTWO-GRID HP SOLVERFormulationElementary Convergence TheoryImplementation DetailsNumerical ExamplesA DOMAIN DECOMPOSITION-BASED PARALLEL IMPLEMENTATION Mesh Repartitioning. Interfacing with Zoltan A Nested-Dissections Parallel Multi-Frontal Solver Parallel Mesh Refinements and Mesh ReconciliationNumerical ExamplesAPPLICATIONS ACOUSTIC SCATTERING PROBLEMS Infinite Element ExamplesELECTROMAGNETIC SCATTERING PROBLEMS Formulation of Scattering Problems EM Infinite ElementA Domain Decomposition ApproachCalculation of Radar Cross SectionAdaptivityExamples3D ELASTICITY AND THIN-WALLED STRUCTURES Introduction Classical Shell Theory-ComparisonSolutions of Complex Thin-Walled StructuresSIMULATION OF RESISTIVITY LOGGING DEVICES Description and Finite Element Modeling of Resistivity Logging Measurements2D Numerical Simulations of Axisymmetric Problems3D Numerical SimulationsCONCLUSIONS AND FUTURE WORK APPENDICESREFERENCESINDEX