UID:
(DE-602)gbv_165249944X
Umfang:
Online-Ressource (XII, 327 p. 49 illus, digital)
ISBN:
9781461471721
Serie:
Springer Proceedings in Mathematics & Statistics 45
Inhalt:
Improving Conservation for First-Order System Least Squares Finite-Element Methods, James Adler, Panayot Vassilevski -- Multiscale Coarsening for Linear Elasticity by Energy Minimization, Heiko Andrae, Marco Buck, Oleg Iliev -- Preconditioners for some matrices of two-by-two block form, with applications, I, Owe Axelsson -- A multigrid algorithm for an elliptic problem with a perturbed boundary condition, Andrea Bonito, Joe Pasciak -- Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs, James Brannick, Yao Chen, Xiaozhe Hu, Ludmil Zikatanov -- Aspects of Guaranteed Error Control in Computational Partial Differential Equations, Carsten Carstensen, Christian Merdon, Johannes Neumann -- A Finite Volume Element Method for a Nonlinear Parabolic Problem, Panagiotis Chatzipantelidis, Victor Ginting -- Multidimensional Sensitivity Analysis of Large-scale Mathematical Models, Ivan Dimov, Rayna Georgieva -- Structures and waves in a nonlinear heat-conducting medium, Stefka Dimova, Milena Dimova, Daniela Vasileva -- Efficient parallel algorithms for unsteady incompressible flows, Jean-Luc Guermond, Peter Minev -- Efficient solvers for some classes of time-periodic eddy current optimal control problems -- Michael Kolmbauer, Ulrich Langer -- Robust Algebraic Multilevel Preconditioners for Anisotropic Problems, Johannes Kraus, Maria Lymbery, Svetozar Margenov -- A weak Galerkin mixed finite element method for biharmonic equations, Lin Mu, Junping Wang, Yanqiu Wang, Xiu Ye -- Domain decomposition scheme for first order evolution equations with nonselfadjoint operators, Petr Vabishchevich, Petr Zakharov -- Spectral coarse spaces in robust two-level methods, Joerg Willems.
Inhalt:
One of the current main challenges in the area of scientific computing is the design and implementation of accurate numerical models for complex physical systems which are described by time-dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles, and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability, and robustness of the algorithms in porous media, structural mechanics, and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful. .
Anmerkung:
Description based upon print version of record
,
Preface; Contents; Improving Conservation for First-Order System Least-Squares Finite-Element Methods; 1 Introduction; 2 First-Order System Least-Squares; 2.1 Sample Problem and Loss of Conservation; 3 Constrained FOSLS; 3.1 ``Galerkin Constraint''; 3.2 ``Least-Squares Constraint''; 3.3 Solvers; 3.3.1 Construction of B; 3.4 Numerical Results; 3.5 Discussion; 4 Locally Constrained FOSLS Correction; 4.1 Overlapping Schwarz Corrections; 4.2 Numerical Results; 5 Conclusions; References; Multiscale Coarsening for Linear Elasticity by Energy Minimization; 1 Introduction
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2 Governing Equations and Their Discretization2.1 The Equations of Linear Elasticity; 2.2 Weak Formulation; 2.3 Finite Element Discretization; 3 The Two-Level Method; 3.1 Two-Level Additive Schwarz; 3.2 Fine and Coarse Triangulation; 3.3 Abstract Multiscale Coarse Space; 4 Energy Minimization for the Elasticity System; 4.1 The Energy-Minimizing Coarse Space; 4.2 Properties of the Energy-Minimizing Coarse Space; 4.3 The Interpolation Operator; 5 Numerical Experiments; 5.1 Coarse Space Robustness; 5.2 Coarse Space Approximation; 6 Discussion; References
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Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I1 Introduction; 2 The Preconditioner and Its Implementation; 3 Condition Number Bounds; 3.1 A Is Symmetric and Positive Semidefinite; 3.2 A Is Symmetric and Positive Definite; 4 Distributed Optimal Control of Elliptic and Oseen Equations; 4.1 An Elliptic State Equation; 4.2 Distributed Optimal Control of the Oseen Problem; References; A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition; 1 Introduction; 2 Preliminaries; 3 The Multigrid Algorithm; 4 Multigrid Analysis
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5 Numerical ResultsReferences; Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs; 1 Introduction; 2 Unsmoothed Aggregation AMG; 3 The Setup Phase; 3.1 A Maximal Independent Set Algorithm; 3.2 Parallel Graph Aggregation Algorithm; 3.3 Aggregation Quality Improvements; 4 Solve Phase; 4.1 Parallel Smoother; 4.2 Prolongation and Restriction; 4.3 K-Cycle; 4.4 Sparse Matrix-Vector Multiplication on GPUs; 5 Numerical Tests; 5.1 Numerical Tests for PAA; 5.2 Numerical Tests for GPU Implementation; References; Aspects of Guaranteed Error Control in CPDEs; 1 Introduction
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2 Review of Guaranteed Energy Norm Error Control2.1 Notation; 2.2 Equilibration Error Estimators; 2.3 Poisson Model Problem with Big Oscillations; 3 Guaranteed Error Control for CR-NCFEM; 3.1 Main Result; 3.2 Guaranteed Upper Bounds for ||Res|||*; 3.3 Guaranteed Upper Bounds for ||||ResNC||||; 3.4 Numerical Experiment with Big Oscillations; 4 Guaranteed Error Control for Curved Boundaries; 5 Guaranteed Goal-Oriented Error Estimation; 5.1 Reduction to L2 Functionals; 5.2 Guaranteed Bounds for Goal Functionals; 5.3 Benchmark Example; References
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A Finite Volume Element Method for a Nonlinear Parabolic Problem
Weitere Ausg.:
ISBN 9781461471714
Weitere Ausg.:
Erscheint auch als Druck-Ausgabe Numerical solution of partial differential equations:Theory, algorithms, and their applications New York : Springer, 2013 ISBN 9781461471714
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Partielle Differentialgleichung
;
Numerisches Verfahren
DOI:
10.1007/978-1-4614-7172-1
URL:
Volltext
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URL:
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