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iliev o numerical solution partial differential equ 2013

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Textbook in PDF format Introduction FirstOrder System LeastSquares Sample Problem and Loss of Conservation Constrained FOSLS ``Galerkin Constraint'' ``LeastSquares Constraint'' Solvers Construction of B Numerical Results Discussion Locally Constrained FOSLS Correction Overlapping Schwarz Corrections Numerical Results Conclusions References Multiscale Coarsening for Linear Elasticity by Energy Minimization Introduction Governing Equations and Their Discretization The Equations of Linear Elasticity Weak Formulation Finite Element Discretization The TwoLevel Method TwoLevel Additive Schwarz Fine and Coarse Triangulation Abstract Multiscale Coarse Space Energy Minimization for the Elasticity System The EnergyMinimizing Coarse Space Properties of the EnergyMinimizing Coarse Space The Interpolation Operator Numerical Experiments Coarse Space Robustness Coarse Space Approximation Discussion References Preconditioners for Some Matrices of TwobyTwo Block Form, with Applications, I Introduction The Preconditioner and Its Implementation Condition Number Bounds A Is Symmetric and Positive Semidefinite A Is Symmetric and Positive Definite Distributed Optimal Control of Elliptic and Oseen Equations An Elliptic State Equation Distributed Optimal Control of the Oseen Problem References A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition Introduction Preliminaries The Multigrid Algorithm Multigrid Analysis Numerical Results References Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs Introduction Unsmoothed Aggregation AMG The Setup Phase A Maximal Independent Set Algorithm Parallel Graph Aggregation Algorithm Aggregation Quality Improvements Solve Phase Parallel Smoother Prolongation and Restriction KCycle Sparse MatrixVector Multiplication on GPUs Numerical Tests Numerical Tests for PAA Numerical Tests for GPU Implementation References Aspects of Guaranteed Error Control in CPDEs Introduction Review of Guaranteed Energy Norm Error Control Notation Equilibration Error Estimators Poisson Model Problem with Big Oscillations Guaranteed Error Control for CRNCFEM Main Result Guaranteed Upper Bounds for ||Res|||* Guaranteed Upper Bounds for ||||ResNC|||| Numerical Experiment with Big Oscillations Guaranteed Error Control for Curved Boundaries Guaranteed GoalOriented Error Estimation Reduction to L Functionals Guaranteed Bounds for Goal Functionals Benchmark Example References A Finite Volume Element Method for a Nonlinear Parabolic Problem Introduction Preliminaries Error Estimates for the Backward Euler Method Existence of the Backward Euler Approximation A Linearized Fully Discrete Scheme Numerical Examples References Multidimensional Sensitivity Analysis of LargeScale Mathematical Models Introduction Problem Setting Modeling and Sensitivity Complexity in Classes of Algorithms The Algorithms ΛΠτ Sobol Sequences The Monte Carlo Algorithms Based on Modified Sobol Sequences: MCAMSS Case Study: VarianceBased Sensitivity Analysis of the Unified Danish Eulerian Model Numerical Results and Discussion Conclusions References Structures and Waves in a Nonlinear HeatConducting Medium Introduction The Radially Symmetric Case, the Main Notions The Basic BlowUp Regimes HSEvolution, Total BlowUp

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iliev o numerical solution partial differential equ 2013