Engineering Mathematics: (As per JNTU Syllabus) Volume I, G. Shanker Rao

Автор: Martinsson, Per-gunnar
Название: Fast direct solvers for elliptic pdes
ISBN: 1611976030 ISBN-13(EAN): 9781611976038
Издательство: Mare Nostrum (Eurospan)
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Цена: 72730.00 T
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Описание: Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE.This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques.Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

Автор: Gunilla Kreiss; Per L?tstedt; Axel M?lqvist; Maya
Название: Numerical Mathematics and Advanced Applications 2009
ISBN: 3662519534 ISBN-13(EAN): 9783662519530
Издательство: Springer
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Цена: 241310.00 T
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Описание: Invited papers.- Discrete Differential Forms, Approximation of Eigenvalue Problems, and Application to the p Version of Edge Finite Elements.- Semi-Implicit DGFE Discretization of the Compressible Navier-Stokes Equations: Efficient Solution Strategy.- Some Numerical Approaches for Weakly Random Homogenization.- Goal Oriented, Anisotropic, A Posteriori Error Estimates for the Laplace Equation.- Contributed papers.- Energy Stability of the MUSCL Scheme.- Numerical Stabilization of the Melt Front for Laser Beam Cutting.- Numerical Optimization of a Bioreactor for the Treatment of Eutrophicated Water.- Finite Element Approximation of a Quasi-3D Model for Estuarian River Flows.- Convergence of a Mixed Discontinuous Galerkin and Finite Volume Scheme for the 3 Dimensional Vlasov-Poisson-Fokker-Planck System.- Infrastructure for the Coupling of Dune Grids.- FEM for Flow and Pollution Transport in a Street Canyon.- Stabilized Finite Element Methods with Shock-Capturing for Nonlinear Convection-Diffusion-Reaction Models.- Finite Element Discretization of the Giesekus Model for Polymer Flows.- A dG Method for the Strain-Rate Formulation of the Stokes Problem Related with Nonconforming Finite Element Methods.- Numerical Simulation of the Stratified Flow Past a Body.- A Flexible Updating Framework for Preconditioners in PDE-Based Image Restoration Algorithms.- Stabilized Finite Element Method for Compressible-Incompressible Diphasic Flows.- An Immersed Interface Technique for the Numerical Solution of the Heat Equation on a Moving Domain.- Lid-Driven-Cavity Simulations of Oldroyd-B Models Using Free-Energy-Dissipative Schemes.- Adaptive Multiresolution Simulation of Waves in Electrocardiology.- On the Numerical Approximation of the Laplace Transform Function from Real Samples and Its Inversion.- A Motion-Aided Ultrasound Image Sequence Segmentation.- A High Order Finite Volume Numerical Scheme for Shallow Water System: An Efficient Implementation on GPUs.- Spectral Analysis for Radial Basis Function Collocation Matrices.- Finite Element Solution of the Primitive Equations of the Ocean by the Orthogonal Sub-Scales Method.- Solution of Incompressible Flow Equations by a High-Order Term-by-Term Stabilized Method.- Solving Large Sparse Linear Systems Efficiently on Grid Computers Using an Asynchronous Iterative Method as a Preconditioner.- Hierarchical High Order Finite Element Approximation Spaces for H(div) and H(curl).- Some Theoretical Results About Stability for IMEX Schemes Applied to Hyperbolic Equations with Stiff Reaction Terms.- Stable Perfectly Matched Layers for the Schrцdinger Equations.- Domain Decomposition Schemes for Frictionless Multibody Contact Problems of Elasticity.- Analysis and Acceleration of a Fluid-Structure Interaction Coupling Scheme.- Second Order Numerical Operator Splitting for 3D Advection-Diffusion-Reaction Models.- Space-Time DG Method for Nonstationary Convection-Diffusion Problems.- High Order Finite Volume Schemes for Numerical Solution of Unsteady Flows.- Multigrid Finite Element Method on Semi-Structured Grids for the Poroelasticity Problem.- A Posteriori Error Bounds for Discontinuous Galerkin Methods for Quasilinear Parabolic Problems.- An A Posteriori Analysis of Multiscale Operator Decomposition.- Goal-Oriented Error Estimation for the Discontinuous Galerkin Method Applied to the Biharmonic Equation.- Solving Stochastic Collocation Systems with Algebraic Multigrid.- Adaptive Two-Step Peer Methods for Incompressible Navier-Stokes Equations.- On Hierarchical Error Estimators for Time-Discretized Phase Field Models.- Nonlinear Decomposition Methods in Elastodynamics.- An Implementation Framework for Solving High-Dimensional PDEs on Massively Parallel Computers.- Benchmarking FE-Methods for the Brinkman Problem.- Finite Element Based Second Moment Analysis for Elliptic Problems in Stochastic Domains.- On Robust Parallel Preconditioning for Incompressible Flow Problems.- Hybrid Modeling