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Author Shen, Xiaoping
Title Recent Advances In Computational Sciences : Selected Papers from the International Workshop on Computational Sciences and Its Education
Imprint Singapore : World Scientific Publishing Company, 2008
©2008
book jacket
Descript 1 online resource (396 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note Intro -- CONTENTS -- Preface -- Generalized Riemann Problems: From the Scalar Equation to Multidimensional Fluid Dynamics M. Ben-Arlizi and J. Falcovitz -- 1. Introduction -- 2. GRP Scheme - Basic Properties -- 3. Self-Similar Solutions in 2-D -- 4. The Analysis of 2-D Riemann-Type Solutions -- 5. The 2-D Guckenheimer Equation -- 6. Euler Equations of Quasi I-D Compressible Inviscid Flow -- 7. The GRP for Quasi l-D Compressible Inviscid Flow -- 8. The GRP Numerical Method for Quasi I-D Compressible Inviscid Flow -- 9. Fluid Dynamical Examples -- 9.1. Wave Dynamics in a Duct with a Converging Segment -- 9.2. Shock diffraction by a square cavity -- 9.3. Second reflection of a shock wave by a double wedge -- 9.4. Lagrange-Euler Scheme for a Gas-Grains Mixture -- References -- Some Observations on a Multiscale Finite Element Method for Problems with Variables Separated Coefficients S. Jiang and Y-Q. Huang -- 1. Introduction -- 2. Formulations -- 2.1. Model problem -- 2.2. Remarks -- 3. Base functions under variables separated condition -- 4. Numerical experiment -- 4.1. Implementation and explanation -- 4.2. Experiment results -- References -- A Finite Element Method for the Simulation of a Liquid Droplet Impinging on a Solid Surface S. Ganesan and L. Tobiska -- 1. Introduction -- 2. Mathematical model -- 2.1. Governing equations -- 2.2. Initial and boundary conditions -- 2.3. Dimensionless form -- 3. Numerical Scheme -- 3.1. Arbitrary Lagrangian Eulerian (ALE) Approach -- 3.2. Variational form -- 3.3. Discretisation in time and linearization -- 3.4. Discretisation in space -- 3.5. Solving the discrete problems -- 3.6. Free surface update -- 3.7. Automatic mesh moving techniques -- 4. Numerical results -- Acknowledgement -- References
Applications of Moving Mesh Methods to the Fourier Spectral Approximations of Phase-Field Equations P. Yu, L. Q. Chen and Q. Du -- 1. Introduction -- 2. Moving mesh methods -- 3. Variational Moving Mesh PDEs and their Fourier Spectral Implementation -- 3.1. A computational domain representation -- 3.2. A physical domain representation -- 3.3. Fourier-Spectral Implementation of MMPDEs -- 3.4. Comparisons of two representations -- 4. Adaptive Spectral Methods for Phase-Field Equations -- 4.1. Allen-Cahn equations -- 4.2. Numerical examples for Allen- Cahn equations -- 5. Extension and Further Discussion -- 5.1. Extension to Cahn-Hilliard equation -- 5.2. Extension to Phase Field Inhomogeneous Elasticity Equations -- 5.3. Switching on the Mesh Adaptation -- 5.4. Further discussion -- Acknowledgments -- References -- On the Comparison of Evolution Galerkin and Discontinuous Galerkin Schemes K. Baumbach and M. Lukacova-Medvidova -- 1. Introduction -- 2. Finite volume evolution Galerkin methods -- 3. Discontinuous Galerkin methods -- 4. Numerical experiments -- 4.1. Shallow Water Equations -- 4.2. Dam break problem -- 4.3. Accuracy and efficiency tests -- 5. Conclusion -- Acknowledgement -- References -- Time-Domain Finite Element Methods for Maxwell's Equations in Dispersive Media: A Review J. Li and Y Chen -- 1. Introduction -- 2. Maxwell's equations and dispersive media -- 3. Finite element methods for dispersive media -- 3.1. Standard error analysis -- 3.2. Superconvergence analysis -- 4. Conclusion and further issues -- 4.1. Regularity -- 4.2. Hp-adaptive methods -- 4.3. A posteriori error estimation -- 4.4. Solvers -- 4.5. Perfectly matched layer (PML) -- References -- Superconvergence and A Posteriori Error Estimates of Nonconforming FEM for Boundary Control Governed by Stokes Equations H. Liu and N. Yan -- 1. Introduction
2. Finite element approximation of boundary control problems -- 3. Superconvergence analysis and recovery for the control u -- 4. Superconvergence analysis for state and co-state and recovery type a posteriori error estimates -- 5. Numerical examples -- 6. Discussions -- Acknowledgments -- References -- Optimal Superconvergent One Step Quadratic Spline Collocation Methods for Helmholtz Problems B. Bialecki, G. Fairweather, A. K arageorghis and Q. N. Nguyen -- 1. Introduction -- 2. Optimal Quadratic Spline Collocation Methods for a Two-Point Boundary Value Problem -- 2.1. Preliminaries -- 2.2. Optimal Quadratic Spline Collocation Methods -- 2.3. Numerical Results -- 3. Helmholtz Problem -- 3.1. New Optimal Quadratic Spline Collocation Method -- 3.2. Numerical Results -- 4. Extensions and Generalizations -- Acknowledgment -- References -- Some Progress on Superconvergence for Mixed Finite Element Methods S. Jia, H. Xie and X Yin -- 1. Introdution -- 2. Operator Expressions -- 2.1. The Eigenvalue Error Expansion for The First Type of Eigenvalue Problems -- 2.2. The Eigenvalue Error Expansion for The Second Type of Eigenvalue Problems -- 3. Mixed FEMs for Second Order Elliptic Eigenvalue Problems -- 3.1. Two Dimensional Rectangular RTo Element -- 3.2. Two Dimensional Rectangular RTk Element -- 3.3. Two Dimensional Rectangular BDF Mk Element -- 3.4. Three Dimensional RTo Element -- 4. Mixed FEMs for Biharmonic Eigenvalue Problems -- 4.1. Q1 Element -- 4.2. Qk Element -- 5. Mixed FEMs for Stokes Eigenvalue Problems -- 5.1. B - R Rectangular Element -- 5.2. Q2 - P 1 Rectangular Element -- 5.3. Hood-Taylor Rectangular Element -- 5.4. Q1 - Qo Rectangular Element -- 5.5. Hood-Taylor Triangular Element -- 5.6. PI - PI Triangular Element -- 5.7. Another Form for Stokes Problems -- 6. Concluding Remarks -- Acknowledgments -- References
Convergence of Green Iterations for Schrodinger Equations M. J. Mohlenkamp and T. Young -- 1. Green Function Iterations -- 2. Background Material -- 3. Proof of Main Result -- 4. Concluding Remarks -- References -- Convolution and Wiener Amalgam Spaces on the Affine Group C. Heil and G. Kutyniok -- 1. Introduction -- 2. Notation and Preliminary Results -- 2.1. General Notation -- 2.2. Preliminary Lemmas -- 2.3. Lemmas on Convolution -- 2.4. Amalgam Spaces on the Affine Group -- 3. Amalgam Spaces and Convolution on the Affine Group -- Acknowledgments -- References -- An Approximation Formula in Hilbert Space Z. Zhang and N. Saito -- 1. Introduction -- 2. A new frame approximation operator (IT -- { ('))1n -- 3. Approximation by (0": -- [ ('»rrt -- References -- The Gibbs Phenomenon: A Digression in Wavelet Hybrid Sampling Series X A. Shen -- 1. Introduction -- 2. Sampling theory based on wavelets -- 2.1. Sampling functions associated with scaling functions -- 2.2. Sampling and hybrid sampling series in scaling spaces -- 3. The Gibbs phenomenon in hybrid sampling series -- 3.1. Abel mean for wavelet with compact support -- 3.2. The positive hybrid sampling series -- 4. Numerical examples -- 5. Summary -- Acknowledgment -- References -- A Unified Framework for Segment ation-Assisted Image Registration J. Liu and W. Yang -- 1. Introduction and Related Work -- 2. Segmentation Guided Registration Model -- 2.1. Frameworks based on intensity homegeneity -- 2.2. Level Set Formulation of the LC-based model -- 2.3. A SSD-based Segmentation + Registration Model -- 3. Experimental Results -- 3.1. Registration based on the Segmentation + Registration Component -- 3.2. Registrations of our Segmentation + Registration LC model -- 4. Conclusions -- References -- Geometric Hermite Interpolation with Pythagorean Hodograph Cubics X-A. Han, Y-C. Ma and H.- Y Sun
1. Introduction -- 2. Geometric Hermite interpolation with a PH cubic -- 3. Examples -- References -- Shape Gradient for the Stokes Flow by Dierentiability of a Saddle Point Z. Gao and Y Ma -- 1. Introduction -- 2. Formulation of the problem -- 3. The Velocity Method -- 4. A Saddle Point Formulation -- 5. Function Space Parametrization -- 6. Function Space Embedding -- Acknowledgments -- References -- Numerical Simulation of Flow Over Two Rotating Self-Moving Circular Cylinders S. Sungnul and N. P. M oshkin -- 1. Introduction -- 2. Mathematical Formulation -- 3. Numerical Algorithm -- 4. Validation of Numerical Algorithm -- 5. Results and Discussion -- 5.1. Streamlines patterns depending on the Reynolds number and rate of rotation -- 5.2. Streamline patterns depending on the gap spacing and the rate of rotation -- 6. Conclusion -- References -- A Note on PPT Forms and Separability of Multipartite States X.-H. Wang, S.-M. Fei and K. Wu -- 1. Introduction -- 2. Main results -- 3. Examples -- 4. Discussions -- References -- A Structured Data Least Squares Algorithm and Its Application in Digital Filtering H. Guo and R. Renaut -- 1. Introduction -- 2. An Algorithm for Structured Data Least Squares -- 2.1. Properties of the SDLS problem -- 2.2. Algorithm Description -- 2.3. Numerical approaches for solving the iteration equation -- 2.3.1. solution of B 18z = f - B! 8),: -- 2.3.2. Solution of B2Bli B! 8), = B2Bl i f - r -- 3. Experiments -- 4. Conclusion -- Appendix A. Algorithm for Data Least Squares -- References -- Short Implementation of Bisection in Matlab L. Chen -- 1. Introduction -- 2. Bisections in adaptive finite element methods -- 2.1. Newest vertex bisection -- 2.2. Longest edge bisection -- 3. Implementation -- 3.1. Data structure -- 3.2. Initial labeling -- 3.3. Marking strategy -- 3.4. Refinement -- 4. Numerical example
Appendix A: Matlab code for bisection
Key Features:Includes an overview of recent developments in computational scienceDraws connections between theory and applications raised in computational problemsIntegrates research and teaching
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Shen, Xiaoping Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education Singapore : World Scientific Publishing Company,c2008 9789812707000
Subject Computer science -- Mathematics -- Congresses.;Computer science -- Mathematics -- Study and teaching -- Congresses
Electronic books
Alt Author Shu, Chi-wang
Jorgensen, Palle
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