Meshfree Methods for Partial Differential Equations VIII

Name: Meshfree Methods for Partial Differential Equations VIII
Brand: Springer
Price: 96.29 EUR
Availability: OnlineOnly

Michael Griebel Marc Alexander Schweitzer(Herausgeber*in)

Springer (Verlag)

Erschienen am 5. April 2017

VIII, 240 Seiten

E-Book

PDF mit Wasserzeichen-DRM

Systemvoraussetzungen

978-3-319-51954-8 (ISBN)

96,29 €inkl. 7% MwSt.

Systemvoraussetzungen

für PDF mit Wasserzeichen-DRM

E-Book Einzellizenz

Als Download verfügbar

Beschreibung

Weitere Details

Weitere Ausgaben

Inhalt

Intro
Preface
Contents
A Two-Level Additive Schwarz Domain Decomposition Preconditioner for a Flat-Top Partition of Unity Method
1 Introduction
2 A Flat-Top Partition of Unity Method
2.1 Partition of Unity
2.2 Generalized Finite Element Space
2.3 Discretization Error Estimate and Conditioning
3 A Two-Level Additive Schwarz Preconditioner
3.1 Coarse Problem
3.2 Local Problems
3.3 The Preconditioner
4 Condition Number Estimates
4.1 Estimate for ?max (BTL Ah)
4.2 Estimate for ?min(BTLAh)
4.3 Estimate for ?(BTLAh)
5 Numerical Results
5.1 Results for the Unit Square
5.1.1 Small Overlap
5.1.2 Generous Overlap
5.2 An L-Shaped Domain
5.2.1 Small Overlap
5.2.2 Generous Overlap
6 Concluding Remarks
References
Extraction of Fragments and Waves After Impact Damage in Particle-Based Simulations
1 Introduction
1.1 Fragmentation
1.2 Impact Damage and Wave Propagation
2 Peridynamics
3 Visualization Techniques
3.1 Clustering
3.2 Visualization of the Stress Tensor
4 Experiments and Their Visual Analysis
4.1 Fragments and Histograms
4.2 Impact Damage and Wave Propagation
5 Conclusion
References
A Meshfree Semi-implicit Smoothed Particle Hydrodynamics Method for Free Surface Flow
1 Introduction
2 Problem Formulation and Models
2.1 The Kernel Function
2.2 Governing Equations
2.3 Hydrostatic Approximation
3 Construction of a Meshfree Semi-implicit SPH Scheme
3.1 The Smoothed Particle Hydrodynamics Method
3.2 Classical SPH Formulation
3.3 SPH Formulation of Vila and Ben Moussa
3.4 Semi-implicit SPH Scheme
3.5 The Free Surface Equation
3.6 Neighboring Search Technique
4 Numerical Results
4.1 A Collapsing Gaussian Bump
5 Conclusion
References
A Meshfree Method for the Fractional Advection-Diffusion Equation
1 Introduction
2 RKPM Approximation for the Fractional Derivative
2.1 Alternative Approximation for the Fractional Derivative Using RKPM
3 Spatial Fractional Advection-Diffusion Equation via RKPM
4 Illustrative Examples
4.1 Steady State Examples
4.2 Time-Dependent Examples
5 Conclusion
References
Meshless Multi-Point Flux Approximation
1 Introduction
2 Fluid Flow Modelling Using SPH
2.1 Kernel Property
3 Meshless Transmissibilities
4 Discontinuous Mobility Case
4.1 Anisotropic Case
5 Numerical Experiments
6 Conclusion
References
Multiscale Petrov-Galerkin Method for High-Frequency Heterogeneous Helmholtz Equations
1 Introduction
1.1 Heterogeneous Helmholtz Problem
1.2 Motivation for a Multiscale Method and Stability Analysis
2 Stability of the Heterogeneous Helmholtz Model
2.1 Statement of Stability, Connections to Inf-Sup Constants, and Boundedness
2.2 Example Coefficients
3 The Multiscale Method
3.1 Meshes and Data Structures
3.2 Definition of the Method
4 Error Analysis
5 Numerical Examples
6 Conclusions
Appendix: Proof of Stability
Technical and Auxiliary Lemmas
Proof of Main Stability Result
References
Error Analysis of Nodal Meshless Methods
1 Introduction
2 Problems and Their Discretizations
2.1 Analytic Problems
2.2 Discretization
2.3 Nodal Trial Approximations
2.4 Testing
3 Error Analysis
3.1 Residuals
3.2 Stability
3.3 Consistency
3.4 Residual Minimization
3.5 Final Relative Error Bound
3.6 Sharpness
4 Dirichlet Problems
5 Consistency Analysis
6 Approximations by Polyharmonic Kernels
7 Stability Analysis
8 Examples
9 Conclusion and Outlook
References
Generalizations of Simple Kriging Methods in Spatial Data Analysis
1 Introduction
2 Initial Ideas
3 Kernel-Based Approximations via Kernel-Based Probabilities
4 Applications in Geostatistics
5 Numerical Examples
6 Final Remarks
References
Evaluation of Local Multiscale Approximation Spaces for Partition of Unity Methods
1 Introduction
1.1 Model Problem
2 Partition of Unity Method
3 Quality Measures for Approximation Spaces
4 Construction of Spaces Wl and Hl
4.1 Hl via Reduction to Homogeneous Problem
4.2 Wl via Oversampling
4.3 Practical Construction of Wl
5 Concrete Choices of Vl
6 Numerical Results
6.1 General Observations
6.2 Contrast Independence and Mesh Dependence of n-Widths
6.3 Influence of Microstructure and Patch ?l on dl,nE
6.4 Contrast Dependence of Vl
6.5 Optimality and Costs of Vl
6.6 Example of Global PUM Solution
7 Concluding Remarks
References
Embedding Enriched Partition of Unity Approximations in Finite Element Simulations
1 Introduction
2 Partition of Unity Method
3 Embedding PUM into Finite Element Simulations
4 Numerical Results
5 Concluding Remarks
References
Building a Numerical Framework to Model Gas-Liquid-Solid Interactions Using Meshfree Interpolation Methods
1 Introduction
2 Numerical Framework
2.1 Multi-Fluid Interface Tracking Using the Connectivity-Free Front Tracking Method
2.1.1 Indicator Construction
2.1.2 Surface Tension Force Without Connectivity
2.1.3 Interface Advection and Points Regeneration Scheme
2.2 Fluid-Solid Interactions Using the Modified Immersed Finite Element Method
2.2.1 Solid and Fluid Domains
2.2.2 Coupling Between Solid and Fluid
2.3 Numerical Examples
2.3.1 Rayleigh-Taylor Instability Test
2.3.2 3-D Floating Object on a Breaking Dam
3 Conclusions
References
Editorial Policy
Lecture Notesin Computational Scienceand Engineering
Monographs in Computational Scienceand Engineering
Texts in Computational Scienceand Engineering

Systemvoraussetzungen

Als PDF speichern Als Link merken