Meshfree Methods for Partial Differential Equations V [electronic resource] /
Griebel, Michael.editor.
Schweitzer, Marc Alexander.editor.
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.
Description based upon print version of record.
""Preface""; ""Contents""; ""Global-local Petrov-Galerkin formulations in the Meshless Finite Difference Method""; ""Slawomir Milewski, Janusz Orkisz""; ""1 Introduction""; ""2 Boundary value problem formulations""; ""3 Meshless local Petrov-Galerkin formulations""; ""4 Meshless local Petrov-Galerkin 5 (MLPG5) formulation""; ""5 Basic Meshless Finite Difference Method solution approach""; ""6 Combination of the MFDM and MLPG5""; ""7 Higher order approximation based on correction terms""; ""8 A-posteriori error analysis""; ""9 Adaptive solution approach""; ""10 Error indicators""
""11 HO MFDM / MLPG5 approach in 1D""""12 HO MFDM / MLPG5 approach in 2D""; ""13 Extensions of the MFDM / MLPG5 solution approach""; ""14 The MFDM / MLPG7 approach""; ""15 Numerical examples""; ""16 Final remarks""; ""References""; ""Treatment of general domains in two space dimensions in a Partition of Unity Method""; ""Marc Alexander Schweitzer, Maharavo Randrianarivony""; ""1 Introduction""; ""2 Particle--Partition of Unity Method""; ""2.1 Numerical Integration""; ""3 Realization on General Domains""; ""3.1 Domain Representation""; ""3.2 Clipping a curved multiply connected domain""
""3.3 Decomposition and parametrization""""3.4 Rectangle-NURBS clipping""; ""4 Numerical Experiments""; ""5 Concluding Remarks""; ""References""; ""Sampling Inequalities and Support Vector Machines for Galerkin Type Data""; ""Christian Rieger""; ""1 Introduction""; ""2 Review on sampling inequalities""; ""2.1 Proof Sketch""; ""3 Sampling Inequalities based on Weak Formulations""; ""3.1 Sampling inequalities based on Pythagoras law""; ""4 Regularization and Machine Learning""; ""References""; ""Meshfree Vectorial Interpolation Based on the Generalized Stokes Problem""; ""Csaba GÃ¡spÃ¡r""
""1 Introduction""""2 Vectorial interpolation""; ""2.1 Divergence-free interpolation based on the stream function""; ""2.2 Multi-elliptic interpolation, scalar problems""; ""3 Multi-elliptic divergence-free interpolation, vectorial problems""; ""3.1 The generalized Stokes problem""; ""4 Solution techniques""; ""4.1 Uzawa's method""; ""4.2 The method of fundamental solutions""; ""5 Summary and conclusions""; ""References""; ""Pressure XFEM for two-phase incompressible flows with application to 3D droplet problems""; ""Sven Gross""; ""1 Introduction""; ""2 Mathematical model""
""3 Numerical methods""""3.1 Overview of numerical methods""; ""3.2 Pressure XFEM space""; ""4 Analysis of pressure XFEM space""; ""4.1 Approximation order of pressure XFEM space""; ""4.2 Stabilization of XFEM basis""; ""5 Numerical experiment""; ""References""; ""Special-relativistic Smoothed Particle Hydrodynamics: a benchmark suite""; ""Stephan Rosswog""; ""1 Introduction""; ""2 Relativistic SPH equations from a variational principle""; ""3 Artificial dissipation""; ""4 Test bench""; ""4.1 Test 1: Riemann problem 1""; ""4.2 Test 2: Riemann problem 2""; ""4.3 Test 3: Riemann problem 3""
""4.4 Test 4: Sinusoidally perturbed Riemann problem""
Includes bibliographical references.
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is an extremely active research field, both in the mathematics and engineering communities. Meshfree methods are becoming increasingly mainstream in various applications. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Fifth International Workshop on Meshfree Methods, held in Bonn in August 2009. The articles address the different meshfree methods and their use in applied mathematics, physics and engineering. The volume is intended to foster this highly active and exciting area of interdisciplinary research and to present recent advances and findings in this field.
Computer mathematics.
Partial differential equations.
Mechanics.
Mechanics, Applied.
Computational Mathematics and Numerical Analysis.
Computational Science and Engineering.
Partial Differential Equations.
Theoretical and Applied Mechanics.
Lecture Notes in Computational Science and Engineering