Ebook: Meshfree Methods for Partial Differential Equations V

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.

---

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.

---

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.
Content:
Front Matter....Pages i-viii
Global-local Petrov-Galerkin formulations in the Meshless Finite Difference Method....Pages 1-26
Treatment of general domains in two space dimensions in a Partition of Unity Method....Pages 27-49
Sampling Inequalities and Support Vector Machines for Galerkin Type Data....Pages 51-63
Meshfree Vectorial Interpolation Based on the Generalized Stokes Problem....Pages 65-80
Pressure XFEM for two-phase incompressible flows with application to 3D droplet problems....Pages 81-87
Special-relativistic Smoothed Particle Hydrodynamics: a benchmark suite....Pages 89-103
An exact particle method for scalar conservation laws and its application to stiff reaction kinetics....Pages 105-124
Application of Smoothed Particle Hydrodynamics to Structure Formation in Chemical Engineering....Pages 125-140
Numerical validation of a constraints-based multiscale simulation method for solids....Pages 141-154
Coupling of the Navier-Stokes and the Boltzmann equations with a meshfree particle and kinetic particle methods for a micro cavity....Pages 155-171
Accuracy and Robustness of Kinetic Meshfree Method....Pages 173-188
Kinetic meshless methods for unsteady moving boundaries....Pages 189-206
Efficient cloud refinement for kinetic meshless methods....Pages 207-217
Fast exact evaluation of particle interaction vectors in the finite volume particle method....Pages 219-234
Parallel summation of symmetric inter-particle forces in smoothed particle hydrodynamics....Pages 235-248
Meshfree Wavelet-Galerkin Method for Steady-State Analysis of Nonlinear Microwave Circuits....Pages 249-263
Back Matter....Pages 264-270

---

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.
Content:
Front Matter....Pages i-viii
Global-local Petrov-Galerkin formulations in the Meshless Finite Difference Method....Pages 1-26
Treatment of general domains in two space dimensions in a Partition of Unity Method....Pages 27-49
Sampling Inequalities and Support Vector Machines for Galerkin Type Data....Pages 51-63
Meshfree Vectorial Interpolation Based on the Generalized Stokes Problem....Pages 65-80
Pressure XFEM for two-phase incompressible flows with application to 3D droplet problems....Pages 81-87
Special-relativistic Smoothed Particle Hydrodynamics: a benchmark suite....Pages 89-103
An exact particle method for scalar conservation laws and its application to stiff reaction kinetics....Pages 105-124
Application of Smoothed Particle Hydrodynamics to Structure Formation in Chemical Engineering....Pages 125-140
Numerical validation of a constraints-based multiscale simulation method for solids....Pages 141-154
Coupling of the Navier-Stokes and the Boltzmann equations with a meshfree particle and kinetic particle methods for a micro cavity....Pages 155-171
Accuracy and Robustness of Kinetic Meshfree Method....Pages 173-188
Kinetic meshless methods for unsteady moving boundaries....Pages 189-206
Efficient cloud refinement for kinetic meshless methods....Pages 207-217
Fast exact evaluation of particle interaction vectors in the finite volume particle method....Pages 219-234
Parallel summation of symmetric inter-particle forces in smoothed particle hydrodynamics....Pages 235-248
Meshfree Wavelet-Galerkin Method for Steady-State Analysis of Nonlinear Microwave Circuits....Pages 249-263
Back Matter....Pages 264-270
....