Ebook: Meshfree Methods for Partial Differential Equations

Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models ar often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretization is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDE from a Lagrangian point of view and the coupling of particle models. The coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.

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Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models ar often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretization is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDE from a Lagrangian point of view and the coupling of particle models. The coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.

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Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models ar often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretization is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDE from a Lagrangian point of view and the coupling of particle models. The coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.
Content:
Front Matter....Pages I-IX
Meshless and Generalized Finite Element Methods: A Survey of Some Major Results....Pages 1-20
Adaptive Meshfree Method of Backward Characteristics for Nonlinear Transport Equations....Pages 21-36
New Methods for Discontinuity and Crack Modeling in EFG....Pages 37-50
SPH Simulations of MHD Shocks Using a Piecewise Constant Smoothing Length Profile....Pages 51-62
On the Numerical Solution of Linear Advection-Diffusion Equation using Compactly Supported Radial Basis Functions....Pages 63-73
New RBF Collocation Methods and Kernel RBF with Applications....Pages 75-86
Tuned Local Regression Estimators for the Numerical Solution of Differential Equations....Pages 87-104
Approximate Moving Least-Squares Approximation with Compactly Supported Radial Weights....Pages 105-116
Coupling Finite Elements and Particles for Adaptivity: An Application to Consistently Stabilized Convection-Diffusion....Pages 117-129
A Hamiltonian Particle-Mesh Method for the Rotating Shallow-Water Equations....Pages 131-142
Fast Multi-Level Meshless Methods Based on the Implicit Use of Radial Basis Functions....Pages 143-160
A Particle-Partition of Unity Method-Part IV: Parallelization....Pages 161-192
Some Studies of the Reproducing Kernel Particle Method....Pages 193-210
Consistency by Coefficient-Correction in the Finite-Volume-Particle Method....Pages 211-221
Do Finite Volume Methods Need a Mesh?....Pages 223-238
An Upwind Finite Pointset Method (FPM) for Compressible Euler and Navier-Stokes Equations....Pages 239-249
Adaptive Galerkin Particle Method....Pages 251-265
An Adaptivity Procedure Based on the Gradient of Strain Energy Density and its Application in Meshless Methods....Pages 267-279
New Developments in Smoothed Particle Hydrodynamics....Pages 281-290
The Distinct Element Method — Application to Structures in Jointed Rock....Pages 291-306
Advance Diffraction Method as a Tool for Solution of Complex Non–Convex Boundary Problems—Implementation and Practical Application....Pages 307-317
On the Stochastic Weighted Particle Method....Pages 319-326
The SPH/MLSPH Method for the Simulation of High Velocity Concrete Fragmentation....Pages 327-338
Stability of DPD and SPH....Pages 339-357
A New Meshless Method — Finite-Cover Based Element Free Method....Pages 359-371
Finite Pointset Method Based on the Projection Method for Simulations of the Incompressible Navier-Stokes Equations....Pages 373-387
LPRH — Local Polynomial Regression Hydrodynamics....Pages 389-400
On Multigrid Methods for Generalized Finite Element Methods....Pages 401-418
The Convergence of the Finite Mass Method for Flows in Given Force and Velocity Fields....Pages 419-440
Survey of Multi-Scale Meshfree Particle Methods....Pages 441-457
Back Matter....Pages 459-471

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Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models ar often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretization is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDE from a Lagrangian point of view and the coupling of particle models. The coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.
Content:
Front Matter....Pages I-IX
Meshless and Generalized Finite Element Methods: A Survey of Some Major Results....Pages 1-20
Adaptive Meshfree Method of Backward Characteristics for Nonlinear Transport Equations....Pages 21-36
New Methods for Discontinuity and Crack Modeling in EFG....Pages 37-50
SPH Simulations of MHD Shocks Using a Piecewise Constant Smoothing Length Profile....Pages 51-62
On the Numerical Solution of Linear Advection-Diffusion Equation using Compactly Supported Radial Basis Functions....Pages 63-73
New RBF Collocation Methods and Kernel RBF with Applications....Pages 75-86
Tuned Local Regression Estimators for the Numerical Solution of Differential Equations....Pages 87-104
Approximate Moving Least-Squares Approximation with Compactly Supported Radial Weights....Pages 105-116
Coupling Finite Elements and Particles for Adaptivity: An Application to Consistently Stabilized Convection-Diffusion....Pages 117-129
A Hamiltonian Particle-Mesh Method for the Rotating Shallow-Water Equations....Pages 131-142
Fast Multi-Level Meshless Methods Based on the Implicit Use of Radial Basis Functions....Pages 143-160
A Particle-Partition of Unity Method-Part IV: Parallelization....Pages 161-192
Some Studies of the Reproducing Kernel Particle Method....Pages 193-210
Consistency by Coefficient-Correction in the Finite-Volume-Particle Method....Pages 211-221
Do Finite Volume Methods Need a Mesh?....Pages 223-238
An Upwind Finite Pointset Method (FPM) for Compressible Euler and Navier-Stokes Equations....Pages 239-249
Adaptive Galerkin Particle Method....Pages 251-265
An Adaptivity Procedure Based on the Gradient of Strain Energy Density and its Application in Meshless Methods....Pages 267-279
New Developments in Smoothed Particle Hydrodynamics....Pages 281-290
The Distinct Element Method — Application to Structures in Jointed Rock....Pages 291-306
Advance Diffraction Method as a Tool for Solution of Complex Non–Convex Boundary Problems—Implementation and Practical Application....Pages 307-317
On the Stochastic Weighted Particle Method....Pages 319-326
The SPH/MLSPH Method for the Simulation of High Velocity Concrete Fragmentation....Pages 327-338
Stability of DPD and SPH....Pages 339-357
A New Meshless Method — Finite-Cover Based Element Free Method....Pages 359-371
Finite Pointset Method Based on the Projection Method for Simulations of the Incompressible Navier-Stokes Equations....Pages 373-387
LPRH — Local Polynomial Regression Hydrodynamics....Pages 389-400
On Multigrid Methods for Generalized Finite Element Methods....Pages 401-418
The Convergence of the Finite Mass Method for Flows in Given Force and Velocity Fields....Pages 419-440
Survey of Multi-Scale Meshfree Particle Methods....Pages 441-457
Back Matter....Pages 459-471
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