Meshfree Methods for Partial Differential Equations

By: M. Griebel, M. a. Schweitzer, Michael Griebel (Editor)

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Paperback | 18 September 2002

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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 are 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 discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and 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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Meshless and Generalized Finite Element Methods: A Survey of Some Major Results	p. 1
Adaptive Meshfree Method of Backward Characteristics for Nonlinear Transport Equations	p. 21
New Methods for Discontinuity and Crack Modeling in EFG	p. 37
SPH Simulations of MHD Shocks Using a Piecewise Constant Smoothing Length Profile	p. 51
On the Numerical Solution of Linear Advection-Diffusion Equation using Compactly Supported Radial Basis Functions	p. 63
New RBF Collocation Methods and Kernel RBF with Applications	p. 75
Tuned Local Regression Estimators for the Numerical Solution of Differential Equations	p. 87
Approximate Moving Least-Squares Approximation with Compactly Supported Radial Weights	p. 105
Coupling Finite Elements and Particles for Adaptivity	p. 117
A Hamiltonian Particle-Mesh Method for the Rotating Shallow-Water Equations	p. 131
Fast Multi-Level Meshless Methods Based on the Implicit Use of Radial Basis Functions	p. 143
A Particle-Partition of Unity Method Part IV: Parallelization	p. 161
Some Studies of the Reproducing Kernel Particle Method	p. 193
Consistency by Correcting Coefficients in the Finite-Volume-Particle Method	p. 211
Do Finite Volume Methods Need a Mesh?	p. 223
An Upwind Finite Pointset Method (FPM) for Compressible Euler and Navier-Stokes Equations	p. 239
Adaptive Galerkin Particle Method	p. 251
An Adaptivity Procedure Based on the Gradient of Strain Energy Density and its Application in Meshless Methods	p. 267
New Developments in Smoothed Particle Hydrodynamics	p. 281
The Distinct Element Method - Application to Structures in Jointed Rock	p. 291
Advance Diffraction Method as a Tool for Solution of Complex Non-Convex Boundary Problems	p. 307
On the Stochastic Weighted Particle Method	p. 319
The SPH/MLSPH Method for the Simulation of High Velocity Concrete Fragmentation	p. 327
Stability of DPD and SPH	p. 339
A New Meshless Method - Finite-Cover Based Element Free Method	p. 359
Finite Pointset Method Based on the Projection Method for Simulations of the Incompressible Navier-Stokes Equations	p. 373
LPRH - Local Polynomial Regression Hydrodynamics	p. 389
On Multigrid Methods for Generalized Finite Element Methods	p. 401
The Convergence of the Finite Mass Method for Flows in Given Force and Velocity Fields	p. 419
Survey of Multi-Scale Meshfree Particle Methods	p. 441
Appendix. Color Plates	p. 459
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Meshfree Methods for Partial Differential Equations

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