The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a active research field both in the mathematics and engineering community. This volume of LNCSE is a collection of the proceedings papers of the Fourth International Workshop on Meshfree Methods held in September 2007 in Bonn.

Circumventing Curse of Dimensionality in the Solution of Highly Multidimensional Models Encountered in Quantum Mechanics Using Meshfree Finite Sums Decomposition.- A Pressure Correction Approach Coupled with the MLPG Method for the Solution of the Navier-Stokes Equations.- Large Scale, Multiresolution Flow Simulations Using Remeshed Particle Methods.- On the Stabilization of Stress-Point Integration in the Element Free Galerkin Method.- The Partition of Unity Meshfree Method for Solving Transport-Reaction Equations on Complex Domains: Implementation and Applications in the Life Sciences.- Solving One Dimensional Scalar Conservation Laws by Particle Management.- Stability of Energy Transfer in the Weak Coupling Method.- Multiscale Approach for Quantum Systems.- A Meshless Technique Based on Integrated Radial Basis Function Networks for Elliptic Partial Differential Equations.- A Higher-Order Finite Volume Method Using Multiresolution Reproducing Kernels.- Interface Tracking in Meshfree Methods and its Applications.- A’posteriori Error Estimation Based on Higher Order Approximation in the Meshless Finite Difference Method.- Exact Bounds for Linear Outputs of the Convection-Diffusion-Reaction Equation Using Flux-Free Error Estimates.- Preparation of CAD and Molecular Surfaces for Meshfree Solvers.- 3D Meshfree Magnetohydrodynamics.- A Particle-Partition of Unity Method Part VIII: Hierarchical Enrichment.- A Framework For Studying The RKEM Representation of Discrete Point Sets.- Coupling of the CFD and the Droplet Population Balance Equation with the Finite Pointset Method.- Hybrid Methods for Fluid-Structure-Interaction Problems in Aeroelasticity.

The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. 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 proceedings papers of the Fourth International Workshop on Meshfree Methods held in September 2007 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this very active and exciting area of interdisciplinary research and to present recent advances and results in this field.

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