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Titlebook: Meshfree Methods for Partial Differential Equations; Michael Griebel,Marc Alexander Schweitzer Conference proceedings 2003 Springer-Verlag

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发表于 2025-3-21 19:48:32 | 显示全部楼层 |阅读模式
书目名称Meshfree Methods for Partial Differential Equations
编辑Michael Griebel,Marc Alexander Schweitzer
视频video
概述Includes supplementary material:
丛书名称Lecture Notes in Computational Science and Engineering
图书封面Titlebook: Meshfree Methods for Partial Differential Equations;  Michael Griebel,Marc Alexander Schweitzer Conference proceedings 2003 Springer-Verlag
描述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.
出版日期Conference proceedings 2003
关键词Regression; Simulation; differential equation; element-free Galerkin methodse; engineering applications;
版次1
doihttps://doi.org/10.1007/978-3-642-56103-0
isbn_softcover978-3-540-43891-5
isbn_ebook978-3-642-56103-0Series ISSN 1439-7358 Series E-ISSN 2197-7100
issn_series 1439-7358
copyrightSpringer-Verlag Berlin Heidelberg 2003
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发表于 2025-3-22 00:10:22 | 显示全部楼层
1439-7358 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 c
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Adaptive Meshfree Method of Backward Characteristics for Nonlinear Transport Equations,n method and the node adaption rules are modified accordingly. The good performance of the resulting method is finally shown in the numerical examples by using two specific nonlinear model problems: . and the ., the latter describing a two-phase fluid flow in a porous medium.
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Do Finite Volume Methods Need a Mesh?,proach, the algorithms of classical and meshfree finite volume method are identical - only the geometrical coefficients (cell volumes, cell surfaces, cell normal vectors) have to be defined differently. We will discuss two such definitions which satisfy certain stability conditions.
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Some Studies of the Reproducing Kernel Particle Method, higher dimensional domains. Finally, the meshfree method is applied to solve 4th-order equations. Since the smoothness of meshfree functions is the same as that of the window function, the meshfree method is a natural choice for conforming approximation of higher-order differential equations.
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Approximate Moving Least-Squares Approximation with Compactly Supported Radial Weights, We compare our new algorithm with three other approximation methods based on compactly supported radial functions: multilevel interpolation, the standard moving least-squares approximation method, and a multilevel moving least-squares algorithm. A multilevel approximate moving least-squares approximation algorithm is also included.
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A Particle-Partition of Unity Method-Part IV: Parallelization,eme for the load balancing problem. We present numerical results in two and three dimensions with up to 128 processors and 42 million degrees of freedom. These results show the optimal scaling behavior of our algorithm in the discretization as well as the solution phase.
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