Results of von Neumann analyses for reproducing kernel semi-discretizations
The Reproducing Kernel Particle Method (RKPM) has many attractive properties that make it ideal for treating a broad class of physical problems. RKPM may be implemented in a mesh-full or a mesh-free manner and provides the ability to tune the method, via the selection of a dilation parameter and window function, in order to achieve the requisite numerical performance. RKPM also provides a framework for performing hierarchical computations making it an ideal candidate for simulating multi-scale problems. Although RKPM has many appealing attributes, the method is quite new and its numerical performance is still being quantified with respect to more traditional discretization methods. In order to assess the numerical performance of RKPM, detailed studies of RKPM on a series of model partial differential equations has been undertaken. The results of von Neumann analyses for RKPM semi-discretizations of one and two-dimensional, first and second-order wave equations are presented in the form of phase and group errors. Excellent dispersion characteristics are found for the consistent mass matrix with the proper choice of dilation parameter. In contrast, the influence of row-sum lumping the mass matrix is shown to introduce severe lagging phase errors. A higher-order mass matrix improves the dispersion characteristics relative to the lumped mass matrix but delivers severe lagging phase errors relative to the fully integrated, consistent mass matrix.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE Office of Financial Management and Controller, Washington, DC (United States)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 658421
- Report Number(s):
- SAND-98-1195C; CONF-980639-; ON: DE98005517; BR: YN0100000; TRN: AHC2DT06%%305
- Resource Relation:
- Conference: 4. world congress on computational mechanics, Buenos Aires (Argentina), 29 Jun - 2 Jul 1998; Other Information: PBD: Jun 1998
- Country of Publication:
- United States
- Language:
- English
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