The method of finite spheres

By Suvranu De, Klaus-Jürgen Bathe. 2000

319 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials, Safety, Risk, Reliability and Quality

View Paper: https://www.semanticscholar.org/paper/5aff15b562ef9e69622a9e375648f153246aa0c0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Mechanics of Materials

In Safety, Risk, Reliability and Quality

Citations in the corpus

Towards an efficient meshless computational technique: the method of finite spheres (2001, methodology): “The rule that allows us to perform numerical cubature on this sector to any desired order of accuracy is computationally expensive since it requires the evaluation of the zeros of a different orthogonal polynomial for every '0 (De and Bathe, 2000).”
A Lagrangian meshless finite element method applied to fluid-structure interaction problems (2003, methodology): “On the other hand, a family of methods called Meshless Methods have been developed both for structural [5,6] and fluid mechanics problems [8-10].”
A meshfree method: meshfree weak–strong (MWS) form method, for 2-D solids (2003, methodology): “In order to alleviate the global integration background mesh, a group of meshfree methods based on the local Petrov-Galerkin weak forms (or short as meshfree local weak-form methods) are proposed and developed, such as the meshless local Petrov-Galerkin (MLPG) method (Atluri and Zhu, 1998, 2002; Atl”
The meshless finite element method (2003, unknown): “Other authors use different integration rules or weighting functions [ 13 ,14]with the same shape functions,.”
An arbitrary order variationally consistent integration for Galerkin meshfree methods (2013, methodology): “A similar technique has been used in the method of finite spheres, as introduced in [10,11].”
On Approximation in Meshless Methods (2005, methodology): “A few examples frequently mentioned in this context are the diffuse element method, [87], the element-free Galerkin (EFG, [13,14,11]), the X-FEM (extended FEM), [84,29,98], the RKPM (reproducing kernel particle method, [72–75,70]), the generalized FEM/partition of unity method ([7,78,79,82,9]), the ”
Local BIEM for transient heat conduction analysis in 3-D axisymmetric functionally graded solids (2003, background): “To each subdomain one can relate the fundamental solution to the corresponding material constants (Zhu et al., 1998; De and Bathe, 2000 ).”
GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE (2004, methodology): “We note however, that an efficient numerical integration scheme for such domains was reported in [De and Bathe (2000)].”