Solving Electrostatic Problems by Using Three-field Domain Decomposition Method and Radial Basis Functions

2011 ◽  
Vol 12 (2) ◽  
pp. 75-83 ◽  
Author(s):  
Abdeljalil Fili ◽  
Ahmed Naji ◽  
Yong Duan
Keyword(s):  
Domain Decomposition ◽  
Radial Basis Functions ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Basis Functions ◽  
Radial Basis ◽  
Electrostatic Problems

Node adaptive domain decomposition method by radial basis functions

2009 ◽  
Vol 25 (6) ◽  
pp. 1482-1501 ◽  
Author(s):  
Pedro González-Casanova ◽  
José Antonio Muñoz-Gómez ◽  
Gustavo Rodríguez-Gómez
Keyword(s):  
Domain Decomposition ◽  
Radial Basis Functions ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Basis Functions ◽  
Radial Basis

scholarly journals Fast Integral Equation Solution of Scattering of Multiscale Objects by Domain Decomposition Method with Mixed Basis Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Ran Zhao ◽  
Hua Peng Zhao ◽  
Zai-ping Nie ◽  
Jun Hu
Keyword(s):  
Integral Equation ◽  
Domain Decomposition ◽  
Mesh Generation ◽  
Electromagnetic Scattering ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Basis Functions ◽  
Equation Solution ◽  
Nonoverlapping Domain Decomposition ◽  
Well Posed

Nonconformal nonoverlapping domain decomposition method (DDM) with mixed basis functions is presented to realize fast integral equation solution of electromagnetic scattering of multiscale objects. The original multiscale objects are decomposed into several closed subdomains. The higher order hierarchical vector basis functions are used in the electrically large smooth subdomains to significantly reduce the number of unknowns, while traditional Rao-Wilton-Glisson basis functions are used for subdomains with tiny structures. A well-posed matrix is successfully derived by the present DDM. Besides, the nonconformal property of DDM allows flexible mesh generation for complicated objects. Numerical results are presented to validate the proposed method and illustrate its advantages.

PROJECTION DOMAIN DECOMPOSITION METHOD

1994 ◽  
Vol 04 (06) ◽  
pp. 773-794 ◽  
Author(s):  
V.I. AGOSHKOV ◽  
E. OVTCHINNIKOV
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Basis Functions ◽  
Galerkin Projection ◽  
Discrete Problem ◽  
The Matrix ◽  
Special Basis ◽  
Projection Approach ◽  
Projection Domain

A domain decomposition method using the projection approach is considered. The original elliptic problem is transformed to a set of analogous problems in subdomains and an abstract equation on the interface between subdomains, the latter being solved using Galerkin projection method with some special basis functions defined on the interface. The condition number of the matrix of the resulting discrete problem is shown to be independent of both the number of basis functions and the coefficients of the original problem. Problems in subdomains can be solved independently with different solvers.

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