Fast multipole accelerated boundary integral equation methods

2002 ◽  
Vol 55 (4) ◽  
pp. 299-324 ◽  
Author(s):  
N Nishimura
Keyword(s):  
Integral Equation ◽  
Wave Equation ◽  
Boundary Integral Equation ◽  
Fast Multipole Method ◽  
Integral Equation Method ◽  
Review Article ◽  
Boundary Integral ◽  
Fast Multipole ◽  
Helmholtz Equations ◽  
Integral Equation Methods

Fundamentals of Fast Multipole Method (FMM) and FMM accelerated Boundary Integral Equation Method (BIEM) are presented. Developments of FMM accelerated BIEM in the Laplace and Helmholtz equations, wave equation, and heat equation are reviewed. Applications of these methods in computational mechanics are surveyed. This review article contains 173 references.

Fast Multipole Accelerated Boundary Integral Equation Method for Evaluating the Stress Field Associated with Dislocations in a Finite Medium

2012 ◽  
Vol 12 (1) ◽  
pp. 226-246 ◽  
Author(s):  
Degang Zhao ◽  
Jingfang Huang ◽  
Yang Xiang
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Boundary Integral Equation ◽  
Fast Multipole Method ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Fast Multipole ◽  
Numerical Examples ◽  
Integral Equation Formulation ◽  
Finite Medium

AbstractIn this paper, we develop an efficient numerical method based on the boundary integral equation formulation and new version of fast multipole method to solve the boundary value problem for the stress field associated with dislocations in a finite medium. Numerical examples are presented to examine the influence from material boundaries on dislocations.

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