Boundary integral equations for computer aided design of near-field optics

1996 ◽  
Vol 79 (11) ◽  
pp. 10-18 ◽  
Author(s):  
Masahiro Tanaka ◽  
Kazuo Tanaka
Keyword(s):  
Integral Equations ◽  
Computer Aided Design ◽  
Boundary Integral Equations ◽  
Near Field ◽  
Boundary Integral ◽  
Near Field Optics ◽  
Computer Aided ◽  
Aided Design

Isogeometric analysis of boundary integral equations: High-order collocation methods for the singular and hyper-singular equations

2016 ◽  
Vol 26 (08) ◽  
pp. 1447-1480 ◽  
Author(s):  
Matthias Taus ◽  
Gregory J. Rodin ◽  
Thomas J. R. Hughes
Keyword(s):  
Integral Equations ◽  
Isogeometric Analysis ◽  
Computer Aided Design ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
High Order ◽  
Collocation Methods ◽  
Algebraic Equations ◽  
Integration Schemes ◽  
Linear Algebraic Equations

Isogeometric analysis is applied to boundary integral equations corresponding to boundary-value problems governed by Laplace’s equation. It is shown that the smoothness of geometric parametrizations central to computer-aided design can be exploited for regularizing integral operators to obtain high-order collocation methods involving superior approximation and numerical integration schemes. The regularization is applicable to both singular and hyper-singular integral equations, and as a result one can formulate the governing integral equations so that the corresponding linear algebraic equations are well-conditioned. It is demonstrated that the proposed approach allows one to compute accurate approximate solutions which optimally converge to the exact ones.

Sign in / Sign up

Export Citation Format

Share Document