A study of the singularities of solutions of a class of nonlinear elliptic partial differential equation

1982 ◽  
Vol 7 (5) ◽  
pp. 609-643 ◽  
Author(s):  
Patricio Aviles
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Elliptic Partial Differential Equation ◽  
Partial Differential ◽  
Nonlinear Elliptic

A NUMERICAL METHOD FOR PROGRESSIVE LENS DESIGN

2004 ◽  
Vol 14 (04) ◽  
pp. 619-640 ◽  
Author(s):  
JING WANG ◽  
FADIL SANTOSA
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Method ◽  
Elliptic Partial Differential Equation ◽  
Computational Method ◽  
Necessary Condition ◽  
Perturbation Approach ◽  
Lens Design ◽  
Partial Differential ◽  
Nonlinear Elliptic

The problem of progressive lens design can be posed as a variational problem. The necessary condition is a fourth-order nonlinear elliptic partial differential equation. The partial differential equation can be linearized using a perturbation approach. A numerical method using a special type of splines, chosen for their smoothness properties, is devised to solve the resulting PDE. The computational method is shown to be both convergent and efficient.

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