Solution of a Class of Minimal Surface Problem with Obstacle

Kefei Liu, Shangwei Zhao, Meizhu Liu


Plateau’s problem is to determine the surface with minimal area that lies above an obstacle with given boundary
conditions. In this paper, a special example of this class of the problem is given and solved with the linear
finite element method. First, we triangulate the domain of definition, and transform the linear finite element
approximation into a constrained nonlinear optimization problem. Then we introduce a simple and efficient
method, named sequential quadratic programming, for solving the constrained nonlinear optimization problem.
The sequential quadratic programming is implemented by the fmincon function in the optimization toolbox of
MATLAB. Also, we discuss the relations between the number of grids and the computing time as well as the
precision of the result.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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