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A Conformal Mapping Approach to Shape Optimization Problems. (Kao, CMC)

April 24 @ 4:15 pm - 5:15 pm

Abstract: In this talk, a conformal mapping approach to shape optimization problems on planar domains will be discussed. In particular, spectral methods based on conformal mappings are proposed to solve Steklov eigenvalues and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov eigenvalue problem in the complex domain via conformal mappings. The eigenfunctions are expanded in Fourier series so the discretization leads to an eigenvalue problem for coefficients of Fourier series. For shape optimization problems, we use gradient ascent approaches to find optimal domains that maximize objective functions involving Steklov eigenvalues.

Details

Date:
April 24
Time:
4:15 pm - 5:15 pm
Event Category:

Venue

Shanahan B460, Harvey Mudd College
301 Platt Blvd.
Claremont, CA 91711 United States
+ Google Map

Details

Date:
April 24
Time:
4:15 pm - 5:15 pm
Event Category:

Venue

Shanahan B460, Harvey Mudd College
301 Platt Blvd.
Claremont, CA 91711 United States
+ Google Map