Evaluation of Laplacian Eigenvalues on Arbitrary Polygonal Domain

Liu Xuefeng (xfliu.math@gmail.com)

Eigenvalue problem :

$$ -\Delta u = \lambda u \text{ in } \Omega, u=0\text{ on }\partial \Omega $$

Canvas configuration:
  • Canvas Range: *  
  • Offset of origin point: , ( 0~200 pixsel)

List of vertices:

Mesh Size:
Compute Verified Eigenvalue ?

(Under maintenance until 2017/04/03)

How to use it?
  • Step 1: Draw a domain counterclockwise by mouse click. If you want draw a hole, click the "Switch draw mode" button.
  • Step 2: Click button "Calculate Eigenvalues" to do computation.
  • The verified computation for non-convex domain will take long time. In this case, only sparse mesh is allowded .

  • 2011/09/13: Be able to terminate when mesh is too dense.
  • 2011/09/12: Site transfered to new server. User can download computation result.
  • 2010/09/23: Page setup.

Notice: This site is set up for demonstration. We take no responsibility for the computation result.

Last updated: 2015/10/28