View Proposal #220
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| ID | 220 |
|---|---|
| First Name | Zhongming |
| Last Name | WANG |
| Institution | Iowa State University |
| Speaker Category | graduate student |
| Title of Talk | Bloch Band Based Level Set Method for the Schrodinger Equation |
| Abstract | We develop a Bloch band based level set method for capturing the semiclassical limit of one-dimensional Schrodinger equations in periodic medium. A hybrid of the WKB approximation and homogenization leads to the Bloch eigenvalue problem and an associated Hamilton-Jacobi system for the phase, with Hamiltonian being the Bloch eigenvalues. Following the level set methodology , we develop a Bloch band based level set method, which are hybrid numerical schemes -- splitting the solution process into several parts: i) band decomposition of the initial data and construction of the initial level set function; ii) solve the Bloch eigenvalue problem; iii) evolve the band level set equation to compute multi-valued velocity and density on each Bloch band; iv)the total position density over a sample set of bands is evaluated using Bloch waves and band densities obtained in step ii) and iii), respectively. Numerical results with different number of bands are provided to demonstrate the good quality of the method. |
| Subject area(s) | |
| Suitable for undergraduates? | No |
| Day Preference | |
| Computer Needed? | |
| Bringing a laptop? | Y |
| Overhead Needed? | |
| Software requests | |
| Special Needs | |
| Date Submitted | 4/10/2008 |
| Year | 2008 |