Name
Title | ||
|---|---|---|
A Level Set Framework for Capturing Multi-Valued Solutions of Nonlinear First-Order Equations |
Abstract | ||
|---|---|---|
We introduce a level set method for the computation of multi-valued solutions of a general class of nonlinear first-order equations in arbitrary space dimensions. The idea is to realize the solution as well as its gradient as the common zero level set of several level set functions in the jet space. A very generic level set equation for the underlying PDEs is thus derived. Specific forms of the level set equation for both first-order transport equations and first-order Hamilton-Jacobi equations are presented. Using a local level set approach, the multi-valued solutions can be realized numerically as the projection of single-valued solutions of a linear equation in the augmented phase space. The level set approach we use automatically handles these solutions as they appear |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s10915-005-9016-1 | J. Sci. Comput. |
Keywords | Field | DocType |
level set method,first order,linear equations,transport equation,level set,phase space | Set function,Linear equation,Mathematical optimization,Nonlinear system,Level set method,Mathematical analysis,Level set,Solution set,Independent equation,Simultaneous equations,Mathematics | Journal |
Volume | Issue | ISSN |
29 | 3 | 0885-7474 |
Citations | PageRank | References |
6 | 1.07 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hailiang Liu | 1 | 88 | 14.62 |
| Li-Tien Cheng | 2 | 214 | 18.96 |
| Stanley Osher | 3 | 7973 | 514.62 |