Back and forth error compensation and correction methods for semi-lagrangian schemes with application to level set interface computations

Back and forth error compensation and correction methods for semi-lagrangian schemes with application to level set interface computations

Semi-Lagrangian schemes have been explored by several authors recently for transport problems, in particular for moving interfaces using the level set method. We incorporate the backward error compensation method developed in our paper from 2003 into semi-Lagrangian schemes with almost the same simplicity and three times the complexity of a first order semi-Lagrangian scheme but with improved o...

Back and Forth Error Compensation and Correction Methods for Semi-lagrangian Schemes with Application to Interface Computation Using Level Set Method

Semi-Lagranging schemes have been explored by several authors recently for transport problems in particular for moving interfaces using level set method. We incorporate the backward error compensation method developed in [2] into the semi-Lagranging schemes with almost the same simplicity and three times the complexity of a first order semi-Lagranging scheme but improve the order of accuracy. W...

Semi-Lagrangian Methods for Level Set Equations

A limiting strategy for the back and forth error compensation and correction method for solving advection equations

We further study the properties of the back and forth error compensation and correction (BFECC) method for advection equations such as those related to the level set method and for solving Hamilton-Jacobi equations on unstructured meshes. In particular, we develop a new limiting strategy which requires another backward advection in time so that overshoots/undershoots on the new time level get e...

A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems

We present a quasi-monotone semi-Lagrangian particle level set (QMSL-PLS) method for moving interfaces. The QMSL method is a blend of first order monotone and second order semiLagrangian methods. The QMSL-PLS method is easy to implement, efficient, and well adapted for unstructured, either simplicial or hexahedral, meshes. We prove that it is unconditionally stable in the maximum discrete norm,...