An efficient algorithm for Hamilton–Jacobi equations in high dimension Export

@article{citeulike:5785968, abstract = {In this paper we develop a new version of the semi-Lagrangian algorithm for first order Hamilton–Jacobi equations. This implementation is well suited to deal with problems in high dimension, i.e. in R m with m=3, which typically arise in the study of control problems and differential games. Our model problem is the evolutive Hamilton–Jacobi equation related to the optimal control finite horizon problem. We will give a step-by-step description of the algorithm focusing our attention on two critical routines: the interpolation in high dimension and the search for the global minimum. We present some numerical results on test problems which range from m=3 to m=5 and deal with applications to front propagation, aerospace engineering, ecomomy and biology.}, author = {Carlini, Elisabetta and Falcone, Maurizio and Ferretti, Roberto}, citeulike-article-id = {5785968}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/s00791-004-0124-5}, citeulike-linkout-1 = {http://www.springerlink.com/content/aqwuh6nb25kng96g}, day = {1}, doi = {10.1007/s00791-004-0124-5}, journal = {Computing and Visualization in Science}, keywords = {adaptive\_grid, dp, numeric}, month = {June}, number = {1}, pages = {15--29}, posted-at = {2009-09-15 12:52:04}, priority = {2}, title = {An efficient algorithm for Hamilton–Jacobi equations in high dimension}, url = {http://dx.doi.org/10.1007/s00791-004-0124-5}, volume = {7}, year = {2004} }

TY - JOUR ID - citeulike:5785968 L3 - citeulike-article-id:5785968 N2 - In this paper we develop a new version of the semi-Lagrangian algorithm for first order Hamilton–Jacobi equations. This implementation is well suited to deal with problems in high dimension, i.e. in R m with m=3, which typically arise in the study of control problems and differential games. Our model problem is the evolutive Hamilton–Jacobi equation related to the optimal control finite horizon problem. We will give a step-by-step description of the algorithm focusing our attention on two critical routines: the interpolation in high dimension and the search for the global minimum. We present some numerical results on test problems which range from m=3 to m=5 and deal with applications to front propagation, aerospace engineering, ecomomy and biology. IS - 1 JF - Computing and Visualization in Science EP - 29 TI - An efficient algorithm for Hamilton–Jacobi equations in high dimension VL - 7 SP - 15 KW - adaptive_grid KW - dp KW - numeric AU - Carlini, Elisabetta AU - Falcone, Maurizio AU - Ferretti, Roberto PY - 2004/06/01/ UR - http://dx.doi.org/10.1007/s00791-004-0124-5 ER -