Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  are interested in some front propagation problems coming from control problems in d-dimensional spaces, with d?2. As opposed to the usual level set method,  localize the front as a discontinuity of a characteristic function. The evolution of the front is computed by solving an Hamilton-Jacobi-Bellman equation with discontinuous data, discretized by means of the antidissipative Ultra Bee scheme.#R##N##R##N# develop an efficient dynamic storage technique suitable for handling front evolutions in large dimension. Then  propose a fast algorithm, showing its relevance on several challenging tests in dimension d=2,3,4.  also compare our method with the techniques usually used in level set methods. Our approach leads to a computational cost as ll as a memory allocation scaling as O(N nb ) in most situations, where N nb is the number of grid nodes around the front. Moreover,  show on several examples the accuracy of our approach when compared with level set methods.
['Olivier Bokanowski', 'Emiliano Cristiani', 'Hasnaa Zidani']
I am writing a research paper on a idea An Efficient Data Structure and Accurate Scheme to Solve Front Propagation Problems
[{"from": "human", "value": "I am writing a research paper on a idea An Efficient Data Structure and Accurate Scheme to Solve Front Propagation Problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  are interested in some front propagation problems coming from control problems in d-dimensional spaces, with d?2. As opposed to the usual level set method,  localize the front as a discontinuity of a characteristic function. The evolution of the front is computed by solving an Hamilton-Jacobi-Bellman equation with discontinuous data, discretized by means of the antidissipative Ultra Bee scheme.#R##N##R##N# develop an efficient dynamic storage technique suitable for handling front evolutions in large dimension. Then  propose a fast algorithm, showing its relevance on several challenging tests in dimension d=2,3,4.  also compare our method with the techniques usually used in level set methods. Our approach leads to a computational cost as ll as a memory allocation scaling as O(N nb ) in most situations, where N nb is the number of grid nodes around the front. Moreover,  show on several examples the accuracy of our approach when compared with level set methods."}]