Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  describe an integral equation approach for simulating diffusion problems with moving interfaces. The solutions are represented as moving layer potentials where the unknowns are only defined on the interfaces. The resulting integro-differential equation (IDE) system is solved using spectral deferred correction (SDC) techniques developed for general differential algebraic equations (DAEs), and the time dependent potentials are evaluated efficiently using fast convolution algorithms. The numerical solver is applied to the BCF model for the epitaxial step-flow growth of crystals, for which the solutions are calculated accurately instead of using quasi-static approximations. Numerical results in 1 + 1 dimensions are compared with available results in the literature.
['Jingfang Huang', 'Ming-Chih Lai', 'Yang Xiang']
I am writing a research paper on a idea An integral equation method for epitaxial step-flow growth simulations
[{"from": "human", "value": "I am writing a research paper on a idea An integral equation method for epitaxial step-flow growth simulations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  describe an integral equation approach for simulating diffusion problems with moving interfaces. The solutions are represented as moving layer potentials where the unknowns are only defined on the interfaces. The resulting integro-differential equation (IDE) system is solved using spectral deferred correction (SDC) techniques developed for general differential algebraic equations (DAEs), and the time dependent potentials are evaluated efficiently using fast convolution algorithms. The numerical solver is applied to the BCF model for the epitaxial step-flow growth of crystals, for which the solutions are calculated accurately instead of using quasi-static approximations. Numerical results in 1 + 1 dimensions are compared with available results in the literature."}]