Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. ,  develop a new generalized multiscale finite element method with the aim of simulating waves at a much lor cost. Our method is based on a mixed Galerkin type method with carefully designed basis functions that can capture various scales in the solution. The basis functions are constructed based on some local snapshot spaces and local spectral problems defined on them. The spectral problems give a natural ordering of the basis functions in the snapshot space and allow systematically enrichment of basis functions. In addition, by using a staggered coarse mesh, our method is energy conserving and has block diagonal mass matrix, which are desirable properties for wave propagation.  will prove that our method has spectral convergence, and present numerical results to show the performance of the method.
['Eric T. Chung', 'Wing Tat Leung']
I am writing a research paper on a idea Mixed GMsFEM for the simulation of waves in highly heterogeneous media
[{"from": "human", "value": "I am writing a research paper on a idea Mixed GMsFEM for the simulation of waves in highly heterogeneous media"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. ,  develop a new generalized multiscale finite element method with the aim of simulating waves at a much lor cost. Our method is based on a mixed Galerkin type method with carefully designed basis functions that can capture various scales in the solution. The basis functions are constructed based on some local snapshot spaces and local spectral problems defined on them. The spectral problems give a natural ordering of the basis functions in the snapshot space and allow systematically enrichment of basis functions. In addition, by using a staggered coarse mesh, our method is energy conserving and has block diagonal mass matrix, which are desirable properties for wave propagation.  will prove that our method has spectral convergence, and present numerical results to show the performance of the method."}]