Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Physical simulation on surfaces and various applications in geometry processing are based on partial differential equations on surfaces. The implicit representation of these eventually evolving surfaces in terms of level set methods leads to effective and flexible numerical tools.  addresses the computational problem of how to solve partial differential equations on level sets with an underlying very high-resolution discrete grid. These highresolution grids are represented in a very efficient format, which stores only grid points in a thin narrow band. Reaction diffusion equations on a fixed surface and the evolution of a surface under curvature motion are considered as model problems. The proposed methods are based on a semi implicit finite element discretization directly on these thin narrow bands and allow for large time steps. To ensure this, suitable transparent boundary conditions are introduced on the boundary of the narrow band and the time discretization is based on a nested iteration scheme. Methods are provided to assemble finite element matrices and to apply matrix vector operators in a manner that do not incur additional overhead and give fast, cache-coherent access to very large data sets.
['Oliver Nemitz', 'Michael Bang Nielsen', 'Martin Rumpf', 'Ross T. Whitaker']
I am writing a research paper on a idea Narrow Band Methods for PDEs on Very Large Implicit Surface.
[{"from": "human", "value": "I am writing a research paper on a idea Narrow Band Methods for PDEs on Very Large Implicit Surface."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Physical simulation on surfaces and various applications in geometry processing are based on partial differential equations on surfaces. The implicit representation of these eventually evolving surfaces in terms of level set methods leads to effective and flexible numerical tools.  addresses the computational problem of how to solve partial differential equations on level sets with an underlying very high-resolution discrete grid. These highresolution grids are represented in a very efficient format, which stores only grid points in a thin narrow band. Reaction diffusion equations on a fixed surface and the evolution of a surface under curvature motion are considered as model problems. The proposed methods are based on a semi implicit finite element discretization directly on these thin narrow bands and allow for large time steps. To ensure this, suitable transparent boundary conditions are introduced on the boundary of the narrow band and the time discretization is based on a nested iteration scheme. Methods are provided to assemble finite element matrices and to apply matrix vector operators in a manner that do not incur additional overhead and give fast, cache-coherent access to very large data sets."}]