Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  construct finite difference discretizations of the acoustic wave equation in complicated geometries and heterogeneous media. Particular emphasis is placed on the accurate treatment of interfaces at which the underlying media parameters have jump discontinuities. Discontinuous media is treated by subdividing the domain into blocks with continuous media. The equation on each block is then discretized with finite difference operators satisfying a summation-by-parts property and patched together via the simultaneous approximation term method. The energy method is used to estimate a semi-norm of the numerical solution in terms of data, showing that the discretization is stable. Numerical experiments in two and three spatial dimensions verifies the accuracy and stability properties of the schemes.
['Kristoffer Virta', 'Ken Mattsson']
I am writing a research paper on a idea Acoustic Wave Propagation in Complicated Geometries and Heterogeneous Media
[{"from": "human", "value": "I am writing a research paper on a idea Acoustic Wave Propagation in Complicated Geometries and 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:  construct finite difference discretizations of the acoustic wave equation in complicated geometries and heterogeneous media. Particular emphasis is placed on the accurate treatment of interfaces at which the underlying media parameters have jump discontinuities. Discontinuous media is treated by subdividing the domain into blocks with continuous media. The equation on each block is then discretized with finite difference operators satisfying a summation-by-parts property and patched together via the simultaneous approximation term method. The energy method is used to estimate a semi-norm of the numerical solution in terms of data, showing that the discretization is stable. Numerical experiments in two and three spatial dimensions verifies the accuracy and stability properties of the schemes."}]