Approximate separability of Green's function is crucial for developing fast algorithms for partial differential equations and integral equations. We present a careful study of the approximate separability of Green's function for Helmholtz equation with large wave number, which is notoriously hard to solve numerically. Our approach is geometric and based on characterization of relations between Green's functions with different source locations. We provide a sharp lower bound for the approximate separability of Green's function in high frequency limit, which shows the growth of degrees of freedom in terms of wavenumber. Applications to special setups of practical interest and implications to fast algorithm development will be discussed. This is a joint work with Bjorn Engquist.
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