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README.md
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@@ -50,10 +50,10 @@ periodic, such as plane waves, but not for nonperiodic sources, e.g. a point sou
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While we solve equations in the frequency domain, the original time-domain problem is:
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where \\(\Delta = \nabla \cdot \nabla\\) is the spatial Laplacian and \\(U\\) the accoustic pressure. The sound-hard boundary \\(\partial \Omega\\) imposes Neumann boundary conditions,
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Upon taking the temporal Fourier transform, we get the inhomogeneous Helmholtz Neumann boundary value problem
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While we solve equations in the frequency domain, the original time-domain problem is:
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\\(\frac{\partial^2 U(t, \mathbf{x})}{\partial t^2} - \Delta U(t, \mathbf{x}) = \delta(t)\delta(\mathbf{x} - \mathbf{x}_0), \\)
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where \\(\Delta = \nabla \cdot \nabla\\) is the spatial Laplacian and \\(U\\) the accoustic pressure. The sound-hard boundary \\(\partial \Omega\\) imposes Neumann boundary conditions,
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\\( U_n(t, \mathbf{x}) = \mathbf{n} \cdot \nabla U = 0, \quad t \in \mathbb{R}, \quad \mathbf{x} \in \partial \Omega. \\)
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Upon taking the temporal Fourier transform, we get the inhomogeneous Helmholtz Neumann boundary value problem
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