Hi Amitvikram, There's no problem here as far as I'm aware: it's just a slightly different choice of basis to exploit a homogeneity in the geometry. In this formulation your global basis functions look like a tensor product of 2D 'spectral element' functions (i.e. where the 2D basis functions are C^0, and polynomials when restricted to an element) and Fourier in the homogeneous direction. For the Helmholtz equation, a representation of a function using that finite expansion is then applied in a Galerkin framework. When you write that weak form down in the integral setting, you can then exploit the Fourier expansion to break down the Helmholtz solve into a series of solves for each Fourier mode, vs. a large 3D solve for the entire system. I'm sure someone will tell me if I got that wrong! Cheers, Dave
On 14 Jun 2018, at 16:57, Amitvikram Dutta <amitvdutta23@gmail.com> wrote:
Hi all,
I wanted to clear up a certain confusion regarding the quasi-3D approach.
As I understand it, a 2D solution is extruded in the third direction using the fourier transform as basis functions. Considering that a default 2D solver uses the Galerkin formulation as basis functions, does the use of a different basis function for the theird direction not cause conflict?
I feel I'm missing a critical theoretical intuition here. I would be greatful if someone cast some light on this.
Sincerely, -- Amitvikram Dutta
Graduate Research Assistant
Fluid Mechanics Research Lab
Multi-Physics Interaction Lab
University of Waterloo
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