Lines Matching refs:parent

340 We'll refer to this mesh as the *parent grid*, as for every "parent" point in the parent grid, ther…
341 …ine a function space on the parent grid as $\mathcal{V}_p^\mathrm{parent} = \{ \bm v(\bm x) \in H^…
342 We enforce that the order of the parent FEM space is equal to the full domain's order.
344 …which results in functions of degree higher than the parent FEM space, $\mathcal{V}_p^\mathrm{pare…
345 To represent these higher-order functions on the parent FEM space, we perform an $L^2$ projection.
353 The projection of a function $u$ onto the parent FEM space would look like:
356 \bm M u_N = \int_0^{L_x} \int_0^{L_y} u \psi^\mathrm{parent}_N \mathrm{d}y \mathrm{d}x
358 …l{V}_p^\mathrm{parent}$, $u_N$ the coefficients of the projected function, and $\psi^\mathrm{paren…
362 …rac{1}{L_z} \int_0^{L_z} \phi(x,y,z,t) \mathrm{d}z \right ] \psi^\mathrm{parent}_N(x,y) \mathrm{d}…
368 \bm M [\langle \phi \rangle_z]_N = \frac{1}{L_z} \int_\Omega \phi(x,y,z,t) \psi^\mathrm{parent}_N(x…
371 We need to evaluate $\psi^\mathrm{parent}_N$ at quadrature points in the full domain.
373 …he full domain have the same $(x,y)$ coordinate location as quadrature points in the parent domain.
388 …z + (T_f - T_0)} \int_\Omega \int_{T_0}^{T_f} \phi(x,y,z,t) \psi^\mathrm{parent}_N \mathrm{d}t \ma…