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Projected densities of states were calculated using the projection scheme implemented in the VASP code for the PAW method, which is an approximation as an unambiguous partitioning is impossible.
They fall into three categories: the eight-wave formulation maintains the constraint to truncation error, the projection scheme enforces the constraint in some discretization by projecting the magnetic field, while the five different versions of the constrained transport/central difference type schemes conserve ∇·B to machine accuracy in some discretization for every grid cell.
Meanwhile, the momentum equations are integrated using a second-order projection scheme.
In this section, we give a relaxed projection scheme of (7).
A demonstration of the projection scheme is shown for a 2-D object in Figure 1.
Then X is called a Banach space with projection scheme (Gamma = { X_{n},P_{n} }).
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More importantly, the spectral-projection scheme can be readily extended to three-dimensional nonaxisymmetric cases.
The new spectral-projection scheme is implemented to simulate unsteady incompressible flows in a cylinder.
The first approach has been described in [16] and consists of a modified Shepp-Logan filtered back-projection scheme adapted to the case of curvilinear trajectories.
Then, the turbulent flow is simulated by the second mode of a Zonal Detached-Eddy Simulation, and a conservative quadrature-projection scheme is adopted to transfer unsteady loads from fluid to structural nodes.
The new spectral-projection scheme is implemented to simulate the unsteady incompressible axisymmetric flow with a singular boundary condition which is approximated to within a desired accuracy by using a smooth boundary condition.
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