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A pressure Poisson equation is inverted following both the predictor and corrector steps using a fast solver.
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Then a reduced linear system associated with the inactive set can be solved by using a fast linear system solver such as the multigrid method or the preconditioned conjugate gradient method.
A refined grid point level set value selection process has been proposed and shown to effectively improve the interface location accuracy through a set of standard advection test cases when using a fast first order accurate semi-Lagrangian solver firstly proposed in [3].
For the forward solver, we relax the atomic positions, then solve the Schrödinger equation using a fast empirical pseudopotential method.
The novelty is the use of a fast solver for the free space heat equation to compute the thermal field.
Here, we use a fast Poisson solver to handle the biharmonic operator in space and step-size controlled Runge Kutta method (Verner, 1993) for the time dependent part.
For a two-dimensional FENE (Finitely Extensible Nonlinear Elastic) model, the structure of the Fokker Planck equation is used to design a fast solver.
In this paper we use a fast algebraic multigrid solver to solve the state and co-state equations.
In this last application, when polar coordinates are considered, a fast solver can be used and the non locality is dealt with a suitable decomposition which reduces the resolution of the gyrokinetic quasi-neutrality equation to a sequence of local 2D elliptic problems.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com