poisson equationの例文

• For instance, in the incompressible fluid flow problem, the Navier Stokes equations must be solved in parallel with a Poisson equation for the pressure.
• The right-hand side is the radial term of the Laplace operator, so this differential equation is a special case of the Poisson equation.
• As discussed earlier box integration method is used in the pCG solver, which allows us to treat the Poisson equation in the most accurate way.
• In the inhomogeneous case, the screened Poisson equation is very similar to the inhomogeneous Helmholtz equation, the only difference being the sign within the brackets.
• In addition, th also directly available from the density distributions and hence there is no extra Poisson equation to be solved as in traditional CFD methods.
• Using the Green's function for the three-variable Laplace equation, one can integrate the Poisson equation in order to determine the potential function.
• Solving the Poisson equation based on an anisotropic permittivity has been incorporated into BioMOCA using the box integration discretization method, which has been briefly described below.
• He showed that the linearized Vlasov Poisson equations have a continuous spectrum of singular normal modes, now known as "'van Kampen modes "'
• In ( Tiwari et al . 2001 ), it has been shown that the Poisson equation can be solved accurately by this approach for any boundary conditions.
• Other than the numerical approach to solve the Poisson equation, the main difference between the two solvers is on how they address the permittivity in the system.
• This is the Poisson equation, and can be physically interpreted as some sort of heat conduction problem, or a problem in potential theory, among other possibilities.
• Vlasov Poisson equations are used to describe various phenomena in plasma, in particular Landau damping and the distributions in a Maxwellian, and therefore inaccessible to fluid models.
• The rigorous mathematical theory is based on solving the Cauchy problem for the evolution equation ( here the partial differential Vlasov Poisson equation ) and proving estimates on the solution.
• The Poisson solver can be adapted to the weighted least squares approximation procedure with the condition that the Poisson equation and the boundary condition must be satisfied on each finite point.
• The first equation is a pressureless governing equation for the velocity, while the second equation for the pressure is a functional of the velocity and is related to the pressure Poisson equation.
• Examples of such matrices commonly arise from the discretization of 1D Poisson equation and natural cubic spline interpolation; similar systems of matrices arise in tight binding physics or nearest neighbor effects models.
• This equation is very similar to the screened Poisson equation, and would be identical if the plus sign ( in front of the " k " term ) is switched to a minus sign.
• In this theory, the gravitational interaction is completely described by the potential \ Phi, which is required to satisfy the Poisson equation ( with the mass density acting as the source of the field ).
• It is based on the particle mesh method, where particles are interpolated onto a grid, and the potential is solved for this grid ( e . g . by solving the discrete Poisson equation ).
• Poisson's equation may be solved using a Green's function; a general exposition of the Green's function for Poisson's equation is given in the article on the screened Poisson equation.