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function phi = W_cycle (phi,f,h) % Recursive W-cycle multigrid for solving the Poisson equation (\nabla^2 phi = f) on a uniform grid of spacing h % Pre-smoothing phi = smoothing (phi, f, h); % Compute Residual Errors r = residual (phi, f, h); % Restriction rhs = restriction (r); eps = zeros (size (rhs)); % stop recursion at smallest grid size, otherwise continue recursion if smallest_grid_size ...
Siméon Denis Poisson. Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics.For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate the corresponding electrostatic or gravitational (force) field.
In mathematics, the discrete Poisson equation is the finite difference analog of the Poisson equation. In it, the discrete Laplace operator takes the place of the Laplace operator . The discrete Poisson equation is frequently used in numerical analysis as a stand-in for the continuous Poisson equation, although it is also studied in its own ...
Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [ 2 ] [ 3 ] [ 4 ] Iterative relaxation of solutions is commonly dubbed smoothing because with certain equations, such as Laplace's equation , it resembles repeated application of a local ...
POISSON SUPERFISH, Poisson Equation Solver for Radio Frequency Cavity ccc-0228 SPAR, High-Energy Muon, Pion, Heavy Ion Stopping-Powers and Ranges
Discrete Poisson equation — discrete analogue of the Poisson equation using the discrete Laplace operator; Stencil (numerical analysis) — the geometric arrangements of grid points affected by a basic step of the algorithm Compact stencil — stencil which only uses a few grid points, usually only the immediate and diagonal neighbours
The WoS method can be modified to solve more general problems. In particular, the method has been generalized to solve Dirichlet problems for equations of the form = + [6] (which include the Poisson and linearized Poisson−Boltzmann equations) or for any elliptic partial differential equation with constant coefficients.
APBS (previously also Advanced Poisson-Boltzmann Solver) is a free and open-source software for solving the equations of continuum electrostatics intended primarily for the large biomolecular systems. [1] [2] It is available under the BSD license. PDB2PQR prepares the protein structure files from Protein Data Bank for use with APBS.