edu.jhu.cs.cisst.algorithms.optimize.fmg.smoother
Interface Smoother

All Known Implementing Classes:

DampedJacobi, RedBlackGaussSeidel

public interface Smoother

This interface defines the smooth() method which is used for smoothing the approximate solution of a linear elliptic partial differential equation (PDE) on a regular cubic grid in 3D before and/or after going to the next coarser grid in the Multigrid (MG) algorithm.

In the theory of the MG algorithm, smoothing refers to the reduction of the high-frequency components of the error of an approximate solution of a PDE. This is usuallu achieved by applying one or more sweeps of a conventional relaxation algorithm. This algorithms are usually good in reducing the high-frequency components of the error, but bad in reducing the low-frequency components of the error, which is the reason why they are slow if applied in isolation to solve a PDE. However, this property is important in the context of the MG algorithm.

The method smooth() is intended to apply one sweep of a smoothing algorithm.

Author:

Gerald Loeffler (Gerald.Loeffler@univie.ac.at)

See Also:

FMG

Method Summary

BoundaryGrid

smooth(ConstBoundaryGrid u, ConstNoBoundaryGrid f) smooth an approximate solution to a linear elliptic PDE on a regular cubic grid in 3D.

Method Detail

smooth

BoundaryGrid smooth(ConstBoundaryGrid u,
                    ConstNoBoundaryGrid f)

smooth an approximate solution to a linear elliptic PDE on a regular cubic grid in 3D.

Let the elliptic PDE be represented by Ax = f, and let u be an approximation to the exact solution x, then this method smoothes (i.e. reduces the high-frequency components of the error of) u.

Parameters:

u - the approximate solution of the PDE sampled at a grid of a certain size

f - the right hand side of the PDE sampled at a grid of the same size

Returns:

the smmothed approximate solution of the PDE

See Also:

PDE