edu.jhu.cs.cisst.algorithms.optimize.fmg.solver
Interface Solver

All Known Implementing Classes:

ArithmeticSolver, SolverThroughSmoother

public interface Solver

The interface to objects that exactly solve a linear elliptic partial differential equation (PDE) on a regular cubic grid in 3D.

Part of the (Full) Multigrid ((F)MG) algorithm is the exact solving of the PDE at the coarsest grid level. This step must be efficient, because it is performed several times during the course of the MG algorithm and once at the beginning of the FMG algorithm.

Not all algorithms suited for exactly solving a PDE work on all grid sizes, so it is important that the coarsest grid of the (F)MG algorithm is of a size that is compatible with the solving algorithm that is implemented by implementing this interface.

Author:

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

See Also:

FMG

Method Summary

BoundaryGrid

solve(ConstBoundaryGrid u, ConstNoBoundaryGrid f) exactly solve a linear elliptic PDE on a regular cubic grid in 3D given an approximation to the solution and the right hand side (source term) of the PDE If Ax = f defines the PDE, this method solves for the true solution x given an approximation u of x and the right hand side f.

Method Detail

solve

BoundaryGrid solve(ConstBoundaryGrid u,
                   ConstNoBoundaryGrid f)

exactly solve a linear elliptic PDE on a regular cubic grid in 3D given an approximation to the solution and the right hand side (source term) of the PDE If Ax = f defines the PDE, this method solves for the true solution x given an approximation u of x and the right hand side f.

Parameters:

u - an approximation to the true solution. Even if the solution algorithm doesn't need to start from an approximation this argument is needed because it serves as a prototype for the construction of the solution grid.

f - the right hand side of the PDE

Returns:

the exact solution x

See Also:

PDE