Class ADI3DStencilBuilder

java.lang.Object

net.finmath.finitedifference.solvers.adi.ADI3DStencilBuilder

public class ADI3DStencilBuilder
extends Object

Builds tridiagonal line matrices for alternating direction implicit (ADI) solves for three-dimensional finite difference models.

The state variables are interpreted generically as

• state variable 0: first spatial direction,
• state variable 1: second spatial direction,
• state variable 2: third spatial direction.

The PDE operator is split into the directional parts

• A1: drift and diffusion terms in the first spatial direction,
• A2: drift and diffusion terms in the second spatial direction,
• A3: drift and diffusion terms in the third spatial direction.

This builder returns the tridiagonal matrix corresponding to

(I - theta * dt * A1)

on one fixed slice of the second and third state variables, or

(I - theta * dt * A2)

on one fixed slice of the first and third state variables, or

(I - theta * dt * A3)

on one fixed slice of the first and second state variables.

The coefficients are obtained from the model drift and factor loading and are discretized by central finite differences on possibly non-uniform grids.

Author:

Alessandro Gnoatto

Constructor Summary

Constructors

Constructor	Description
ADI3DStencilBuilder(FiniteDifferenceEquityModel model, double[] x0Grid, double[] x1Grid, double[] x2Grid)	Creates a stencil builder for three-dimensional ADI line solves.

Method Summary

Modifier and Type	Method	Description
TridiagonalMatrix	buildFirstDirectionLineMatrix(double time, double dt, double theta, int x1Index, int x2Index)	Builds the tridiagonal matrix for the implicit solve in the first spatial direction on a fixed slice of the second and third state variables.
TridiagonalMatrix	buildSecondDirectionLineMatrix(double time, double dt, double theta, int x0Index, int x2Index)	Builds the tridiagonal matrix for the implicit solve in the second spatial direction on a fixed slice of the first and third state variables.
TridiagonalMatrix	buildThirdDirectionLineMatrix(double time, double dt, double theta, int x0Index, int x1Index)	Builds the tridiagonal matrix for the implicit solve in the third spatial direction on a fixed slice of the first and second state variables.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

ADI3DStencilBuilder

public ADI3DStencilBuilder(FiniteDifferenceEquityModel model,
 double[] x0Grid,
 double[] x1Grid,
 double[] x2Grid)

Creates a stencil builder for three-dimensional ADI line solves.

Parameters:

model - The finite difference model providing drift and factor loadings.

x0Grid - The grid for the first state variable.

x1Grid - The grid for the second state variable.

x2Grid - The grid for the third state variable.

Method Details

buildFirstDirectionLineMatrix

public TridiagonalMatrix buildFirstDirectionLineMatrix(double time,
 double dt,
 double theta,
 int x1Index,
 int x2Index)

Builds the tridiagonal matrix for the implicit solve in the first spatial direction on a fixed slice of the second and third state variables.

The returned matrix represents

(I - theta * dt * A1)

where A1 contains only first-direction drift and diffusion terms.

Parameters:

time - The running time at which coefficients are evaluated.

dt - The time step size.

theta - The ADI weight.

x1Index - The fixed index in the second state-variable grid.

x2Index - The fixed index in the third state-variable grid.

Returns:

The tridiagonal matrix for the first-direction implicit line solve.

buildSecondDirectionLineMatrix

public TridiagonalMatrix buildSecondDirectionLineMatrix(double time,
 double dt,
 double theta,
 int x0Index,
 int x2Index)

Builds the tridiagonal matrix for the implicit solve in the second spatial direction on a fixed slice of the first and third state variables.

The returned matrix represents

(I - theta * dt * A2)

where A2 contains only second-direction drift and diffusion terms.

Parameters:

time - The running time at which coefficients are evaluated.

dt - The time step size.

theta - The ADI weight.

x0Index - The fixed index in the first state-variable grid.

x2Index - The fixed index in the third state-variable grid.

Returns:

The tridiagonal matrix for the second-direction implicit line solve.

buildThirdDirectionLineMatrix

public TridiagonalMatrix buildThirdDirectionLineMatrix(double time,
 double dt,
 double theta,
 int x0Index,
 int x1Index)

Builds the tridiagonal matrix for the implicit solve in the third spatial direction on a fixed slice of the first and second state variables.

The returned matrix represents

(I - theta * dt * A3)

where A3 contains only third-direction drift and diffusion terms.

Parameters:

time - The running time at which coefficients are evaluated.

dt - The time step size.

theta - The ADI weight.

x0Index - The fixed index in the first state-variable grid.

x1Index - The fixed index in the second state-variable grid.

Returns:

The tridiagonal matrix for the third-direction implicit line solve.