Class Divergence

java.lang.Object

org.episteme.core.mathematics.analysis.vectorcalculus.Divergence

public class Divergence
extends Object

Computes the divergence of a vector field.

The divergence measures the magnitude of a field's source or sink at a given point.

Definition: ∇·F = ∂F₁/∂x₁ + ∂F₂/∂x₂ + ... + ∂Fₙ/∂xₙ

Physical interpretation: - Positive divergence: source (field lines emanating outward) - Negative divergence: sink (field lines converging inward) - Zero divergence: incompressible flow - Gauss's law: ∇·E = ρ/ε₀ (electric field divergence equals charge density) - Continuity equation: ∂ρ/∂t + ∇·(ρv) = 0

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Divergence()

Method Summary

Modifier and Type	Method	Description
static ScalarField<PointND>	asField(VectorField<PointND> field, Real h)	Returns a scalar field representing the divergence of the vector field.
static Real	compute(VectorField<PointND> field, PointND point, Real h)	Computes the divergence of a vector field at a point using finite differences.

Methods inherited from class Object

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

Constructor Details

Divergence

public Divergence()

Method Details

compute

public static Real compute(VectorField<PointND> field,
 PointND point,
 Real h)

Computes the divergence of a vector field at a point using finite differences.

Uses central difference for each component: ∂Fᵢ/∂xᵢ ≈ (Fᵢ(x + h*eᵢ) - Fᵢ(x - h*eᵢ)) / (2h)

Parameters:

field - the vector field

point - the point at which to compute divergence

h - the step size for numerical differentiation

Returns:

the divergence (scalar value)

asField

public static ScalarField<PointND> asField(VectorField<PointND> field,
 Real h)

Returns a scalar field representing the divergence of the vector field.

Parameters:

field - the vector field

h - the step size for numerical differentiation

Returns:

the divergence as a scalar field