Rodin/Variational/LT.h file

Less-than comparison operator for functions.

This file defines the LT class, which implements the less-than comparison operation between functions. This operator creates a boolean function indicating where one function is less than another.

Mathematical Foundation

For functions $ f, g : \Omega \to \mathbb{R} $ , the less-than operator:

\[ (f < g)(x) = \begin{cases} 1 & \text{if } f(x) < g(x) \\ 0 & \text{otherwise} \end{cases} \]

Applications

  • Negative region indicators: $ \mathbb{1}_{u < 0} $
  • Subdomain identification
  • Constraint violation detection
  • Thresholding operations

Usage Example

auto negative_region = (u < 0.0);  // Boolean: true where u is negative

Namespaces

namespace Rodin
The Rodin library for Shape and Topology Optimization.
namespace Rodin::Variational
Module which provides the necessary tools for constructing variational problems.