Rodin/Variational/LEQ.h file

Less-than-or-equal comparison operator for functions.

This file defines the LEQ class, which implements the less-than-or-equal comparison operation between functions. This operator creates a boolean function indicating where one function does not exceed another.

Mathematical Foundation

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

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

Applications

  • Bounded region indicators: $ \mathbb{1}_{u \leq M} $
  • Feasibility checking for optimization problems
  • Level set definitions: $ \{x : \phi(x) \leq 0\} $
  • Truncation and clipping operations

Usage Example

auto bounded_region = (u <= 1.0);  // Boolean: true where u ≤ 1

Namespaces

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