Rodin/Variational/GT.h file

Greater-than comparison operator for functions.

This file defines the GT class, which implements the greater-than comparison operation between functions. This operator creates a boolean function that indicates where one function exceeds another.

Mathematical Foundation

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

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

Applications

  • Indicator functions for regions: $ \mathbb{1}_{u > 0} $
  • Contact problems: identify contact/separation zones
  • Adaptive mesh refinement: flag elements where error exceeds tolerance
  • Phase field methods: distinguish phases

Usage Example

auto positive_region = (u > 0.0);  // Boolean: true where u is positive

// Adaptive refinement indicator
auto refine_flag = (error_estimate > tolerance);

Namespaces

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