Rodin/Variational/GEQ.h file

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

This file defines the GEQ class, which implements the greater-than-or-equal comparison operation between functions. This operator creates a boolean function indicating where one function is at least as large as another.

Mathematical Foundation

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

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

Applications

  • Non-negative region indicators: $ \mathbb{1}_{u \geq 0} $
  • Constraint satisfaction checking
  • Admissible set definitions
  • Complementarity conditions

Usage Example

auto non_negative = (u >= 0.0);  // Boolean: true where u is non-negative

Namespaces

namespace Rodin
The Rodin library for finite element methods and shape optimization.
namespace Rodin::Variational
Namespace Rodin::Variational.

Classes

template<class LHSDerived, class RHSDerived>
class Rodin::Variational::GEQ<FunctionBase<LHSDerived>, FunctionBase<RHSDerived>>
Pointwise greater-or-equal comparison of two function expressions.