transformation.hpp

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// Copyright (c) 2010-2023, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details

#ifndef TRANSFORMATION_HPP
#define TRANSFORMATION_HPP

#include "mfem.hpp"

namespace mfem
{
namespace spde
{

/// Base class to transform a grid function.
class GFTransformer
{
public:
   GFTransformer() = default;
   virtual ~GFTransformer() = default;
   virtual void Transform(ParGridFunction &x) const = 0;
};

/// This transformations is a pointwise transformation to
/// transform a Gaussian random field to a random field following a uniform
/// distributions. Specifically, we implement the transformations as described
/// in the following paper:
/// Lazarov, B.S., Schevenels, M. & Sigmund, O. Topology optimization
/// considering material and geometric uncertainties using stochastic
/// collocation methods. Struct Multidisc Optim 46, 597–612 (2012).
/// https://doi.org/10.1007/s00158-012-0791-7
/// Equation (19).
class UniformGRFTransformer : public GFTransformer
{
public:
   UniformGRFTransformer() = default;
   UniformGRFTransformer(double min, double max) : min_(min), max_(max) {}
   ~UniformGRFTransformer() override = default;
   /// Transforms a GridFunction representing a Gaussian random field to a
   /// uniform random field between a and b.
   void Transform(ParGridFunction &x) const override;

private:
   double min_ = 0.0;
   double max_ = 1.0;
};

/// Adds an constant offset to a grid function, i.e. u(x) = u(x) + offset.
class OffsetTransformer : public GFTransformer
{
public:
   OffsetTransformer() = default;
   explicit OffsetTransformer(double offset) : offset_(offset) {}
   ~OffsetTransformer() override = default;
   /// Offsets a grid function by an constant offset.
   void Transform(ParGridFunction &x) const override;

private:
   double offset_ = 0.0;
};

/// Transforms a grid function by scaling it by a constant factor.
class ScaleTransformer : public GFTransformer
{
public:
   ScaleTransformer() = default;
   explicit ScaleTransformer(double scale) : scale_(scale) {}
   ~ScaleTransformer() override = default;
   /// Scales a grid function by an constant factor.
   void Transform(ParGridFunction &x) const override;

private:
   double scale_ = 1.0;
};

/// Level Set Transformer, 1 for u(x) >= threshold, 0 otherwise.
class LevelSetTransformer : public GFTransformer
{
public:
   LevelSetTransformer() = default;
   explicit LevelSetTransformer(double threshold) : threshold_(threshold) {}
   ~LevelSetTransformer() override = default;
   /// Applies a level set to the GridFunction.
   void Transform(ParGridFunction &x) const override;

private:
   double threshold_ = 0.0;
};

}  // namespace spde
}  // namespace mfem

#endif  // TRANSFORMATION_HPP