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/***********************************************/
/**
* @file kernelStokes.h
*
* @brief Stokes kernel (gravity anomalies).
* @see Kernel
*
* @author Torsten Mayer-Guerr
* @date 2003-09-20
*
*/
/***********************************************/
#ifndef __GROOPS_KERNELSTOKES__
#define __GROOPS_KERNELSTOKES__
// Latex documentation
#ifdef DOCSTRING_Kernel
static const char *docstringKernelStokes = R"(
\subsection{Anomalies}
Gravity anomalies in linearized form are defined by
\begin{equation}
\Delta g = -\frac{\partial T}{\partial r}-\frac{2}{r}T.
\end{equation}
The Stokes kernel is given by
\begin{equation}
K(\cos\psi,r,R) = \frac{2R^2}{l}-3\frac{Rl}{r^2}-\frac{R^2}{r^2}\cos\psi
\left(5+3\ln\frac{l+r-R\cos\psi}{2r}\right),
\end{equation}
and the coefficients in \eqref{eq.kernel} are
\begin{equation}
k_n = \frac{R}{n-1}.
\end{equation}
)";
#endif
/***********************************************/
#include "classes/kernel/kernel.h"
/***** CLASS ***********************************/
/** @brief Stokes kernel (gravity anomalies).
* @ingroup kernelGroup
* @see Kernel */
class KernelStokes : public Kernel
{
public:
KernelStokes(Config &/*config*/) {}
Double kernel (const Vector3d &p, const Vector3d &q) const;
Double radialDerivative (const Vector3d &p, const Vector3d &q) const;
Vector3d gradient (const Vector3d &p, const Vector3d &q) const;
Tensor3d gradientGradient (const Vector3d &p, const Vector3d &q) const;
Double inverseKernel (const Vector3d &p, const Vector3d &q, const Kernel &kernel) const;
Double inverseKernel (const Time &time, const Vector3d &p, const GravityfieldBase &field) const;
Vector coefficients (const Vector3d &p, UInt degree) const;
Vector inverseCoefficients(const Vector3d &p, UInt degree, Bool interior) const;
};
/***********************************************/
#endif
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