diff --git a/src/invert/laplace/impls/naulin/naulin_laplace.hxx b/src/invert/laplace/impls/naulin/naulin_laplace.hxx index edcc562c99..f857ca8356 100644 --- a/src/invert/laplace/impls/naulin/naulin_laplace.hxx +++ b/src/invert/laplace/impls/naulin/naulin_laplace.hxx @@ -5,8 +5,8 @@ /// \f{eqnarray} /// \nabla^2(\phi[i+1]) /// + 1/DC(C_1 D)\nabla_\perp(DC(C_2))\nabla_\perp(\phi[i+1]) -/// + DC(A/D)\phi[i+1] \\ -/// = rhs(\phi[i]) +/// + DC(A/D)\phi[i+1] +/// \\ = rhs(\phi[i]) /// + 1/DC(C_1 D)\nabla_\perp(DC(C_2))\nabla_\perp(\phi[i]) /// + DC(A/D)\phi[i] /// \f} @@ -28,17 +28,17 @@ /// In an orthogonal system, we have that: /// /// \f{eqnarray}{ -/// \Omega^D &=& \nabla\cdot(n\nabla_\perp \phi)\ \ -/// &=& n \nabla_\perp^2 \phi + \nabla n\cdot\nabla_\perp \phi\\ -/// &=& n \Omega + \nabla n\cdot\nabla_\perp \phi\\ -/// &=& n \Omega + \nabla_\perp n\cdot\nabla_\perp \phi +/// \Omega^D &=& \nabla\cdot(n\nabla_\perp \phi) +/// \\ &=&n \nabla_\perp^2 \phi + \nabla n\cdot\nabla_\perp \phi +/// \\ &=&n \Omega + \nabla n\cdot\nabla_\perp \phi +/// \\ &=&n \Omega + \nabla_\perp n\cdot\nabla_\perp \phi /// \f} /// /// Rearranging gives /// /// \f{eqnarray}{ -/// \Omega &=& \frac{\Omega^D}{n} - \nabla_\perp \ln(n)\cdot\nabla_\perp \phi\ \ -/// \nabla_\perp^2 \phi +/// \Omega &=& \frac{\Omega^D}{n} - \nabla_\perp \ln(n)\cdot\nabla_\perp \phi +/// \\ \nabla_\perp^2 \phi /// &=& \frac{\Omega^D}{n} - \nabla_\perp \ln(n)\cdot\nabla_\perp \phi /// \f} ///