%---------------------------------------------------------------------
% Notation
%---------------------------------------------------------------------

\def\XDomain{\Omega}
\def\XDomainBoundary{\Gamma}
%\def\XDomainBoundary{{\partial \XDomain}}

\def\XBound{{\cal B}}
\def\XBCCoeffi{\eta}
\def\XBCCoeffii{\zeta}
\def\XBCCoeffiii{\psi}

%------------------------------
% continuous variables

\def\Xpor{\phi}                  % porosity
\def\Xden{\rho}                  % density
\def\Xsolidden{\rho_{s}}         % solid density
\def\Xvis{\mu}                   % viscosity
\def\XS{S}                       % saturation
\def\Xk{{\bar k}}                % intrinsic permeability tensor
\def\Xkr{k_r}                    % relative permeability
\def\Xp{p}                       % pressure
\def\XQ{Q}                       % source term
\def\Xh{h}                       % pressure head
\def\XK{{\bar K}}                % hydraulic conductivity tensor
\def\Xgravity{g}                 % gravity constant
\def\Xg{{\vec g}}                % gravity vector
\def\Xv{{\vec v}}                % velocity vector
\def\XV{{\vec V}}                % Darcy velocity vector
\def\Xgp{\bar{p}}                % gauge pressure
\def\Xscale{\gamma}              % scale factor
\def\Xq{{\vec q}}                % flux vector
\def\Xn{{\vec n}}                % unit normal
\def\Xmob{{\lambda}}             % mobility

\def\Xc{c}                       % contaminant
\def\XF{F}                       % mass concentraion

%------------------------------
% phase specific variables

\def\Xdeni{\Xden_i}
\def\Xvisi{\Xvis_i}
\def\XSi{\XS_i}
\def\Xkri{k_{ri}}
\def\Xpi{\Xp_i}
\def\XQi{\XQ_i}
\def\Xhi{\Xh_i}
\def\XKi{\XK_i}
\def\Xvi{\Xv_i}
\def\XVi{\XV_i}
\def\Xqi{\Xq_i}
\def\Xmobi{\Xmob_i}

\def\XindIk{\Omega^{I}_{k}}         % injection well region
\def\XindEk{\Omega^{E}_{k}}         % extraction well region

\def\XwellrateIik{\gamma^{I;i}_{k}} % injection well rate
\def\XwellrateEik{\gamma^{E;i}_{k}} % extraction well rate

\def\Xdegj{\lambda_j}               % degradation rate

\def\Xcij{\Xc_{i,j}}
\def\XFij{\XF_{i,j}}
\def\Xcbarkij{{\bar c}^{k}_{ij}}

\def\XKdj{K_{d;j}}               % distribution coefficient

\def\XKT{\XK_T}                  % total hydraulic conductivity
\def\XmobT{\Xmob_T}              % total mobility
\def\XVT{\XV_T}                  % total Darcy velocity

%------------------------------
% miscellaneous variables

\def\Xgrad{\nabla}
\def\Xx{{\vec x}}
\def\Xdt{{\Delta t}}
\def\Xdx{{\Delta x}}
\def\Xdxx{{(\Xdx)^2}}
\def\Xdy{{\Delta y}}
\def\Xdyy{{(\Xdy)^2}}
\def\Xdz{{\Delta z}}
\def\Xdzz{{(\Xdz)^2}}

\def\Xnphases{\nu}
\def\Xnphases{n_p}
\def\Xnc{n_c}
\def\Xnx{n_x}
\def\Xny{n_y}
\def\Xnz{n_z}
\def\XnI{n_{I}}
\def\XnE{n_{E}}

%---------------------------------------------------------------------
% General
%---------------------------------------------------------------------

\def\slfrac#1#2#3{\mbox{#3\raisebox{0.2ex}{#1}\hspace{-0.13em}/%
                        \hspace{-0.13em}\raisebox{-0.4ex}{#2}}   }
\def\half{\mathchoice{\slfrac{1}{2}{\scriptsize}}%
                     {\slfrac{1}{2}{\scriptsize}}%
                     {\slfrac{1}{2}{\tiny}}%
                     {\slfrac{1}{2}{\tiny}}       }
\def\dvop{\nabla \cdot}

%---------------------------------------------------------------------
% Multigrid Definitions
%---------------------------------------------------------------------

\def\XG{{\cal G}}
\def\XGc{\XG ^ {c}}

\def\vhalf{\mbox{\Large $\frac{1}{2}$}}   % vertical 1/2

