%%%
%%% New Command Definition
%%%

\newcommand{\unknownfigure}[1]{\vspace{.5in} {\em #1} \vspace{.5in}}

\newcommand{\future}[1]{[ {\bf #1} ]}
\newcommand{\sigarrow}{- \!\! >}

%%\newcommand{\gets}{\leftarrow}
\newcommand{\procname}[1]{{\it #1}}
\newcommand{\keyword}[1]{{\bf #1}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%%  HYPHENATION
%%%

\hyphenation{make-zone-array}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%%  MACROS FOR EQUATIONS
%%%

%% commonly used terms

\newcommand{\Gdiv}{{\it Gdiv}}
\newcommand{\Vdiv}{{\it Vdiv}}

\newcommand{\vel}{\vec{v}}
\newcommand{\Gvel}{\vec{G_{v}}}
\newcommand{\G}{\vec{G}}
\newcommand{\dvel}{\vec{\nabla}}
\newcommand{\fvel}{\vec{f}}
\newcommand{\Fvel}{\vec{F}}
\newcommand{\Dvel}{\vec{D}}

\newcommand{\veln}{\vel^{n}}
\newcommand{\un}{u^{n}}
\newcommand{\vn}{v^{n}}
\newcommand{\wn}{w^{n}}
\newcommand{\Pn}{p^{n}}
\newcommand{\Tn}{T^{n}}
\newcommand{\Sn}{S^{n}}
\newcommand{\rn}{\rho^{n}}

\newcommand{\velinit}{\vel^{0}}
\newcommand{\Pinit}{p^{0}}
\newcommand{\Tinit}{T^{0}}
\newcommand{\Sinit}{S^{0}}
\newcommand{\rinit}{\rho^{0}}

\newcommand{\velfinal}{\vel^{final}}
\newcommand{\Pfinal}{p^{final}}
\newcommand{\Tfinal}{T^{final}}
\newcommand{\Sfinal}{S^{final}}
\newcommand{\rfinal}{\rho^{final}}

\newcommand{\veli}{\vel^{*}}
\newcommand{\Gveli}{\Gvel^{*}}
%%\newcommand{\ui}{u^{*}}
%%\newcommand{\vi}{v^{*}}
%%\newcommand{\wi}{w^{*}}
%%\renewcommand{\Pi}{p^{*}}
\newcommand{\Ti}{T^{*}}
\newcommand{\Si}{S^{*}}

\newcommand{\velm}{\vel^{n+1}}
\newcommand{\um}{u^{n+1}}
\newcommand{\vm}{v^{n+1}}
\newcommand{\wm}{w^{n+1}}
\newcommand{\Pm}{p^{n+1}}
\newcommand{\Tm}{T^{n+1}}
\newcommand{\Sm}{S^{n+1}}

%%\newcommand{\Gun}{G_{u}^{n}}
%%\newcommand{\Gvn}{G_{v}^{n}}
%%\newcommand{\Gwn}{G_{w}^{n}}

%%\newcommand{\Gui}{G_{u}^{*}}
%%\newcommand{\Gvi}{G_{v}^{*}}
%%\newcommand{\Gwi}{G_{w}^{*}}

%%\newcommand{\GTn}{G_{\Tn}^{n+1}}
%%\newcommand{\GTi}{G_{\Ti}^{n+1}}
%%\newcommand{\GSn}{G_{\Sn}^{n+1}}
%%\newcommand{\GSi}{G_{\Si}^{n+1}}

\newcommand{\Gt}{G_{T}}
\newcommand{\Gti}{G_{T}^{*}}
\newcommand{\Ft}{F_{T}}
\newcommand{\Dt}{D_{T}}

\newcommand{\Gs}{G_{S}}
\newcommand{\Gsi}{G_{S}^{*}}
\newcommand{\Fs}{F_{S}}
\newcommand{\Ds}{D_{S}}

\newcommand{\delt}{\triangle t}
\newcommand{\irhoz}{\frac{1}{\rho_{0}}}

%% differential terms

\newcommand{\dt}[1]{\frac{\partial {#1}}{\partial t}}
\newcommand{\dx}[1]{\frac{\partial {#1}}{\partial x}}
\newcommand{\dy}[1]{\frac{\partial {#1}}{\partial y}}
\newcommand{\dz}[1]{\frac{\partial {#1}}{\partial z}}
\newcommand{\dxs}{\frac{\partial^2}{\partial x^2}}
\newcommand{\dys}{\frac{\partial^2}{\partial y^2}}
\newcommand{\dzs}{\frac{\partial^2}{\partial z^2}}

\newcommand{\delx}[1]{\frac{\triangle {#1}}{\triangle x}}
\newcommand{\dely}[1]{\frac{\triangle {#1}}{\triangle y}}
\newcommand{\delz}[1]{\frac{\triangle {#1}}{\triangle z}}

\newcommand{\deltax}{\triangle x}
\newcommand{\deltay}{\triangle y}
\newcommand{\deltaz}{\triangle z}

%%
%% Elliptic solver
%%

\newcommand{\A}{{\bf A}}
\newcommand{\K}{{\bf K}}
\newcommand{\Idm}{{\bf I}}
\newcommand{\Cm}{{\bf C}}
\newcommand{\D}{{\bf D}}
\newcommand{\Lh}{{\bf L}}
\newcommand{\Uh}{{\bf U}}
\newcommand{\E}{{\bf \varepsilon}}

\newcommand{\ipop}{\cdot}
\newcommand{\ip}[2]{{#1} \ipop {#2}}

\newcommand{\pz}{p^{0}}
\newcommand{\pfinal}{p^{final}}
\newcommand{\rz}{r^{0}}
\newcommand{\bz}{b^{0}}

\renewcommand{\pi}{p^{i}}
\newcommand{\ri}{r^{i}}
\newcommand{\bi}{b^{i}}
\newcommand{\Ai}{\alpha}
\newcommand{\Bi}{\beta}

\newcommand{\pj}{p^{i+1}}
\newcommand{\rj}{r^{i+1}}
\newcommand{\bj}{b^{i+1}}
%%\newcommand{\Aj}{\alpha^{i+1}}
%%\newcommand{\Bj}{\beta^{i+1}}

\renewcommand{\pc}{p_C}
\newcommand{\pu}{p_U}
\newcommand{\pl}{p_L}
\newcommand{\pn}{p_N}
\newcommand{\ps}{p_S}
\newcommand{\pw}{p_W}
\newcommand{\pe}{p_E}

\newcommand{\pcj}[1]{p_{C_{#1}}}
\newcommand{\puj}[1]{p_{U_{#1}}}
\newcommand{\plj}[1]{p_{L_{#1}}}
\newcommand{\pnj}[1]{p_{N_{#1}}}
\newcommand{\psj}[1]{p_{S_{#1}}}
\newcommand{\pwj}[1]{p_{W_{#1}}}
\newcommand{\pej}[1]{p_{E_{#1}}}

\newcommand{\half}{\frac{1}{2}}
\newcommand{\dterm}{-(1 + 2 \epsilon)}
\newcommand{\bterm}{-(\half + 2 \epsilon)}

