I provide not an answer, I demonstrate a caveat of the accepted solution, in hope for a more robust solution.
I used Heiko Oberdiek's solution, which is based on Manuel's solution. It has always worked well with the pdflatex compiler, thanks for that. But a while back I had to use the regular latex compiler, and the dot product then appears as a usual \bullet
in the dvi file:

2020-06-08 update. For those interested, several solutions that work with dvi:
\documentclass{article}
\usepackage{lmodern}
\usepackage[T1]{fontenc}
\usepackage{scalefnt}
\usepackage{relsize}
\usepackage{mathtools}
\newcommand{\dotp}{
\mathop{
\mathchoice{\vcenter{\hbox{\LARGE$\cdot$}}}
{\vcenter{\hbox{\LARGE$\cdot$}}}
{\vcenter{\hbox{\normalsize$\cdot$}}}
{\vcenter{\hbox{\small$\cdot$}}}
}
}
\begin{document}
\noindent
d\raisebox{-0.5ex}{\LARGE $\cdot$}b ~ d\parbox[c][0pt][c]{0.5em}{\LARGE$\cdot$}b ~ d$\vcenter{\hbox{\LARGE$\cdot$}}$b ~ d$\vcenter{\hbox{\scalefont{1.75}$\cdot$}}$b ~ d$\vcenter{\hbox{\relsize{+2.5}$\cdot$}}$b ~ d$\vcenter{\hbox{$\mathlarger{\mathlarger{\mathlarger{\mathlarger{\cdot}}}}$}}$b
\begin{align*}
d\raisebox{-0.5ex}{\LARGE $\cdot$}b\\
d\parbox[c][0pt][c]{0.5em}{\LARGE$\cdot$}b\\
d\vcenter{\hbox{\LARGE$\cdot$}}b\\
d\vcenter{\hbox{\scalefont{1.75}$\cdot$}}b\\
d\vcenter{\hbox{\relsize{+2.5}$\cdot$}}b\\
d\vcenter{\hbox{$\mathlarger{\mathlarger{\mathlarger{\mathlarger{\cdot}}}}$}}b
\end{align*}
d $\dotp$ b
\begin{align*}
d \dotp b\\
a_{d \dotp b}
\end{align*}
\end{document}

Only the \dotp
solution is robust. The others require manual intervention for super- and subscripts for example. You probably do want to insert some negative kerning left and right of the \dotp
.
For the record, Hosein's answer to use \boldsymbol{\cdot}
is also what the physics
package uses. It also works in dvi. Still, I find that dot too small.