  Let $F$ be convex and homogeneous of degree $1$, its polar $F^{o}$ represent
a finsler metric on $\mathbb{R}^{n}$, and $\Omega$ be any bounded open set in
$\mathbb{R}^{n}$. In this paper, we first construct the theoretical structure
of anisotropic harmonic transplantation. Using the anisotropic harmonic
transplantation, co-area formula, limiting Sobolev approximation method,
delicate estimate of level set of Green function, we investigate the optimal
concentration level of the Trudinger-Moser functional \[
\int_{\Omega}e^{\lambda_{n}|u|^{\frac{n}{n-1}}}dx \] under the anisotropic
Dirichlet norm constraint $\int_{\Omega}F^{n}\left( \nabla{{u}}\right)
dx\leq1$, where $\lambda_{n}=n^{\frac{n}{n-1}}\kappa _{n}^{\frac{1}{n-1}}\ $
denotes the sharp constant of anisotropic Trudinger-Moser inequality in bounded
domain and $\kappa_{n}$ is the Lebesgue measure of the unit Wulff ball. As an
application. we can immediately deduce the existence of extremals for
anisotropic Trudinger-Moser inequality on bounded domain. Finally, we also
consider the optimal concentration level of the anisotropic singular
Trudinger-Moser functional. The method is based on the limiting Hardy-Sobolev
approximation method and constructing a suitable normalized anisotropic
concentrating sequence.
