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The Poisson-Boltzmann equation (PBE) is a nonlinear elliptic parametrized partial
differential equation that is ubiquitous in biomolecular modeling. It determines a
dimensionless electrostatic potential around a biomolecule immersed in an ionic solution
\cite{Chen}. For a monovalent electrolyte (i.e. a symmetric 1:1 ionic solution) it
is given by \[\label{PBE} -\vec{\nabla}.(\epsilon(x)\vec{\nabla}u(x)) + \bar{\kappa}^2(x) \sinh(u(x))
= \frac{4\pi e^2}{k_B T}\sum_{i=1}^{N_m}z_i\delta(x-x_i) \quad \textrm{in} \quad
\Omega \in \mathbb{R}^3, \] \[\label{eq:Dirichlet} u(x) = g(x) \quad \textrm{on} \quad \partial{\Omega}, \] where $\epsilon(x)\(and \)\bar{k}^2(x)\(are discontinuous functions at the interface between the charged biomolecule and
the solvent, respectively. \)\delta(x-x_i)\(is the Dirac delta distribution at point \)x_i$. In this study, we treat the PBE as an interface problem by employing the recently
developed range-separated tensor format as a solution decomposition technique \cite{BKK_RS:16}.
This is aimed at separating efficiently the singular part of the solution, which is
associated with $\delta(x-x_i)$, from the regular (or smooth) part. It avoids building numerical approximations to
the highly singular part because its analytical solution, in the form of $u_{\textrm{s}}(x) = \alpha \sum_{i=1}^{Nm}z_i/ \lvert x-x_i \rvert\(exists, hence increasing the overall accuracy of the PBE solution.\\On the other hand, numerical computation of \eqref{PBE} yields a high-fidelity full
order model (FOM) with dimension of \)\mathcal{O}(10^5)\(\)\sim\(\)\mathcal{O}(10^6)$, which is computationally expensive to solve on modern computer architectures for
parameters with varying values, for example, the ionic strength, $I \in \bar{k}^2(x)$. Reduced basis methods are able to circumvent this issue by constructing a highly
accurate yet small-sized reduced order model (ROM) which inherits all of the parametric
properties of the original FOM \cite{morRozHP08}. This greatly reduces the computational
complexity of the system, thereby enabling fast simulations in a many-query context.
We show numerical results where the RBM reduces the model order by a factor of approximately
$350,000\(and computational time by \)7,000\(at an accuracy of \)\mathcal{O}(10^{-8})$. This shows the potential of the RBM to be incorporated in the available software
packages, for example, the adaptive Poisson-Boltzmann software (APBS).

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