arXiv subjects

Michal Bosy

Publications and source records attributed to Michal Bosy.

5 recordsLinked to original sources

arXiv2025

A Self-Adjusting FEM-BEM Coupling Scheme for the Nonlinear Poisson-Boltzmann Equation

The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as nucleic acids. This work presents a solution method for the nonlinear Poisson-Boltzmann equation based on a coupled finite/boundary element scheme that automatically finds an optimal relaxation parameter, ensuring fast and reliable convergence of the nonlinear solver without user intervention. We validated our solver against APBS for a spherical cavity, and used RNA-based structures to perform a thorough study of the different algorithmic choices, and to test our implementation. We found that the best alternative to solve the Poisson-Boltzmann equation was using a Newton-Raphson method where the nonlinearity was gradually introduced with a cubic approximation in the first iteration. Newton-Raphson was also the best method to find the optimal relaxation factor, reducing the number of iterations by 40%. Including other optimisation techniques, we were able to obtain a 1.37x speed-up with respect to the best hand-picked relaxation factor for 1HC8 (molecule with highest charge in our tests), avoiding any trial-and-error process to find the relaxation factor.

physics.comp-ph↗

arXiv2025

Multichannel Steganography: A Provably Secure Hybrid Steganographic Model for Secure Communication

Secure covert communication in hostile environments requires simultaneously achieving invisibility, provable security guarantees, and robustness against informed adversaries. This paper presents a novel hybrid steganographic framework that unites cover synthesis and cover modification within a unified multichannel protocol. A secret-seeded PRNG drives a lightweight Markov-chain generator to produce contextually plausible cover parameters, which are then masked with the payload and dispersed across independent channels. The masked bit-vector is imperceptibly embedded into conventional media via a variance-aware least-significant-bit algorithm, ensuring that statistical properties remain within natural bounds. We formalize a multichannel adversary model (MC-ATTACK) and prove that, under standard security assumptions, the adversary's distinguishing advantage is negligible, thereby guaranteeing both confidentiality and integrity. Empirical results corroborate these claims: local-variance-guided embedding yields near-lossless extraction (mean BER $<5\times10^{-3}$, correlation $>0.99$) with minimal perceptual distortion (PSNR $\approx100$,dB, SSIM $>0.99$), while key-based masking drives extraction success to zero (BER $\approx0.5$) for a fully informed adversary. Comparative analysis demonstrates that purely distortion-free or invertible schemes fail under the same threat model, underscoring the necessity of hybrid designs. The proposed approach advances high-assurance steganography by delivering an efficient, provably secure covert channel suitable for deployment in high-surveillance networks.

cs.CR↗

arXiv2024

Some challenges of diffused interfaces in implicit-solvent models

The standard Poisson-Boltzmann model for molecular electrostatics assumes a sharp variation of the permittivity and salt concentration along the solute-solvent interface. The discontinuous field parameters are not only difficult numerically, but also are not a realistic physical picture, as it forces the dielectric constant and ionic strength of bulk in the near-solute region. An alternative to alleviate some of these issues is to represent the molecular surface as a diffuse interface, however, this also presents challenges. In this work we analysed the impact of the shape of the interfacial variation of the field parameters in solvation and binding energy. However we used a hyperbolic tangent function ($\tanh(k_p x)$) to couple the internal and external regions, our analysis is valid for other definitions. Our methodology was based on a coupled finite element (FEM) and boundary element (BEM) scheme that allowed us to have a special treatment of the permittivity and ionic strength in a bounded FEM region near the interface, while maintaining BEM elsewhere. Our results suggest that the shape of the function (represented by $k_p$) has a large impact on solvation and binding energy. We saw that high values of $k_p$ induce a high gradient on the interface, to the limit of recovering the sharp jump when $k_p\to\infty$, presenting a numerical challenge where careful meshing is key. Using the FreeSolv database to compare with molecular dynamics, our calculations indicate that an optimal value of $k_p$ for solvation energies was around 3. However, more challenging binding free energy tests make this conclusion more difficult, as binding showed to be very sensitive to small variations of $k_p$. In that case, optimal values of $k_p$ ranged from 2 to 20.

physics.chem-ph↗

arXiv2023

Coupling finite and boundary element methods to solve the Poisson--Boltzmann equation for electrostatics in molecular solvation

The Poisson--Boltzmann equation is widely used to model electrostatics in molecular systems. Available software packages solve it using finite difference, finite element, and boundary element methods, where the latter is attractive due to the accurate representation of the molecular surface and partial charges, and exact enforcement of the boundary conditions at infinity. However, the boundary element method is limited to linear equations and piecewise constant variations of the material properties. In this work, we present a scheme that couples finite and boundary elements for the Poisson--Boltzmann equation, where the finite element method is applied in a confined {\it solute} region, and the boundary element method in the external {\it solvent} region. As a proof-of-concept exercise, we use the simplest methods available: Johnson--N\'ed\'elec coupling with mass matrix and diagonal preconditioning, implemented using the Bempp-cl and FEniCSx libraries via their Python interfaces. We showcase our implementation by computing the polar component of the solvation free energy of a set of molecules using a constant and a Gaussian-varying permittivity. We validate our implementation against the finite difference code APBS (to 0.5\%), and show scaling from protein G B1 (955 atoms) up to immunoglobulin G (20\,148 atoms). For small problems, the coupled method was efficient, outperforming a purely boundary integral approach. For Gaussian-varying permittivities, which are beyond the applicability of boundary elements alone, we were able to run medium to large sized problems on a single workstation. Development of better preconditioning techniques and the use of distributed memory parallelism for larger systems remains an area for future work. We hope this work will serve as inspiration for future developments for molecular electrostatics with implicit solvent models.

physics.comp-ph↗

arXiv2020

A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers

In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit the tensor product structure at the patch level. To this purpose, we extend to the isogeometric framework the so-called All-Floating variant of FETI, that allows us to use the Fast Diagonalization method at the patch level. We construct then a preconditioner for the whole system and prove its robustness with respect to the local mesh-size $h$ and patch-size $H$ (i.e., we have scalability). Our numerical tests confirm the theory and also show a favourable dependence of the computational cost of the method from the spline degree $p$.

math.NA↗