Publications

A self-adjusting FEM–BEM coupling scheme for the nonlinear Poisson–Boltzmann equation, Guerrero-Montero M., Bosy M., Cooper C. D., Computer Physics Communications, 2026 · PDF 

Extends the FEM–BEM framework to the nonlinear Poisson–Boltzmann equation for highly charged molecular systems. The self-adjusting solver reduces dependence on manually selected relaxation parameters and achieved a 1.37× speed-up relative to the best manually tuned setting in the reported tests.

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Some challenges of diffused interfaces in implicit-solvent models, Guerrero-Montero M., Bosy M., Cooper C. D., Journal of Computational Chemistry, 2024 · PDF 

Analyses how the shape of the solute–solvent interface affects solvation and binding energy accuracy, using a coupled FEM–BEM scheme.

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Coupling finite and boundary element methods to solve the Poisson–Boltzmann equation, Bosy M., Scroggs M. W., Betcke T., Burman E., Cooper C. D., Journal of Computational Chemistry, 2023 · PDF 

First coupled FEM–BEM solver for molecular electrostatics, validated against established tools, scaled to proteins of over 20,000 atoms, and able to handle varying permittivity that boundary element methods alone cannot.

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Hybrid coupling of finite element and boundary integral methods, Betcke T., Bosy M., Burman E., Numerical Algorithms, 2022 · PDF 

A flexible Nitsche-type hybridised coupling framework applicable to problems on infinite domains, a key theoretical building block that directly enabled the molecular simulation work above, with proven energy error estimates and solver convergence.

A domain decomposition method for isogeometric multipatch problems with inexact local solvers, Bosy M., Montardini M., Sangalli G., Tani M., Computers & Mathematics with Applications, 2020 · PDF 

Develops a scalable domain-decomposition solver for multi-patch isogeometric analysis, reducing representative computations from hours to seconds. The work demonstrates how advanced numerical solvers can make high-order, CAD-integrated simulation substantially more practical.

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Hybrid discontinuous Galerkin discretisation and domain decomposition preconditioners for the Stokes problem, Barrenechea G. R., Bosy M., Dolean V., Nataf F., Tournier T.-H., Computational Methods in Applied Mathematics, 2019 · PDF 

A parameter-free solver for viscous fluid flow: the method automatically determines interface conditions that classical approaches require manual tuning to find, while outperforming those classical choices in both accuracy and scalability.

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Numerical assessment of two-level domain decomposition preconditioners, Barrenechea G. R., Bosy M., Dolean V., Electronic Transactions on Numerical Analysis, 2018 · PDF

Introduces scalable two-level preconditioners for Stokes and elasticity equations, solving the scalability bottleneck of one-level methods when the number of subdomains grows.

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Stabilised hybrid discontinuous Galerkin methods for the Stokes problem, Barrenechea G. R., Bosy M., Dolean V., Lecture Notes in Computational Science and Engineering, 2020 · PDF 

Extends the parameter-free discretisation framework to equal-order velocity–pressure approximation, broadening the class of problems the solver handles.

Maximum likelihood estimation for discrete exponential families and random graphs, Bogdan K., Bosy M., Skalski T., ALEA: Latin American Journal of Probability and Mathematical Statistics, 2022 · PDF 

Characterises the existence of maximum-likelihood estimators for discrete exponential families, with connections to linear programming, random graphs and statistical mechanics. The work developed from my earlier research in probability and mathematical statistics.

Efficient discretisation and domain decomposition preconditioners for incompressible fluid mechanics, Bosy M., PhD Thesis, University of Strathclyde, 2017 · PDF 

Full treatment of hybrid DG discretisation and two-level domain decomposition for Stokes and elasticity equations, the foundational work behind several of the papers above.